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Prediction of Topographic and Bathymetric Measurement Performance of Airborne Low-SNR Lidar Systems

Permanent Link: http://ufdc.ufl.edu/UFE0024246/00001

Material Information

Title: Prediction of Topographic and Bathymetric Measurement Performance of Airborne Low-SNR Lidar Systems
Physical Description: 1 online resource (154 p.)
Language: english
Creator: Cossio, Tristan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: bathymetry, counting, lidar, lsnr, photon, simulation
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: PREDICTION OF TOPOGRAPHIC AND BATHYMETRIC MEASUREMENT PERFORMANCE OF AIRBORNE LOW-SNR LIDAR SYSTEMS Government and commercial airborne lidar systems have enabled extensive measurement of the Earth s surface. Modern lidar systems provide high resolution topographic mapping through a design emphasis on high signal-to-noise ratio (SNR). Recent technological advances have enabled the development of experimental airborne lidar systems based on a low SNR paradigm. These systems rely on the detection of events on the order of a single photoelectron and are therefore sensitive to both signal and background noise events. A sensor simulator has been developed to model the expected output from low SNR laser altimeter systems and predict their performance. Simulated topographic and bathymetric measurements under a variety of conditions are presented, with comparison to field measurements from the University of Florida s prototype when applicable. Target detection capability is investigated through design and application of a novel analysis procedure.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Tristan Cossio.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Slatton, Kenneth C.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024246:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024246/00001

Material Information

Title: Prediction of Topographic and Bathymetric Measurement Performance of Airborne Low-SNR Lidar Systems
Physical Description: 1 online resource (154 p.)
Language: english
Creator: Cossio, Tristan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: bathymetry, counting, lidar, lsnr, photon, simulation
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: PREDICTION OF TOPOGRAPHIC AND BATHYMETRIC MEASUREMENT PERFORMANCE OF AIRBORNE LOW-SNR LIDAR SYSTEMS Government and commercial airborne lidar systems have enabled extensive measurement of the Earth s surface. Modern lidar systems provide high resolution topographic mapping through a design emphasis on high signal-to-noise ratio (SNR). Recent technological advances have enabled the development of experimental airborne lidar systems based on a low SNR paradigm. These systems rely on the detection of events on the order of a single photoelectron and are therefore sensitive to both signal and background noise events. A sensor simulator has been developed to model the expected output from low SNR laser altimeter systems and predict their performance. Simulated topographic and bathymetric measurements under a variety of conditions are presented, with comparison to field measurements from the University of Florida s prototype when applicable. Target detection capability is investigated through design and application of a novel analysis procedure.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Tristan Cossio.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Slatton, Kenneth C.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024246:00001


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1 PREDICTION OF TOPOGRAPHIC AND BATHYMETRIC MEASUREMENT PERFORMANCE OF AIRBORNE LOW -SNR LIDAR SYSTEMS By TRISTAN COSSIO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF T HE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Tristan Cossio

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3 To my friends and family

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4 ACKNOWLEDGMENTS I thank my friends and family for helping me through t his whole process. I also thank my professor Clint Slatton, for his patience and wisdom.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 8 LIST OF FIGURES .............................................................................................................................. 9 ABSTRACT ........................................................................................................................................ 13 CHAPTER 1 INTRODUCTION ....................................................................................................................... 15 Introduction to Laser Altimetry .................................................................................................. 15 Fundamental Concept of Operation .................................................................................... 15 Lidar Sy stem Design ........................................................................................................... 15 Limitations of the Traditional ALSM Approach ............................................................... 17 The Low SNR Approach to Laser Altimetry ............................................................................ 18 Concept ................................................................................................................................. 18 Previous Applications .......................................................................................................... 19 Motivation .................................................................................................................................... 20 2 SIMULATOR DESIGN AND IMPLEMENTATION FOR TOPOGRAPHIC MEASUREMENT ...................................................................................................................... 24 Overview ...................................................................................................................................... 24 Range Acquisition ....................................................................................................................... 24 Optical Scanner .................................................................................................................... 25 Ground Point Estimation ..................................................................................................... 27 Signal Strength Estimation ......................................................................................................... 29 Noise Estimation ......................................................................................................................... 31 Pulse Distortion and Delay ......................................................................................................... 32 Laser Phenomena ........................................................................................................................ 33 Speckle ................................................................................................................................. 33 Shot Noise ............................................................................................................................ 34 Scintillation .......................................................................................................................... 35 Construction of Range Gate ....................................................................................................... 36 Data Output .................................................................................................................................. 36 3 TOPOGRAPHIC RESULTS AND ANALYSIS ...................................................................... 44 Simulation Setup ......................................................................................................................... 44 Solar Background Noise ............................................................................................................. 44 Si gnal -to Noise Ratio .................................................................................................................. 46 Signal Strength ............................................................................................................................ 48

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6 Elevation Statistics ...................................................................................................................... 49 Sample Data from Preliminary CATS Testing .......................................................................... 50 Discussion .................................................................................................................................... 51 4 SIMULATOR DESIGN AND IMPLEMENTATION FOR BATHYMETRIC MEASUREMENT ...................................................................................................................... 57 Ocean Environment Overview ................................................................................................... 57 Water Surface near the Coast ..................................................................................................... 58 Sea Foam .............................................................................................................................. 58 Wave Influence .................................................................................................................... 59 Integrated Surface Model .................................................................................................... 61 Backscatter from Water Column ................................................................................................ 61 Returns from Ocean Bottom ....................................................................................................... 64 5 BATHYMETRIC RESULTS AND ANALYSIS ..................................................................... 65 Simulation Setup ......................................................................................................................... 65 Depth Performance...................................................................................................................... 67 Sea Foam Coverage ..................................................................................................................... 70 Bottom Reflectance ..................................................................................................................... 71 Sea Depth ..................................................................................................................................... 71 Discussion .................................................................................................................................... 71 6 TARGET DETECTION ALGORITHM DESIGN AND IMPLEMENTATION................... 76 Overview ...................................................................................................................................... 76 Spatial Correlation Feature ......................................................................................................... 77 Concept ................................................................................................................................. 77 Parameter Selection ............................................................................................................. 78 Distribution of Data ............................................................................................................. 79 Topographic DTM Generation ................................................................................................... 80 CRR Background ................................................................................................................. 80 Sliding CRR Concept .......................................................................................................... 81 Parameter Selection ............................................................................................................. 82 Results .................................................................................................................................. 84 Bathymetric DTM Generation .................................................................................................... 84 Results .......................................................................................................................................... 87 Discrimination of Target Areas .................................................................................................. 88 Sliding CRR vs. SCF ........................................................................................................... 88 Summary .............................................................................................................................. 89 7 QUANTITATIVE ASSESSMENT OF TARGET DETECTION PERFORMANCE ........... 97 O verview ...................................................................................................................................... 97 Topographic Results ................................................................................................................... 98

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7 Target Properties .................................................................................................................. 98 Terrain S hape ....................................................................................................................... 99 System Specifications .......................................................................................................... 99 Bathymetric Results .................................................................................................................... 99 Water Cl arity and Depth ................................................................................................... 100 System Specifications ........................................................................................................ 100 Discussion .................................................................................................................................. 101 8 CONCLUSIONS ....................................................................................................................... 112 Research Scope .......................................................................................................................... 112 Simulator Overview .................................................................................................................. 113 Simulat ion Results .................................................................................................................... 115 Conclusions ............................................................................................................................... 119 APPENDIX CATS HARDWARE AND SOFTWARE ................................................................. 123 Introduction ............................................................................................................................... 123 Hardware Design ....................................................................................................................... 123 Optics Design and Implementation .................................................................................. 123 Receiver Design and Implementation .............................................................................. 125 Processing and Analysis Tools ................................................................................................. 126 Processing ........................................................................................................................... 127 Analysis .............................................................................................................................. 133 Field Testing .............................................................................................................................. 134 Scanner Motion and Processing ........................................................................................ 134 Channel Orientation ........................................................................................................... 134 Range Accuracy ................................................................................................................. 135 Detector Sensitivity ........................................................................................................... 135 Water Penetration .............................................................................................................. 135 Return Signal Stability ...................................................................................................... 136 Beam Polarization .............................................................................................................. 136 Outstanding Issues ............................................................................................................. 137 LIST OF REFERENCES ................................................................................................................. 149 BIOGRAPHICAL SKETCH ........................................................................................................... 154

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8 LIST OF TABLES Table page 2 1 Effect of slope and roughness on temporal width of the return pulse. ............................... 43 3 1 Atmospheric parameters used for simulation. ...................................................................... 55 3 2 System parameters used for simulation. ............................................................................... 55 3 3 Mean and sta ndard deviation of number of signal events detected per channel at nadir, for various surface reflectances. ................................................................................. 55 3 4 Mean, median, and mode elevation (Z) values in meters, calculated for a virtu al level surface at 1 m elevation. ........................................................................................................ 56 5 1 IOPs for bathymetric simulations. ......................................................................................... 74 5 2 Standard parameters for bathymetric simulatio ns. ............................................................... 74 5 3 Estimated distribution parameters from simulated data over coastal water. ...................... 74 5 4 Mean number of signal events from the ocean bottom per beamlet as foam coverage is varied from 0% to 60%. ..................................................................................................... 75 5 5 Mean number of signal events from the ocean bottom per beamlet as reflectance coefficient is varied from 0.05 to 0. 50. ................................................................................. 75 5 6 Mean number of signal events from the ocean bottom per beamlet as sea depth is varied from 1 m to 7 m. ......................................................................................................... 75 6 1 Error s tatistics for topographic DTMs with surface reflectivity set to 0.15. ...................... 96 6 2 Error statistics for bathymetric DTMs with surface reflectivity set to 0.15. ...................... 96 7 1 Reflectivity characteristics of common construction materials, at a wavelength of 550 nm. ................................................................................................................................. 111

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9 LIST OF FIGURES Figure page 1 1 Examples of various scan patterns that can be generated on the ground by a dual wedge Risley prism scanner .................................................................................................. 22 1 2 Plot of efficiency versus receiver threshold (in photoelectrons) ......................................... 23 1 3 CFD extraction of returns on a multi -modal waveform ...................................................... 23 2 1 Modular design of LSNR lidar simulator showing transmitting, pr opagation, and receiving blocks ...................................................................................................................... 38 2 2 CATS footprint composition and overlap ............................................................................. 39 2 3 The dimensions of the boundary box (blue da shed box) are determined using the maximum height of the terrain surface,max gz, in order to restrict the size of the array of candidate intersection points ............................................................................................. 40 2 4 Calculation of the perpendicular distance between the candidate ground points and the laser pointing vector. ........................................................................................................ 40 2 5 Determination of the interpolated ground point using intersection of the laser vector w ith a polygon defined by sample points 1 S 2 S and 3 S on the virtual ground truth surface ..................................................................................................................................... 41 2 6 Probability of registering at le ast one signal event, given a single photoelectron threshold, as a function of the expected signal strength in photoelectrons (p. e.). ............ 41 2 7 Normalized standard deviation of signal intensity due to shot noise as a function of expected signal strength ......................................................................................................... 42 2 8 Simulated range gate for a single CATS footprint (96 channels) over a flat level surface ..................................................................................................................................... 42 2 9 Projection of the point cloud in Fig. 2 8 into a XYZ coordinate frame ............................. 43 3 1 Elevation histograms for 200 shots using CATS nominal pa rameters (96 beamlets per shot) and a ground elevation of 1.0 m ............................................................................ 52 3 2 SNR plotted as a function of solar zenith angle ................................................................... 53 3 3 SN R plotted as a function of solar zenith angle ................................................................... 53 3 4 Standard deviation of elevation values in a 2 meter window centered about the true terrain ...................................................................................................................................... 54

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10 3 5 Standard deviation of elevation values in a 2 meter window centered about the true terrain ...................................................................................................................................... 54 5 1 Elevation histograms for 200 simulated footprints over pure sea water ............................. 73 5 2 Elevation histograms for 200 simulated footprints over coastal ocean conditions ............ 73 6 1 Illustration of the SCF as a neighborhood operation ........................................................... 90 6 2 Acrosstrack displacement between adjacent footprints across the laser swath ................ 90 6 3 Probability distribu tion function for beamlet footprints, estimated by Parzen windowing simulated returns using a 2D Gaussian kernel .................................................. 91 6 4 Histogram of weighted SCF .................................................................................................. 91 6 5 Illustration of the CRR concept ............................................................................................. 92 6 6 Typical bathymetric lidar return waveform .......................................................................... 92 6 7 Estimated retur n waveform after application of 2D LPF to the footprint event histogram ................................................................................................................................ 93 6 8 Surface -based detection scheme............................................................................................ 93 6 9 Surface tru th for the simulated scene .................................................................................... 94 6 10 Resulting point cloud from simulation of 1000 footprints in the scene depicted in Figure 6 9 ................................................................................................................................ 94 6 11 Remaining data points after filtering by SCF value ............................................................. 95 6 12 DTM generated for the point cloud shown in Fig. 6 10 ...................................................... 95 6 13 Overhead ( XY ) view of the classified point cloud .............................................................. 96 7 1 Representative surfaces for the random terrain shapes ...................................................... 103 7 2 Operating characteristic curves for CATS parameters over flat terrain ........................... 104 7 3 Operating characteristic curves for CATS parameters ...................................................... 105 7 4 Operating characteristic curves for selected laser PRF values .......................................... 106 7 5 Operating characteristic curves for CATS parameters over pure sea water of 2 m depth ...................................................................................................................................... 107 7 6 Operating characteristic curves for CATS parameters over coastal waters of 2 m depth ...................................................................................................................................... 108

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11 7 7 Operating characteristic curves for CATS pa rameters over coastal water of varying depth ...................................................................................................................................... 109 7 8 Operating characteristic curves for selected laser PRF values, over 5 m of pure water .. 110 7 9 Operating characteristic curves for selected transmitted pulse energy values, over 5 m of coastal water ................................................................................................................ 111 A 1 Schematic showing the conceptual design of the CATS sensor he ad. ............................. 137 A 2 Image of CATS hardware prototype. .................................................................................. 138 A 3 Receiver block diagram for n channels. .............................................................................. 138 A 4 Binary data structure of the event history file output by CATS ........................................ 139 A 5 Top down view of scanner with telescoping mounting cover removed ........................... 139 A 6 Rotational period of one scanner optical wedge calculated for CATS field data (obtained August 2008) ....................................................................................................... 140 A 7 Several errors corrupt the sho t time tag entries in CATS data .......................................... 140 A 8 (Top) Image of investigated building, 320 m away from sensor. (Bottom) Isometric view of reconstructed point cloud ....................................................................................... 141 A 9 (Top) Image of investigated building, 550 m away from sensor. (Bottom) Topdown view of reconstructed point cloud ....................................................................................... 142 A 10 CATS footprint centered on 12 x 12 painted wood target .............................................. 142 A 11 Histogram of hits for each channel ..................................................................................... 143 A 12 With the central four beamlets positioned on a target of high reflectivity (white painted metal), channels 14, 15, 22, and 23 registered a high number of returns from the target surface .................................................................................................................. 143 A 13 Measured building dimensions, using CATS (left) and ILRIS (right) point cloud data 144 A 14 Number of recorded signal events, at three PMT voltage settings: 2300V (blue), 2400V (green), and 2500V (red) ......................................................................................... 144 A 15 Total number of atmospheric scatter events at three PMT voltage settings: 2300V (left), 2400V(center), and 2500V (right) ............................................................................ 145 A 16 Target configuration for gr ound-based CATS water penetration evaluation ................... 146 A 17 Pure water was used to test CATS penetration through waters of high clarity ................ 146

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12 A 18 Sea water retrieved from Cedar Key FL was used to test CATS penetration through waters of high turbidity ........................................................................................................ 147 A 19 Signal strength over a 10 second data set, using a 10000 shot window to estimate the necessary statistics ............................................................................................................... 1 47 A 20 CATS beamlets incident on white painted wood ............................................................... 148 A 21 Moving sum window of hits per shot, as a function of shot number ................................ 148

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13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Phi losophy PREDICTION OF TOPOGRAPHIC AND BATHYMETRIC MEASUREMENT PERFORMANCE OF AIRBORNE LOW -SNR LIDAR SYSTEMS By Tristan Cossio August 2009 Chair: K. Clint Slatton Major: Electrical and Computer Engineering Low signal to -noise ratio (LSNR) lidar (light detection and ranging) is an alternative paradigm to traditional lidar based on the detection of return signals at the single photoelectron level. The objective of this work was to predict low altitude (600 m) LSNR lidar system performance with regards to elevation measurement and target detection capability in topographic (dry land) and bathymetric (shallow water) scenarios. A modular numerical sensor model has been developed to provide data for further analysis due to the dearth of operational low altitude LSNR lidar systems. This simulator tool is described in detail, with consideration given to atmospheric effects, surface conditions, and the effects of laser phenomenology. Measurement performance analysis of the simulated topographic data showed results comparable to commercially available lidar systems, with a standard deviation of less than 12 cm for calculated elevation values. Bathymetric results, although dependent largely on water turbidity, were indicative of meter -scale horizontal data spacin g for sea depths less than 5 m. The high prevalence of noise in LSNR lidar data introduces significant difficulties in data analysis. Novel algorithms to reduce noise are described, with particular focus on their integration into an end to -end target dete ction classifier for both dry and submerged targets (cube

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14 blocks, 0.5 m to 1.0 m on a side). The key characteristic exploited to discriminate signal and noise is the temporal coherence of signal events versus the random distribution of noise events. Targ et detection performance over dry earth was observed to be robust, reliably detecting over 90% of targets with a minimal false alarm rate. Comparable results were observed in waters of high clarity, where the investigated system was generally able to dete ct more than 70% of targets to a depth of 5 m. The results of the study show that CATS, the University of Floridas LSNR lidar prototype, is capable of high fidelity (decimeter -scale) coverage of the topographic zone with limited applicability to shallow w aters less than 5 m deep. To increase the spatial temporal contrast between signal and noise events, laser pulse rate is the optimal system characteristic to improve in future LSNR lidar units.

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15 CHAPTER 1 INTRODUCTION Introduction to Laser Altimetry Las er ranging first emerged as a promising measurement technique in the early 1970s, as part of the Apollo Command and Service Module project [ 1 ]. Data collection from laser altimetry was attempted successfully in the Apollo 15, 16, and 17 missions. In the three decades since laser ranging has become a dominant technology in the high resolution measurement of topography. Laser altimeters on airborne and spaceborne platforms have proven capable of providing detailed mapping of a wide variety of surfaces, including lunar and earth topography, coastal water bathymetry forest canop y structure and ice sheet elevation [1 ],[ 2 ], [3 ], [4 ],[ 5 ]. Fundamental Concept of Operation Laser altimetry is an active remote sensing process similar to radar but instead using optical wavelengths (typically in the 400 1500 nm range), in the form of laser li ght as the illuminating source. A range measurement is acquired through the precise measurement of the two -way propagation time of the emitted laser pulse. Within this general paradigm, there is flexibility in system structure and device characteristics S ystem details are selected based on the desired mission. Lidar System Design The design of a l idar system centers on the following main components: Laser transceiver Opto -mechanical scanner Computer subsystem for control of data acquisition Storage me dia for data acquisition

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16 GPS (global position ing system) and IMU (inertial measurement unit) Platform The laser ranging unit is composed of the laser itself, transmitter and receiver optics, the photodetector, and electronic components. The laser is chose n based on the desired operational wavelength, pulse energy, pulse rate, and system power budget The advantages and disadvantages of various optical wavelength s must be weighed according to the mission goals; in some cases, multiple wavelengths are suffi ciently complementary to warrant their inclusion in the same system [6 ], [7 ]. In traditional l idar design, high pulse energies are favored due to the decreased probability of a false positive retur n (i.e. a registered event from a noise source such as solar background light). Pulse energies for airborne laser altimeters are therefore typically on the order of hundreds of microJoules. Laser pulse widths are typically around 10 15 ns. Transmitter an d receiver optical components are chosen to limit noise levels beam spread, and system field of view. The electronic subsystems control pulsing of the laser, operation of the photodetector, and timing of return events. The scanner is responsible for alte ring the laser beam path so that a 3 -dimensional image can be constructed from a single flight path (or orbit) Precise control of the scanner motion is essential so that the exact pattern of the swath can be accurately reconstructed when projecting the d ata into geocentric coordinates A simple s canner such as a n oscillating mirror is sufficient for a standard sawtooth scan, while more complicated designs allow for greater flexibility in swath pattern (Fig. 1 1) Spaceborne lidar systems can opt to us e a pushbroom setup (a linear array of detectors) to avoid moving parts while still providing spatial expanse of returns [8 ]. The data product of l idar systems generally comes in one of two forms: discrete point return s and f ull y digitized waveform s In discrete return systems, a constant fraction

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17 discriminator (CFD) or similar component is used to record multiple discrete returns (typically from 2 to 5) for each laser pulse. This is the analog to digital conversion methodol ogy favored in high pulse rate (> 100 kHz) systems, as the rate of incoming data necessary for waveform digitization can not be adequately handled by standard commercially available electronics. Full waveform systems provide a more detailed measurement of the vertical structure intercepted by each laser pulse, at the cost of higher data complexity. For low er pulse rate (<100 kHz) systems, such as those used in large -footprint airborne or spaceborne applications the waveform format is preferred due to its detailed imaging of 3 -dimensional structure [ 9 ] Vertical resolution of the final data product is largely determined by the precision of the timing electronics the GPS and IMU realizations, and the laser pulse characteristics. Horizontal resolution (point spacing) is determined by a combination of factors, including platform altitude, scan type, scan rate, and laser pulse rate. Limitations of the Traditional ALSM Approach T he small -footprint, multiple discrete return form of l idar has become the most widely used for solid earth sensing because of the higher resolution spatial sampling it offers [10]. These ALSM (airborne laser swath mapping) systems are available from commercial manufacturers T he ir basic design emphasizes a simplified detection scheme that is feasible only when high pulse energies are used so that background noise contributions rarely exceed the threshold in the CFD System size and weight are therefore dependent on the high ene rgy requirements of the laser and its associated electronics. This limits the application of these l idar systems to missions where power, size, and weight are not prohibitive constraints. It has been shown that s uch designs do not make the most efficient use of the available return photons (Fig. 1 2) [11].

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18 Additionally laser pulse width plays a significant role in determining effective system resolution In discrete event data, there exists a dead time following an event in which a subsequent return cannot be registered [12]. This effect is evident when using a CFD for signal detection (Fig. 1 3) Closely spaced or irregular surfaces can create a multi -modal return waveform that cause s the s ystem to miss successive returns. This limits the effectiveness of ALSM in mapping densely packed canopy structure such as understory and in bathymetric mapping of shallow water (depths less than 5 m) The Low SNR Approach to Laser Altimetry With recent technological advances in micro laser and photod etector technology, an alternative paradigm to traditional ALSM has emerged. LSNR l idar is based on emitting a train of much low er energy pulses (<10 microJoules) and detecting return signals on the single p hotoelectron level. Concept T he components necessary for LSNR ALSM implementations allow for low system size, weight, and power. Implementation is therefore possible on unmanned aerial vehicles and other platforms where there are significant size and we ight restrictions. The use of low energy pulses allows for short laser pulse widths (few hundred picoseconds). When short pulses are combined with fast response photodetectors, the effective dead time is much smaller than in traditional ALSM This allo ws for the detection of densely packed returns without loss of detail. Currently available pulsed (Q -switched) Nd:YAG micro lasers suitable for LSNR lidars offer pulse rates of only about 10 kHz, slow compared to current generation high -SNR airborne lidar s. This low pulse rate can be offset by employing larger laser footprints and multi -channel photodetectors so that decimeter -scale horizontal resolution is maintained.

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19 There are, however, significant drawbacks to the LSNR l idar approach. The high sensi tivity of the photodetector can result in a large number of recorded noise events from solar background illumination Care must be given in the system design process in order to alleviate this problem. Through implementation of a small receiver aperture, narrow spectral bandpass filter s and temporal filter ing through the use of a range gate, noise levels can be decreased to manageable levels Even during daytime operation, there is sufficient contrast between the signal and noise to allow for extraction of the underlying topography through post processing algorithms [13]. The other central drawback is inherent to the use of low pulse energy. In traditional ALSM, a detectable reflected signal can be expected from a majority of surfaces, regardless of reflectivity or orientation, due to the sheer volume of photons incident o n the surface. In LSNR l idar this is not necessarily the case; surfaces with very low reflectivity at the chosen wavelength may not register any events an d may go undetected by the system. The same concept extends to bathymetric applications; the a bility to record returns from the ocean bottom will be largely dependent on water depth and clarity Previous Applications The LSNR lidar approach is similar to the photon-counting (PC) paradigm that ha s been successfully implemented in MIT Lincoln Laboratorys JIGSAW, Los Alamos National Laboratorys RULLI and prototype sensors developed by NASA [14],[ 15],[ 16]. A distinction in nomenclature is used to emphasize th e concept that instead of repeated pulsing of the same area in order to count returns and form a contrast between signal and noise cells LSNR l idar attempts to dis tinguish surface from noise using a single pass. CATS : The University of Florida, along with partners Sigma Space, Inc. and Fibertek, Inc., ha s developed a LSNR ALSM system, referred to as the Coastal Area Tactical -mapping

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20 System (CATS), for mapping of be ach and surf zones [17]. A frequency -doubled Nd:Y A G laser, operating at 532 nm, was chosen to allow for shallow penetration of littoral waters for bathymetry and submerged target detection. Although the laser pulse rate is re latively low (about 8 kHz), high resolution mapping is achieved by using a beam expander/holographic element to split the outgoing beam into an array of 10 10 beamlets with nominally equal power. A 10 x 10 multi -channel photo-multiplier tube ( PMT ) detector array in conjunction with a multi -channel multi -stop event timer is used to record return signal events. D ue to the fact that each of the 6 data capture b oards accommodates 16 channels, only 96 of the beamlets are effectively operational during system operation. The system clock speed is set at 2 GHz, allowing for path length resolution of 7.5 cm. CATS uses a Risley prism assembly in which two circular prism wedges are rotated independently. The phase offset rotation rate and direction of each wed ge can be varied, allowing the user to specify a variety of scan patterns. Full details on CATS, including design details and experimental results, are included in Appendix A. Motivation The potential for LSNR l idar to serve as a cost -effective alternat iv e approach to conventional lidar topographic mapping is promising but its actual viability has not yet been fully investigated due to the limited number of existing prototypes Low SNR introduces complications in analysis of the resulting data set and th erefore requires a more complicated signal detection scheme causing some domain experts (e.g. military, geologists, foresters) to take a wait and see approach to this technology. With the limited number of operational LSNR and PC l ida r systems current ly in existence there is a need to build up a modeling capacity to analyze performance of LSNR l idars as a function of system specifications and mission environment. The goal of this work is to provide such a capacity, with specific emphasis on evaluatio n of the expected topographi c and

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21 bathymetric performance of CATS, the University of Floridas low altitude (600 m) LSNR lidar prototype In Chapter 2, we present the mathematical models for the simulator relevant to topograph ic operation followed by pred icted measurement results in Chapter 3 [18]. In Chapter 4, we present additional mathematical models for the simulator relevant to shallow water bathymetr y followed by bathymetric results in Chapter 5 [18]. We present an end to -end target detection algorithm designed for LSNR lidar data in Chapter 6, followed by simulated topographic and bathymetric target detection evaluation in Chapter 7 [19]. Finally, in Chapter 8 we provide conclusions and suggestions for future work.

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22 Fig. 1 1. Examples of various scan patterns that can be generated on the ground by a dual wedge Risley prism scanner (Upper left) side to -side linear (sawtooth ) scan oriented orthogonally to the nominal direction of flight. (Upper right) linear scan oriented 45 to the nominal direction of flight. (Lower left) conical scan. (Lower right) rosette scan. The xy axes indicate horizontal dimensions in meters on a flat level ground assuming a flying altitude of 600m. One complete scan with zero aircraft motion is shown in each case for clarity.

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23 Fig. 1 2. Plot of efficiency versus receiver threshold (in photoelectrons). Traditional laser altimeter designs favor high SNR over efficiency. Fig. 1 3. CFD extraction of returns on a multi -modal waveform. Since the CFD requires the signal level to drop below a certain threshold before recording the next return, the second lobe is ignor ed. A red dot indicates the single recorded event.

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24 CHAPTER 2 SIMULATOR DESIGN AND IMPLEMENTATION FOR TOPOGRAPHIC MEAS UREMENT Overview It wa s our objective to simulate entire low altitude LSNR lidar test flights and quantify measurement performance for a variety of system characteristics and environmental conditions. The simulator design has therefore focused on study and implementation of efficient analytical algorithms rather than computationally -intensive Monte Carlo methods. In order to present perf ormance analysis of a LSNR lidar with respect to environmental conditions, it is necessary to fix the configuration parameters for a single design (that of CATS). It should be noted, however, that the simulator can model a variety of other sensor configur ations. The timing and ranging model is based on a temporally specified range gate, with discrete range bins used to record each return. The overall simulator hierarchy is modular, with components that can be replaced to fit the preferred system or opera ting conditions (Fig. 2 1). For example, while the default optical scanner implementation is the dual Risley prism wedge design, it is possible to implement a different type of scanner with minimal coding. The simulator has been designed to avoid hard -co ding, allowing the user to input both system specifications and environmental conditions. Range Acquisition The first significant output of the simulator is the nominal 3D location of all received laser reflections. This consists of an estimation of the i ntersection between each beamlet with the virtual ground surface The sensor heads position and orientation are assumed known, as is the case in ALSM systems with modern GPS and IMU trajectory and attitude solutions. Spatial and angular offsets for each beamlet are obtained from laboratory measurements of the 10 10 hologram element. In Fig. 2 2, a nominal footprint is shown for an assumed flying altitude of

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25 600 m. The resulting footprint is approximately 2 m by 2 m in size. Additionally, a subset of footprint outlines near nadir is shown from a single period of a side to -side linear scan to indicate that the footprint overlap is sufficient to achieve continuous ground illumination near nadir. For near -nadir footprints, there is an expected area overl ap of 3% for two adjacent footprints (across track neighbors) and an overlap of 22% for two footprints separated by half a scan p eriod (along track neighbors). The small inter -footprint gaps shown in Figure 2 2 can be eliminated through use of a linear sc an rotated 45 resulting in an approximately 30% reduction in effective swath width. Optical Scanner The sensor aperture is directly exposed to the atmospheric medium and therefore there is no bending of the light due to a change in refractive index as the beam exits the aircraft. The scanner model is implemented through repeated application of Snells law. Individual beamlet rays are traced through the rotating prisms to provide both along track and across -track pointing angles for every outgoing laser pulse (or shot) to be simulated. First, the local horizontal and vertical projections of the wedge angles, relative to the fixed frame of the sensor window, are determined 2 1) 2 2 2 1 1 1 2 2 2 1 1 1cos cos sin sin t w t t w t t w t t w twedge w wedge w wedge w wedge w wedge is the wedge angle, 1w is the angular velocity of the inner wedge, 2w is the angular velocity of the outer wedge, 1 is the phase offset of the inner wedge, and 2 is the phase offset of the outer wedge. t is the time state variable The projected angles through the inner wedge

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26 can then be calculated for each beamlet i using the known angular offsets of the holographic diffraction element. 2 2) air in w ris out ris i holo w air in air in w ris out ris i holo w air inn t i t n t i n t n t i n t i t n t i n t n t i ; sin sin ; sin sin ; ; sin sin ; sin sin ;1 1 1 1 1 1 1 1 1 1 1 1 1 1 airn and risnare the refractive indices of the atmosphere and the optical wedges, respectively. i holo and i holo are the horizontal and vertical angular offsets of beamlet i due to the holographic element. A similar process is repeated for projection through the second (outer) optical wedge. 2 3) air in w ris out ris out air in air in w ris out ris out air inn t i t n t i n t i n t i n t i t n t i n t i n t i ; sin sin ; ; sin sin ; ; sin sin ; ; sin sin ;2 2 1 2 1 1 2 2 2 1 2 1 1 2 The across -track and alongtrack propagation angles for each beamlet can then be ca lculated. 2 4) t t i t i t t i t iw out v w out v 2 2 2 2 ,; ; ; ; The propagation of each optical wave can be described using ray -tracing because the size of scattering objects in the virtual scene is much less than the wavelength of the incident

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27 radiation [20]. The beamlets are therefore treated, unless otherwise noted, as rays along which the transmitted and received laser pulses propagate. Ground Point Estimation The true terrain is then specified, either by choosing a pre -set topography array of v alues or importing DEM data. The resolution of the resulting grid is specified by the user to allow for tradeoff between simulation accuracy and computation time. The ground truth can include uniquely structured target areas if desired (e.g. scarps, chan nels, man -made targets). An additional array is defined to store the reflectance coefficients for every coordinate on the grid, allowing for different surface materials to appear in a single simulated scene. While the size of the truth grid is restricted to allow for quicker computation, the process of determining where each laser pointing vector intersects the ground topography remains computationally intensive due to the number of beamlet footprints and possible intersection points. Using an algorithm internally labeled as the boundary box discrimination algorithm candidate ground points are first restricted to a known volume, resulting in a significant reduction in computation time (Fig. 2 3). The length of the boundary box in the across -track direct ion, boundx is calculated according to Equation 2 5 2 5 ) v g boundz xtanmax max gz is the maximum elevation of the ground truth array. A similar relationship can be used to determine the length of the boundary box i n the along -track dimension, replacing v with v the scan angles along -track component. For cases where the scanner is restricted to one dimension (or none, for profiling mode), the appropriate boundary box dime nsion is set to a small constant (greater than the truth data resolution) to allow for population of candidate ground points. The origin of the boundary box is the intersection of the projected beamlet with a XY plane

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28 underlying all c andidate ground points; we chose to use a plane at 0 Z imposing the condition that all points in the ground truth array have a non -negative elevation. The boundary box origin is calculated using the beamlet propagation angle and the platform attitude as shown in Equation 2 6 2 6) v AC v AC proj v AC v AC projz z yz z x tan cos tan sin tan sin tan cos and are the yaw, roll, and pitch angles, respectively and ACz is the platform altitude The candidate ground point array is then populated by constraining the truth array to points within this formed volume. To arrive at the final intersection point, the distance from each point in the candidate array to the laser pointing vector is calculat ed. vL is defined as the vector from the sensor position to the beamlet footprint projection on a bottom dwelling Z plane as before The vectors 1,,Nww between all N points in the candidate array and the footprint projection are calculated. Equations 2 7 and 2 8 then give a measure of the perpendicular distance id between the thi candidate point to the projected r ay and the length vLiw of the projection of iw onto vL [21],[ 22]. 2 7 ) vLi iwvLwvL 2 8 ) iidvLwvL The point in the candidate array associated with the minimum perpendicular distance ( minid ) is selected as the ground truth surface point closest to the act ual laser beam footprint (Fig. 2 4 ).

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29 Computational speed and memory constraints restrict the resolution at which the ground truth array can be specified. Due to the relatively sparse resolution of the ground truth array, simply taking the candidate point with the minimal distance to the line defined by the pointing vector is not accurate enough. The simulated range data should approximate actual beam -terrain interactions as closely as possible. Therefore some form of interpolation is required. The type of interpolation between sample points on the virtual ground truth surf ace can have an effect on modeling precision. Fig. 2 5 shows the geometry for interpolation using a formed polygon between three points on the virtual surface. Sample point S1 is the point on the virtual surface with closest absolute distance to the lase r beam vector. Sample points S2 and S3 are neighboring points to S1 on the virtual surface grid. The final ground point is then taken to be where the laser vector intersects the formed triangular polygon as determined by the ray -triangle intersection alg orithm [23]. Signal Strength Estimation Now that the final ground point has been determined for a given laser pointing vector, the calculation of the range value is straightforward using the speed of light through the atmospher ic medium (assumed homogeneous over our relatively short path lengths). The surface reflectance at the ground point is the value determined using bilinear interpolation between the known reflectance values on the regularly gridded surface. A similar proc ess is used to calculate the slope components of the surface at the final ground point. Then, given the xand y slope normals to the surface in conjunction with the laser pointing vector, the net incident angle of the laser beam on the virtual surface i s calculated. Signal strength is estimated using a form of the familiar lidar link equation that accounts for the major elements of our nominal lidar design [11]. Optical reflection from natural ground surfaces is generally m odeled as diffuse scatter, and therefore specular components are omitted

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30 [24]. Because of the retro reflection geometry observed by laser altimeters (0 phase angle with parallel illumination and view angles), the surface will exhibit a sharp surge in its viewed brightness, called the hot spot effect or reflection opposition surge [10]. This effect is not included in the surface model due to its dependence on surface composition and roughness, which are not assumed known a priori here. Because opposition effects increase the effective reflectance of a surface, assuming a purely isotropic reflecting surface provides a conservative estimate of signal counts and is therefore reasonable for nominal perf ormance prediction. Assuming a collimated beam, we can estimate the expected number of photoelectrons generated at the lidar detector using Equation 2 9. 2 9 ) 2 2)] [exp( cos R R A h E ne r t r q h s h is the hologram efficiency, q is the detector quantum efficiency, r is the receiver optical efficiency, tE is the transmitted energy per beamlet pulse with units of Joules, h is Plancks constant (6 .626068e 34 Js), is the photon frequency in Hz, is the wavelengthdependent surface reflectance coefficient, is the local incidence angle on the surface rA is the collecting area of the receiver aperture, e is the atmospheric extinction coefficient in m1, and R is the range as calculated in the previous section. The hologram efficiency quantifies the losses associated with passing the transmitted light through the diffraction element in order to create the 10x10 beamlet pattern. It is only present in the lidar transmit path. The detector quantum efficiency refers to how efficiently the PMT converts the inc ident received photons into photoelectrons (measurable current). The receiver optical efficiency refers to the fraction of received light that passes through the optical aperture, including the spectral filter. A spectral filter is employed on most lidar systems to reject incoming light outside a narrow spectral band

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31 centered at the lasers wavelength (532 nm in this case). Individual losses associated with propagation through other optical elements (e.g. scan wedges) in the transmit and receive paths ar e less than one percent, and therefore considered negligible relative to the described efficiencies. Noise Estimation Degnan (2002) describes the expected noise rate for high altitude laser altimeters at nadir view [11]. That development can be adapted to the low altitude case by adjusting the atmospheric transmission terms for the lower troposphere and including a term for off -nadir scan angle. The expected rate of (noise) photoelectrons batmn due to sol ar background illumination (isotropic atmospheric scatter of sunlight) is then estimated from Equation 210. 2 10) sec()exp() (sec()sec()1exp() 0 ,01 4(sec()sec())a s a sc s sch h h h qr rr batm sNBAT nT h N is the input exoatmospheric solar irradiance at the laser wavelength with units of W(m2)1, B is the spectral filter bandwidth in r is the receiver field of view in steradians, 0T is the one -way atmospheric transmission, s is the solar zenith angle in radians relative to the local earth surface, ah is the lidar altitude in meters, and sch is the atmospheric vertical scale height in meters. Likewise, the expected rate of (noise) photoelectrons due to Lambertian solar scatter at the surface is estimated from Equation 2 11 [11]. 2 11) sc a sh h r r r q surf bT A B N h nexp 1 sec sec 0 Note that the above quantities give the total number of noise photoelectrons col lected by the receiver. For a multiple channel detector, the counts must be divided by the number of channels

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32 to get the appropriate mean count per channel. Quantum and receiver efficiencies appear in the solar noise equations because solar noise enters through the receive path. All PMTs exhibit dark noise, a general term that refers to spurious generation of photoelectrons in the PMT due to such things as photocathode thermo -emission cosmic rays, and spontaneous emission under transient electric pote ntials in the lidar sensor head [25]. Nominal PMT dark noise rates are typically reported in PMT manufacturer specifications. The total mean number of noise photoelectrons per range bin is then given by Equation 2 12. 2 12) ,,,()bbatmbsurfbdarkbnnnn bdarkn is the PMT dark noise rate in counts per second and b is the length of a range bin in seconds. Pulse Distortion and Delay Additional distortion of the return pulse shape can occur due to noninstantaneous reflection of the transmitted pulse caused by non-zero surface slope and roughness. Interception of the beam by vegetation canopies and building edges can distort the return pulses to the point of producing complicated multi -modal waveforms, but in this work we generally focus on the illumination of terrain surfaces. Hence, all return pulses are modeled as unimodal waveforms. The temporal characteristics for short pulse laser altimeters developed by Gardner are used to calculat e the estimated arrival time of the return pulse centroid at the receiver, as well as the rms return pulse width (temporal spreading of the pulse) [24]. Assuming a laser beam with Gaussian cross section, the expected pulse del ay for a given target range R is given by Equation 2 13. 2 13) 221tans airR T c

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33 aircis the speed of light through air is the half -width beam divergence in radians, and sT denotes the ensemble average. The expected mean square pulse width is given by Equation 2 14. 2 14) 2 222 422 2224()4 tantantan cos()shf air airVarR cc h is the rms receiver impulse response (assumed to be Gaussian), f is the transmitted laser pulse width, and is the continuous -valued profile of surface elevations. The simulator allows for specification of the surface roughness () Var (m2) at each point on the truth grid, allowing for variable roughness across the virtual surface. Terrain slope modulates the local incidence angle Table 2 1 shows the effect of terrain slope and roughness on return pulse width, based on CATS system parameters. La ser Phenomena In addition to noise, a number of phenomena that arise from interactions between the laser light and the environment contribute to fluctuation in the received signal. Here, we discuss the most important of those phenomena and the magnitudes of their individual expected impacts on the return waveform of LSNR ALSM systems. Speckle Speckle refers to the randomly distributed constructive and destructive interference events that occur when coherent electromagnetic energy scatters off a rough surfa ce. Laser speckle causes a random modulation in the observed intensity of the coherent light. The measured intensity at the receiver can be considered an integrated version of a point intensity speckle pattern [26]. The obse rved intensity of a single speckle grain obeys negative exponential statistics; as the number of independent speckle grains in the integrated pattern increases, the

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34 probability density function of the observed intensity approaches a Gaussian of increasingl y narrow width. The essential quantity in determining the magnitude of the speckle effect is therefore the number of independent speckle grains viewed by the receiver, which can be approximated using Equation 2 15 [ 27]. 2 1 5 ) M cS M S M S is the receiver area and cS is the speckle correlation area. The speckle correlation area is given by Equation 2 16. 2 1 6 ) 2 2 2 T z cw d S zd is the distance between the target plane and the receiver plane and Tw is the laser spot radius (distance from the spot center where the optical intensity drops to 1/e2). Calculations using CATS nominal parameters show that a single footp rint can be considered to be an integration of hundreds of speckle grains, suggesting that the observed intensity follows a Gaussian pattern of insignificant width. The effects of speckle are therefore considered negligible. Shot Noise Because of the low signal levels expected at the receiver of a LSNR sensor, quantum fluctuations (also known as shot noise) will have a significant impact on the number of detected photoelectrons tn Poisson statistics describe the quantum noise in PMT detection under constant radiation field intensity [28]. The probability that there are tn detected photoelectrons is given by Equation 2 17. 2 1 7 ) (,) !tsnn s ts tne Pnn n

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35 sn is the expected number of generated photoelectrons from Eq uation 2 9 If we assume that a signal event is the detection of a single photoelectron (i.e. we use a single photoelectron threshold), we can estimate the probability of detecting at least one signal event as a function of sn (Fig. 2 6). Using Eq uation 2 1 7 we find that w ith an expected signal of one photoelectron, there is a 36.8% probability that there will be no signal event registered The standard deviation o f the Poisson process normalized by its mean can be written as Equation 2 1 8 2 1 8 ) 1shot sn The high variance of the Poisson process at low signal levels implied by Eq. 2 1 8 warrants careful consideration when implementing the digitization of the return waveform in the range gate (Fig. 2 7 ). For our purposes, the radiation field intensity within the time intervals of individual range bins ( realizations. Because time intervals between occurrences of a Poisson process are described by an exponential distribution, event realizations can be created through the generation of ex ponentially -distributed time signatures, with the distribution parameter based on the previously calculated expected signal strength. Scintillation Scintillation (variation in the irradiance intensity due to small -scale atmospheric density fluctuations ari sing from turbulence) may be expected to have a significant effect on the return signal. For near earth applications, atmospheric models, such as the SLC Day Model [29] can be used as an approximation of the re fractive index structure coefficient 2 NC which, combined with assumption of a point detector and uniform distribution of turbulence, can be used to

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36 estimate the normalized standard deviation of intensity modulation due to scintilla tion [30]. For a 600 m one -way path, the resulting estimate is 0.15. The two-way path contribution will be at most the square root of the sum of the squares of the one -way path contributions. Taking into acc ount the finite aperture of the system will reduce the deviation considerably due to an averaging effect. CATS parameters correspond to an aperture averaging factor of 0.05 or less, resulting in a final estimate of 0.01 for the normalized standard deviati on [31]. Comparing this value to the deviation induced by shot noise, it is determined that irradiance fluctuation due to scintillation is not significant for our application. Construction of Range Gate Now t hat both the temporal characteristics and intensity of the return waveform are known, the range -gated data can be generated. The expected signal level for each range bin is determined. Then an exponentially distributed time signature is generated based on this mean value. If the time signature is less than the duration of a single range bin, then the event is recorded by the system and the process is repeated until the generated time exceeds the maximum allowed value. This process is repeated for each r ange bin within the range gate. Dead Time : The effective receiver dead time for each channel in the multi -channel PMT is implemented as a binary toggle, preventing events from occurring within a specified duration of each other. A n algorithm steps throug h all of the time signatures within a range gate and eliminates those that occur before the dead time has elapsed after a previously registered event. Data Output A resulting realization of a single footprints range gate is shown in Fig. 2 8, assuming sol ar illumination near the horizon (zenith angle of 75 degrees). The actual number of channels is set to 96 in Fig. 2 8 to simulate the CATS receiver. The platform altitude was set to 600 m, flying over flat terrain with an elevation of 1 m.

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37 The resultin g data is now ready for output. Although a variety of file formats can be generated using the simulated data, we typically follow the output format of lidar data used to form a point cloud, in which the ,, XYZ geo -referenced coordinat es are recorded for each event in the range gate. The resulting point cloud is a projection of the entire set of events from each range gate ( Fig. 2 9 ).

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38 Fig. 2 1. Modular design of LSNR lidar simulator showing transmit ting, propagation, and receiving blocks. Environmental interactions, including atmospheric extinction and surface reflection are handled in the propagation block. Components can be replaced or modified to fit user specifications. Ellipses represent inputs.

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39 Fig. 2 2 CATS footprint composition and overlap. (Top) The distribution of beamlet centers inside a single footprint, projected onto flat level ground with the sensor at an altitude of 600 m. Total beam spread has been measured to be 3.3 mrad, resulting in an approximately 2 m by 2 m footprint on the ground. Individual beamlet divergence half angles have been measured to be approximately .13 mrad. Beamlet diameters at 600 m are approximately 15 cm. (Bottom) Adjac ent footprints shown about nadir from a single scan period using the standard linear scan. At a nominal aircraft speed of 60 m/s, laser pulse rate of 8 kHz, and scan period of 20 Hz, unsampled gaps are small relative to footprint size (<15% near nadir) a nd nearly continuous footprint illumination of the terrain can be achieved. Relative time indices are shown for each footprint starting at the i th laser pulse (nadir view) on the left to right scan pass. After k laser pulses, representing half a scan period, the right to left scan pass returns to nadir.

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40 Fig 2 3. The dimensions of the bound ary box (blue dashed box) are determined using the maximum height of the terrain surf ace,max gz, in order to restrict the size of the array of candidate intersection points. The XYZ coordinates denote a non internal, Earth fixed reference frame, with the direction of flight nominally in the Y direction (into the plane of the figure) is the across -track scan angle. Blue points are those that are considered to be candidate points. Red points are rejected. Note that only the across -track dimension is shown here. Fig 2 4. Calculation of the perpendicular distance between the candidate ground points and the laser pointing vector. c andidate ground point p rojected g round footprint l ocation sensor position Y X Z s pecified ground truth vL w d

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41 Fig 2 5. Determination of the interpolated ground point using inter section of the laser vector with a polygon defined by sample points 1 S 2 S and 3 S on the virtual ground truth surface. 1 S is the grid point associated with the minimum di stance to the laser pointing vector, while 2 S and 3 S correspond to the appropriate neighbor points that define the polygon in which the intersection of the laser pointing vector and the surface occurs. Fig. 2 6. Probability of registering at least one signal event given a single photoelectron threshold, as a function of the expected signal strength in photoelectrons (p. e.)

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42 Fig. 2 7 Normalized s tandard deviation of signal intensity due to shot noise as a function of expected signal strength. For the typical signal levels expected in LSNR lidar applications (roughly 1 p.e.), shot noise will be the dominant factor in return signal variability. Fig 2 8 Simulated range gate for a single CATS footprint (96 channels) over a flat level surface. Signal events are plotted as blue dots and noise events appear as green xs. Solar zenith angle was set to 75 degrees from earth normal (to simulate mode rate to low noise levels). Range gate specifications include the onset value (500 m in this case) and duration (150 m). A range gate duration of 150 m is used here to illustrate the distribution of solar noise. A lidar altitude of 600 m is assumed.

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43 Fi g 2 9 Projection of the point cloud in Fig. 2 8 into a XYZ coordinate frame Signal events are plotted as blue dots and noise events as green xs. Solar zenith angle was set to 75 degrees from earth normal. Table 2 1. Effect of slope and roughness on temporal width of the return pulse. Terrain Slope (deg) Surface Var (m2) RMS Pulse Width (ps) 0 0 211 30 0 363 0 0.01 699 30 0.01 851 The transmitted pulse width is set to 205 ps (RMS) and receiver impulse response to 50 ps, which are the nominal values for CATS Note that a zero scan angle is assumed here to demonstrate the effect of slope magnitude.

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44 CHAPTER 3 TOPOGRAPHIC RESULTS AND ANALYSIS Simulation Setup Illustrative simulations were run using the parameters shown in Table 31 and Table 3 2 unless otherwise noted. Environmental parameters were chosen to be representative of a standard clear atmosphere. Although near -shore air can contain salt spray, the majority of the lidar to -ground path length is often clear. The system characteristics were selected to represent the components of CATS. Alt hough the experimental value for effective dead time has yet to be determined, a conservative value of 1.0 ns was selected to avoid over -estimation of signal returns. Unless otherwise noted, the simulations were run at nadir view, with a flat level ground located at an elevation of 1 meter and with reflectance coefficient and surface profile variance of 0.3 and 0.001 m2, respectively. Solar Background Noise The realization of a photonic return event in a given range bin is effectively a binary event. Eit her a photoelectron was generated and subsequently cascaded in the dynode chain of the PMT to generate a measurable electric signal or not. Because any single photon incident at the face of each of the 96 PMT channels is capable of generating a photoelect ron, there is no way for the range -gated circuitry to discern whether the incident photon or photons were the result of laser backscatter or random sunlight scatter. Thus, the intensity of background noise due to the described sources is a concern when an alyzing low SNR lidar data. Fig. 3 1 shows comparative histograms (for 200 shots) between scenarios with no solar background noise (night time) and worst -case solar background noise (sun at zenith), with histogram bin size set to 7.5 cm. A negative skew in the histograms is apparent, and occurs due to the effects of receiver dead time and range bin quantiza t ion included in the sensor model.

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45 Note that even in the worst -case scenario, the noise floor is not clearly visible when plotted on the same scale a s the return signal counts. The noise floor in this case has a mean value of 27.7 counts per histogram bin at nadir and 23.9 at scan angle extrema. The histogram plots show that there will be significant spreading in the return elevations. This is due to a combination of factors: primarily, electronic characteristics (transmitted pulse width and receiver impulse response) and surface roughness. Scan angle also had a slight impact on effective signal spread. A 1.23 m rms was observed at nadir, versus 1. 46 m rms at maximum scan angle (for the night time simulations). Most airborne lidar systems employ basic left right sawtooth scans via a 1D galvanometric scanning mirror. The nominal CATS airborne operation will employ a linear scan spanning from roughl y 15 to +15 At day time the rms values increase d substantially to 42. 0 m and 51.0 m due to the solar background noise events spread throughout the range gate Although the number of noise events in the individual histogram bins is shown to be small the collective effect of their presence throughout the range gate induces significant error in the rms elevation. Using these values to directly measure performance is misleading however, due to the uniform distribution of noise events and the high temp oral coherence of signal events, as can be observed in the histogram plots. Further discussion of an improved performance measure is presented in the next section. It should be noted that the spread in ranges depicted in Fig. 3 1 does not reflect the unce rtainties in the aircrafts position and orientation. The data in Fig. 3 1 represent 200 simulated laser shots. At a laser pulse rate of 8 kHz, that is much less than one second, during which time the aircrafts position and orientation are essentially f ixed. Over data sets of several seconds, the uncertainties in the aircrafts trajectory and attitude will compound any uncertainties in the terrain range data itself. Furthermore, in real lidar systems, noise and interpolation in the

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46 recorded scan angles can inject further uncertainty. Incorporating such error sources in the simulation is a simple matter of adding random perturbation terms to the sensor state vector and the recorded scan angle. However, such an analysis is not presented here because our focus is to study the range of expected sensor performance independent of any particular GPS/IMU solution or scan angle encoding scheme. Signal -to -Noise Ratio We define SNR as the ratio of collected signal energy to collected noise energy; for our purpose s, this is equivalent to the ratio of the recorded number of signal events to the recorded number of noise events. To calculate the SNR, the total number of events E is first determined. The number of events in a temporal window centered about the signal region SE is then extracted from the elevation data. Although for our analysis here we have perfect knowledge of the ground truth, the window could be similarly located using histogram analysis or probab ilistic estimation (as demonstrated in Chapter 6) The window size must be chosen to be sufficiently large to include all possible signal returns accounting for pulse spread. Given the range gate duration g and temporal window s ize S the estimated number of signal events is defined by Equation 3 1. 3 1) S SS gSEEE S gS is the ratio of specified window size to the remaining non-windowed port ion of the range gate. SNR can then be represented by Equation 3 2. 3 2) SNR E

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47 Fig. 3 2 is a plot of the estimated SNR as a function of solar zenith angle as the surface reflectance is varied from 0.05 to 0.50. In the practical application of LSNR lidar to coastal environments, a variety of natural and/or artificial surfaces might be encountered in a single flight. The corresponding reflectance values for these materials will vary widely. Measured reflectance values for wet sand a lone range from 0.05 (beach sand in Newport, Rhode Island) to as high as 0.46 (quartz sand in Fort Walton Beach, FL) depending on material composition [32]. Testing over a range of reflectance values is therefore necessary to accurately gauge system performance. The range chosen for simulation was selected to include appropriate surfaces for expected applications of LSNR lidar (soil, sand, stone, and road/construction materials). In the presence of significant solar background noise, the estimated SNR was observed to be higher at lower surface reflectances. This seems counter intuitive; one would normally expect a reflective target surface to create a better signal contrast. This effect occurs due to the fact that solar background noise scattered off the surface varies proportionally to the surface reflectance and is distributed uniformly across the range gate, while the number of signal returns registered for any given shot is limited by the effective dead time and return pul se duration. It is also interesting to note the relatively flat SNR over a large range of daytime solar angles from 0 to 60 degrees, suggesting that sun angle need not be a critical concern in mission planning for daytime operations. The dramatic increase in SNR from 60 degrees to 90 degrees does imply, however, that night time operation could be beneficial. Fig. 3 3 further investigates SNR as the effective receiver dead time is varied from 0.5 ns to 2.0 ns while holding the surface reflection coeffic ient constant. As the effective receiver dead time increases, the number of signal returns that can be recorded is reduced by pulse duration and signal spread effects, while the number of recorded noise counts is generally unaffected,

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48 resulting in a decre ase in SNR. The effective receiver dead time of CATS has not been experimentally determined but will likely be limited by the rise/fall time of the PMT to a value between 0.5 ns and 1.0 ns. Signal Strength The mean and standard deviation of the number of signal events (those events due to laser light) are valuable measures of signal strength and stability, and will not vary due to solar induced noise. Table 3 3 shows the mean number of signal events per beamlet (i.e. per PMT channel) for various surface r eflectance values. The expected number of signal events is seen to increase with surface reflection coefficient since nadir viewing is assumed in Table 3 3. In general, highly reflective specular surfaces may return fewer photons in the backscatter direct ion when incidence angles are large. F or the limited scan angles of most lidar systems (less than +/ 20 degrees) and the Lambertian quality of most natural surfaces, the number of signal events will generally increase with surface reflectance. The numbe r of recorded signal events is expected to be fairly robust with regards to surface roughness. Footprints incident on rough or jagged surfaces may result in higher standard deviations of the elevations due to increased signal spread, but that spreading wi ll also mitigate receiver dead time and allow more signal events to be recorded, allowing for more reliable estimation of the mean elevation. It is also worth mentioning that while LSNR lidar systems are sometimes designed to have an expected return signa l level of less than 1 photoelectron per shot, this is not the case for the low altitude design illustrated here, as can be seen from Figure 3 1 and Table 3 3. With a short effective dead time (comparable to transmitted pulse length), low altitude sensors can be expected to register multiple returns for a single shot over rough surfaces with sufficient reflectivity.

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49 Over surfaces of low reflectance, the deviation in number of signal events is large relative to the mean. While low signal levels (and result ing low probability of detection) may cause some channels in any given footprint to record no signal events, the number of independent channels in the 10 10 micro-channel plate PMT and the overlap in subsequent laser footprints compensates for occasional missing data points. Signal strength was observed to not have a strong statistical trend in relation to scan angle. The slant path does not induce significant additional attenuation because of the low platform altitude and clear atmospheric medium. Ele vation Statistics Mean, mode, and median values of elevations for the complete range of solar zenith angles are shown in Table 3 4. The increased number of noise events due to solar background noise can induce a bias in the mean (when the terrain elevatio n is not centered in the range gate window) but does not generally affect the median and mode because of the spatial coherence of the signal returns. Even in worst case scenarios, median and mode are not generally affected because the total quantity of no ise events remains comparable to that of signal events. Small biases in the median and mode relative to the mean are caused by the same factors as the negative histogram skew in Figure 3 1: receiver dead time and range bin quantization. Plotting the stand ard deviation of elevation values for every return event does not provide meaningful information because of the coherence of signal returns as compared to the sparse and uniformly distributed noise events throughout the range gate. Instead, we specify a w indow about the expected terrain elevation (as could be expected from basic histogram analysis or the output of a filtering algorithm) and calculate the standard deviation of all events within this region. Window size is selected based on two criteria: 1) large enough to contain the entire signal region, allowing for pulse spread effects, and 2) small enough to avoid excessive noise

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50 counts. As there is no method to distinguish signal events from noise events within the window, any noise events contained w ithin the window will contribute to the standard deviation measurements. Fig. 3 4 shows the standard deviation of elevation values in a +/ 1 m range window centered about the expected terrain elevation as a function of solar zenith angle. As the quantity of noise events due to solar background decreases, the variation in elevation values also decreases significantly (a 47% decrease in standard deviation from worst -case to best -case). The impact of scan angle on effective signal spread proved to be minima l. At conditions of moderate to high surface profile variance, the standard deviation was dominated by surface roughness properties, with no obvious trend apparent when varying scan angle from nadir to extrema. Only at low surface profile variances were the effects of scan angle on effective signal spread visible (see Fig. 3 5). Sample Data from Preliminary CATS Testing Night time ground -based ranging has been accomplished with the CATS prototype. The instrument was pointed towards a target approximately 550 m away. The target was a flat uniform surface, covered with white matte paint, arranged perpendicular to the boresight. Measurements of the footprint dimensions and beamlet spot size agreed with predicted values. The standard deviation in range val ues was determined to be 11.4 cm. The average number of signal events per channel was estimated to be 3.47, with a standard deviation of 1.00. Simulations to mimic this test scenario were run using the assumed CATS parameters and a reflectance coefficient of 0.8, as extracted from data presented for white acrylic paint [ 33]. The standard deviation in range values was calculated to be 7.8 cm, with an average of 1.83 signal events per channel. The standard deviation of signal e vents per channel was 0.39. Differences in performance between simulated and experimental results can be attributed to uncertainties in

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51 the receiver dead time and reflection coefficient, as well as imperfect alignment to the target in the experimental set up. Discussion Predicted performance results, as derived from the LSNR lidar numerical sensor model, show the CATS system to be robust with regards to topographic measurement.. The standard deviation due to noise in the filtered topographic elevations was approximately 12 cm in the worst -case scenario, which is comparable to modern airborne lidar systems that use conventional high SNR approaches [ 12]. Scan angle also had an impact on the variability, although i n daytime conditions solar noise is the dominant limiting factor. As mentioned, the final elevation uncertainty for an actual airborne lidar data set will depend on the environmental and system parameters discussed here, as well as the quality of the est imates of the platform position and orientation obtained from onboard GPS and IMU measurements. In Chapter 6, we present a filtering algorithm based on the temporal coherence of signal returns to reduce the effective uncertainty in surface elevations [ 13]. Since the receiver dead time will be on the order of the laser pulse duration, its precise value will not have a drastic effect on the performance of the system. Simulations indicate that dead time may have greater impact ov er very rough surfaces with high reflectance since numerous signal events may then be observed if the receiver dead time is sufficiently low. Such cases are not likely to be encountered over sandy beaches though.

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52 A ) Solar -zenith = 90 (night time) B) S olar -zenith = 0 (worst -case) Fig. 3 1. Elevation histograms for 200 shots using CATS nominal parameters (96 beamlets per shot) and a ground elevation of 1.0 m Histogram bin size was chosen to match range bin resolution (7.5 cm). Plots on the top (block A) show night -time operation while those on the bottom (block B) have worst case solar background noise. The scan angle is shown at 0 (nadir) in the left column and 15 (extrema) in the right column. X axis values are in meters. Even with overhead sol ar illumination, the noise floor is not clearly visible. Because of the uniform distribution of noise events throughout the range gate, the ensemble density of noise, even in worst -case scenarios, is not comparable to that of signal returns.

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53 Fig. 3 2 S NR plotted as a function of solar zenith angle. The surface reflectance coefficient was varied from 0.05 to 0.5. As expected, the highest SNR occurs at a solar zenith of 90 degrees. The upper bound on SNR at 90 degrees is determined by the expected signal c ounts and the dark noise rate. Fig. 3 3 SNR plotted as a function of solar zenith angle. The effective receiver dead time was varied from 0.5 ns to 2.0 ns. A surface reflection coefficient of 0.3 is assumed.

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54 Fig. 3 4. Standard deviation of elevation values in a 2 meter window centered about the true terrain. Observations were made at nadir view. Fig 3 5. Standard deviation of elevation values in a 2 meter window centered about the true terrain Solar zenith angle was set to 90 degrees (night time) to make the effect of scan angle more apparent.

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55 Table 3 1. Atmospheric parameters used for simulation. Refractive Index 1.0003 Atmospheric Scale Height 1.2 km Extinction Coefficient .297e-3 m-1 Table 3 2. System parameters used for simulation. Platform Altitude 600 m Number of Receiver Channels 96 Laser Pulse Frequency 8 kHz Laser Beam Duration (FWHM) 480 ps Laser Wavelength 532 nm Transmitted Energy per Pulse Beamlet Divergence (half-angle) .128 mrad Inter-Beamlet Spread .367 mrad Hologram Efficiency 0.8 Telescope Radius 0.033 m Receiver IFOV 1.1e-5 sr Spectral Filter Bandpass .25 nm Receiver Optical Efficiency 0.4 Detector Quantum Efficiency 0.28 Detector Dark Count (entire PMT) 30e3 cps Effective Dead Time 1.0 ns Range Bin Length 0.5 ns Range Gate Length Table 3 3. Mean and standard deviation of number of signal events detected per channel at nadir, for various surface reflectances. Reflectance Coefficient Mean signal events per channel Standard Deviation Surface Profile Variance = 0 m 0.1 0.79 0.44 0.3 1.09 0.32 0.5 1.22 0.41 Surface Profile Variance = 0.01 m 0.1 1.02 0.68 0.3 1.86 0.66 0.5 2.27 0.63 Overall surface slope is assumed zero here. The roughness values were selected to demonstrate two extremes, perfectly smooth and very r ough.

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56 Table 3 4. Mean, median, and mode elevation (Z) values in meters, calculated for a virtual level surface at 1 m elevation. Solar Zenith (deg) Mean Z Median Z Mode Z 90 1.02 1.07 1.07 80 8.45 1.07 1.07 70 14.44 1.07 1.07 60 16.32 1.07 1.07 50 16.91 1.07 1.07 40 17.34 1.07 1.07 30 17.57 1.07 1.07 20 17.81 1.07 1.07 10 17.83 1.07 1.07 0 17.96 1.07 1.07

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57 CHAPTER 4 SIMULATOR DESIGN AND IMPLEMENTATION FOR B ATHYMETRIC MEASUREME NT Ocean Environment Overvie w Because one of the primary motivating applications for developing LSNR lidar is sensing in the coastal zone, we must consider performance over shallow marine waters as well as over land. Once values for the instrument specifications, atmospheric extinct ion, and solar illumination are fixed, modeling of lidar returns from the ground depends mainly on the local surface reflection coefficient and slope. Simulating returns from coastal waters, however, requires the consideration of three additional signal c omponents: returns from the ocean surface, returns from the water column, and returns from the ocean bottom. Ideally, a small portion of the incident beam is reflected from the surface (to aid in the determination of the water depth) while the remainder i s refracted through the surface, traverses through the water column along a slant path, is diffusely reflected by the ocean bottom (or target), and travels back along the same optical path to the sensor [ 34]. Modeling this se quence of interactions comprises the core of the simula tors ocean environment model. The ocean environment model, as implemented here, is not intended to provide detailed estimates of laser interactions with the water on a shot -by -shot basis The relativ ely small footprints of LSNR laser altimeters will interact with the local ocean surface over decimeter to meter scales. Thus, the surface and optical properties can vary greatly from pulse to pulse. A rigorous approach to simulating the performance for e ach shot would necessarily involve creating a complex spatially -explicit realization of the water surface and optical properties for each incident beamlet. Our focus here is to develop an approximate method to model the expected performance over a large n umber of shots in order to provide overall performance estimates of entire test flights in a reasonable computation time.

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58 Water Surface near the Coast Near the coastline, wave setup and breaking of waves are more common than in the open ocean. As a result two aspects of the coastal ocean surface make significant contributions to the return waveform: diffuse reflection from oceanic whitecaps and specular glints from the wave structure. Algorithms detailing each aspect separately are described, followed by discussion on how the two processes are integrated into a functioning coastal ocean surface model. As a result, we do not specify the spatial distribution of sea foam or the exact wave geometry. Sea Foam Oceanic whitecaps are typically assumed to be broa dband (strong reflectance over visible wavelengths) isotropic reflectors [ 35]. This allows the straightforward application of the signal return equations discussed earlier to the description of returns from the surface sea foa m. The fractional coverage of oceanic white caps is often assumed to depend solely on wind speed. In general however, the distribution of sea foam near the coast, and therefore its effect on shallow water optics, is not well -documented due to its complex dependence on bathymetry, wind speed, and wind and wave direction relative to the coastline. For near -shore shallow waters, the equation for fractional coverage of the ocean surface by oceanic whitecaps given by Monahan and MacNiocaill (1986) does not apply [ 36]. Breaking waves in the surf zone induce a higher fractional coverage than that predicted for open ocean conditions. For this reason, the fractional coverage *W was designed as a direct user in put in the simulator. This allows one to test the sensors bathymetric performance as a function of possible foam prevalence. The reflectance of fresh dense sea foam has been studied in a laboratory setting to be ~55% [37]. T his value is considered to be an overestimation when applied to a natural setting due to the fact that foam patches of different ages (and thus varying reflectances) will contribute to the return signal [ 35]. The effective val ue of whitecap reflectance calculated by Koepke (1984) as

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59 22% is a more realistic value, given no a priori knowledge of foam age, and is therefore used here. Wave Influence The ocean surface can be considered to be a distorted mirror like surface that prod uces specular reflections or glints from wave facets that are aligned for backscattering to the laser receiver [ 38]. Wave slopes that are perpendicular to the incident beam (local surface normal parallel to the incident beam) will therefore result in specular glints at the receiver. The estimation of lidar backscatter from a highly specular, randomly structured surface is exacerbated by the use of a small laser footprint because the probability density function of the backscatt er pulse energy has been shown to vary widely as a function of wind speed and incident angle [ 38]. Because most of those factors are not known a priori in a spatially explicit manner, we employ Buftons derivation of the mean backscattered energy from an ocean surface [ 38] for the expected return signal. Using this ensemble value, applied to each beamlet footprint, will not produce the high shot to -shot variability seen in experimental data, but it will allow us to arrive at an average performance measure for the entire data set. Following Bufton, et al (1983), equation (2 9 ) can be adapted for backscatter from the sea surface by substituting with an effective Lambertian reflectance eff for the water surface, as defined by Equation 4 1. 4 1) 52 int 22sec tan exp 4ss effr SS intr is the reflectance of the air -water interface, sis the angle of incidence on the mean ocean surface, and 2S is the 2 D mean square wave slope [ 38]. The reflectance coefficient at the air -

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60 water interface is described by the Fresnel equation f or unpolarized incident radiant energy (Eq uation 4 2). 4 2) 22 intsin()tan() 1 2sin()tan()sr sr sr srr r is the refracted angle in the water medium as given by Snells law. Although laser light is generally polarized, this formula serves as a generalization given the highly variable natu re of the polarization vectors orientation relative to the surface facets over an entire lidar flight, particularly near nadir (i.e. for small incidence angles). Wave setup in shallow coastal waters is the result of complex interactions among the local w ind, currents, and bathymetry, which are not generally known in advance. E xpressions for the 2 D mean square wave slope in the open ocean, as simple functions of wind speed, were developed by Cox and Munk (1954), and Wu (1972) [ 39], [ 40]. These equations typically under predict slopes in shallow coastal waters, but are used as a conservative estimate (lower bound) for wave slope values in Equation 4 1, given nominal wind speed values. To estimate t he centroid of the return signal from the wave structure, the expression for expected pulse delay developed by Tsai and Gardner (1982) is used [ 41]. 4 3) 2 2 3 2tan 2 1 cos 2 tan 1 2 S c c R Ts s air air airs s is the incident angle on the mean sea surface. 3 is the sea surface skewness factor. It is meant to accommodate possible asymmetry in the vertical distribution of wave heights, such that a value of 0 represents a perfectly Gaussian distribution. is the rms wave height, and airR is

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61 simply the range in air (to the water surface). See that the first term in Equation 4 3 is simply Equation 2 13. The expected mean square pulse width is likewise similar to Equation 2 14, and is given by Equation 4 4. 4 4) s air air s s air f h sc R S c 2 2 4 2 2 2 2 2 2 3 2 2 2 2 2 2tan tan tan 4 tan 2 1 1 cos 4 Integrated Surface Model For each beamlet footprint incident on the ocean surface, a sample random variable is generated from a uniform distribution ) 1 0 ( U w The realization value of w for each beamlet is then compared to the user -specified fractional coverage parameter *W to determine if the footprint is incident on sea foam. The beamlet is assumed incident on foam if *wW and incident on open water otherwise. Foam is treated as a surface feature of infinitesimal thickness, and therefore absorption is not considered. For each footprint incident on a patch of sea foam, a por tion of the incident energy is diffusely reflected while the remainder is transmitted through the foam. After accounting for the reflection loss due to the foam, the attenuated beam is assumed incident on the water surface, the refracted component is comp uted based on the wave structure, and the beam is propagated through the water column. Backscatter from Water Column As the laser propagates through the water column, there are two primary losses to consider: absorption and scattering. These losses are de scribed by the spectral absorption and scattering coefficients a and b which are defined as the wavelength -dependent spectral absorptance and scatterance per unit distance in the medium. These values are consid ered inherent optical

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62 properties (IOPs) since they depend only on the medium and are independent of the strength or polarization of incident light field [ 42]. In general, IOP values in natural water bodies can vary with depth, particularly in littoral zone waters which often contain suspended sediment. In this work, however, the effect of any suspended sediment on a and b is assumed to be vertically uniform. We do this for two reason s. First, we are most interested in predicting return strength from the bottom, which depends on the integrated effect of sediment in the water column. Secondly, our anticipated system operation is over shallow waters (0 to 5 m deep), which limits the potential impact of stratified optical properties of the water. Values for a and b can be taken from in situ measurements or derived from optical models. For our purposes, nominal values were obtained for pure se a water and coastal waters [ 43]. All the losses of radiant power from a collimated beam of photons can be accounted for using the total beam attenuation coefficient c [42]. This quantity is described by Equation 4 5. 4 5) b a c Wells (1973) proposed using a more realistic attenuation coefficient that accounts for scattering within the receiver field of view [ 44]. B ecause of the small receiver aperture design in most airborne lidars, the signal contribution made by this addition is negligible. The simple attenuation coefficient calculated above is therefore fine for our purposes. If all light scattered out of the co llimated beam is considered lost and there are to be no sources due to inelastic scatter or emission, a Beers law approximation is appropriate to describe the attenuation of the light through the water column. Given initial energy 0E incident at the water surface, a general expression for signal energy after traveling a distance wR in the water medium is given by Equation 4 6.

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63 4 6) w wR c E R E exp0 It is the backscattered component that is of interes t to us however. Backscattering is accounted for via the spectral volume scattering function, which is defined as the fraction of incident power scattered out of the beam at an angle The angle is known as the scattering angle, and its value lies on the interval from zero (forward scatter) to (backscatter). Due to the small spot radius viewed by the receiver, single scattering will dominate the re ceived signal and multiple scattering effects can be ignored [ 45]. The instantaneous expected backscatter energy reaching the water interface from a path length distance wR will be the incident energy reaching that depth ()wER times the energy backscattered from the beam multiplied by the transmission on the return trip to the water interface. 4 7) 2 0exp expw r w r w w bR c E R c R E R E Since airwRR r the receiver field of view, is considered constant in the water column. After considering the two-way transmittance of the water interface, propagation through the atmosphere back towards the receiver, and receiver efficiency characteristics, the expr ession for the expected signal (expected number of photoelectrons) from water column backscatter can be written as Equation 4 8. 4 8) 2 2 int 2 ,exp 1 2 exp 1air e s w r t r q h col sR r c R c h E n The temporal component of the water column signal corresponds to an exponential profile since it is proportional to the beam intensity at depth, and therefore alignment of the expected waveform with the discrete temporal range gate is straightforward.

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64 Returns from Ocean Bottom Development of the expected signal strength from the ocean bottom resembles the process used in the air -only case, but terms for transmission loss through the air -water interface and through the water medium must be included, as well as adjustments to the beamlet direction vector to account for surface refraction. The previous e xpression for the Fresnel transmittance of the interface and the previous assumption of exponential decay of the beam through the water column are used to derive the signal intensity expression. Assuming the bottom surface acts as a Lambertian reflector, E quation 4 9 gives the expected number of photoelectrons generated by the ocean bottom signal 4 9) 2 2 2 int 2 ,exp exp 1 cosw air e s w air r t t r q h bottom sR c R r R R A h E n t is the incident angle on the ocean bottom (of the refracted daughter ray inside the medium). To calcula te the return pulse centroid delay and rms pulse width, the earlier expressions for air -water interface returns are modified to include terms for distortion due to the wave surface and geometric delay. Multipath time broadening is ignored due to the singl e scattering approximation. The signal waveform is then mapped to the range gate of the receiver electronics as before. Development of the accompanying noise terms follows the process described in the earlier Noise Model section, with adjustments for a w ater medium similar to those detailed above. The probability of noise events is again modeled as uniformly distributed across the range gate and therefore implementation is straightforward.

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65 CHAPTER 5 BATHYMETRIC RESULTS AND ANALYSIS Simulation Setup Bat hymetric simulations were run for a variety of environmental conditions. Direct analysis of the initial recorded ranges leads to erroneous results due to refraction effects, so further processing is required. To correct the erroneous elevation values, the mean sea surface must be estimated and a decision boundary between the sea surface and the underlying bottom must be determined. The following is a description of the algorithm responsible for correction of elevation values from the sea bottom. The retur n waveform from the water -covered surface is modeled as a Gaussian mixture (GM) model, and the well known expectation maximization (EM) algorithm [46] is employed to segment the sea surface returns from the bottom returns. Dec omposition of complex waveforms using Gaussian mixture models and the EM algorithm has been previously demonstrated in the lidar literature [ 6 ]. The sea surface and bottom distribution parameters are extracted from the output of the EM algorithm. Given the lidar platform position and assuming a flat (zero -mean slope) sea surface, the refracted daughter ray through the water medium is then computed for each geo -referenced data point i i iz y x below the sea surface The intersection point between the beamlet vector (propagating through the atmosphere) and the sea surface plane is computed using Equation 5 1. 5 1) sea AC i AC sea AC i AC AC i AC sea AC i ACz z z z z y y y z z z z x x x z y x ) (int int int AC AC ACz y x is the position of the platform and seaz is the mean sea surface elevation as extracted from the EM GM algorithm. The erroneous underwater travel distance, as projected into the point cloud, is then given by Equation 5 2.

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66 5 2) i i i uiz y x z y x R ,int int int The underwater range component is adjusted for the sea waters index of refraction, as shown in Equation 5 3. 5 3) water air ui uin n R R airn and watern are the refractive indices for atmosphere and water. The beamlet propagation angles used to project the point cloud data also must be corrected. The direction of the daughter ray, as given by the original data projection, is given by Equation 5 4. 5 4) int int 1 int int 1tan tan z z y y z z x xAC AC ui AC AC ui The corrected underwater propagation angles are given by Equation 5 5. 5 5) ui water air ui ui water air uin n n n sin sin sin sin 1 1 T he new coordinate i i iz y x is projected from the intersection of the laser vector with the estimated sea surface (Equation 5 6) 5 6) ui i i ui i i ui ui i iz z y y z z x x R z z tan tan tan tan 1 int int int int 2 2 2 int

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67 Values for the IOPs obtained for pure sea water and typical coastal w ater are shown in Table 5 1 [ 42]. Simulation parameters are selected to be representative of coastal conditions and are set as shown in Table 5 2, unless otherwise stated. A solar zenith angle of 90 degrees is selected to pre sent measurement p erformance results independent of any specific filtering solution (design of such an algorithm and its implementation are discussed in Chapter 6.) Depth Performance A 2 Gaussian mixture model is appropriate for bathymetric lidar data sets in which a water -penetrating wavelength (e.g. 532 nm) is used and the ranges from the sea surface and sea bottom are the two dominant features of interest. When returns from water column backscatter (or solar illumination noise) become comparable in quantity to these two features, a 2 Gaussian mixture may not be adequate. Although the ensemble water column returns will generally follow an exponential distribution, our goal was to keep the extraction of surface and bottom returns as simple as possible. T herefore, modeling of the water column returns as a Gaussian is a reasonable approximation for our purposes. We found that in the presence of significant backscatter from the water column, a 3 Gaussian mixture model was sufficient for our depth performanc e analysis. In order to better study the impacts of water clarity (pure sea water versus coastal water), water depth, and scan angle, we examine d the return statistics with a solar zenith of 90 degrees (night time). Furthermore, the introduction of signif icant solar noise introduces complications beyond those of water column backscatter and can not be accounted for with simple adjustments to the GM EM algorithm. To properly extract mean sea surface height and bottom elevation in the presence of significan t solar noise, filtering algorithms must be applied to isolate the signal components from the background noise. This process is addressed in Chapter 6

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68 Before correction for index of refraction effects can be made, depth statistics are first extracted fro m the EM GM model in simulated trials. Ocean depth is varied from 2 m to 5 m, with the bottom elevation set to 1 m. The water surface elevation is therefore either 3 m or 6 m. Scan angle is varied from zero (nadir) to maximum (15 degrees). The sea surf ace height and sea bottom elevation are taken from the largest and smallest mean values in the 3Gaussian mixture model (with the intermediate water column value discarded). The decision boundary for the elevation correction is chosen as the midpoint in the water column between the water surface and sea bottom to insure that all sea bottom returns are included in the appropriate region. This conservative decision boundary approach allows us to impose the refraction correction to the bathymetric surface elevations without running a detailed and computationally expensive algorithm to precisely locate the extent of the water surface in each shot. Further analysis is then performed on the corrected data. Table 5 3 shows the estimated depth statistics from a pplication of the EM GM model to corrected data of 200 simulated footprints over coastal water. The 3 Gaussian mixture model performed well in extracting the mean sea surface height, with a maximum error of 5%. The mixture model also performed adequately in extracting the bottom surface elevation, with a maximum error of 9%. The Bhattacharyya distance is often used as a distance measure between distribution functions, and is used here as a metric of the separability between ocean surface and bottom (in th e corrected data) [ 47]. For the case of univariate Gaussian distributions, the Bhattacharyya distance is given by Equation 5 7. 5 7 ) 2 1 2 2 2 1 2 2 2 1 2 2 12 ln 2 1 4 1 bhatD

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69 i and 2 i are the mean and var iance of class i [48]. As one would expect, the separability between the ocean surface and bottom increases with greater depth. Scan angle also increases separability, due to the weaker return signal from the ocean surface and the extended slant path. Even with nadir view and a depth of 2 m, given sufficient sampling of the ocean bottom, separability between surface and bottom returns should not be a limiting issue. Due to reduced water clarity, the prima ry metric of concern with regards to coastal water is the expected signal count from the surface bottom. Therefore, more telling than the mean and standard deviations of the sea surface and bottom returns are the histograms that reveal the signal counts. Figure 5 1 shows histograms for corrected elevation values in pure sea water, and Figure 5 2 shows similar analysis for coastal waters. Note that an artifact appears in the water column portion of the histograms due to the corrected projection of elevatio n values below the EM GM decision boundary. The correction of points below the decision boundary but within the water column induces a slight overlap in the elevation values near the decision boundary, resulting in a higher than expected number of counts near the EM GM threshold; this phenomenon can be ignored as the water column returns are extraneous. In our work, analysis of the water column returns is not considered consequential. As a result, the slight artifact in the water column histogram that re sults from the fast decision boundary approach mentioned above is acceptable. In the pure sea water conditions, the surface is easily distinguishable from the sea bottom at both depths. Using a short laser pulse allows distinction between surface returns and bottom returns for shallower depths than in traditional bathymetric lidar. The surface elevation is still relatively well separated from the bottom elevation in the coastal water example when looking at

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70 the means, but the low signal counts from the bo ttom in the 5 m deep coastal water will likely reduce the robustness of bottom estimates in practice. At scan angle extrema, the quantity of returns from the sea surface decreases significantly since less energy is backscattered from the water surface to ward the receiver. Wave facets perpendicular to the incident laser beam are more probable at low incident angles (near nadir) and therefore more likely to cause specular glints. The observations here corroborate the recommendation that for applications w here minimizing specular returns from the sea surface is desirable, a conical scan pattern is favorable over the traditional sawtooth scan to avoid nadir views [ 49]. For turbid water or large depths, however, a greater inciden t angle causes significant attenuation in signal intensity due to a longer slant path. The introduction of additional attenuation due to realistic media properties greatly limits the signal strength from the sea bottom for depths as large as 5 m. Extrac tion of the return signal in non -optimal conditions will rely on correlation of the signal returns both within a footprint and between adjacent footprints. Horizontal spacing of the final data set will greatly depend on littoral conditions but is still ex pected to exceed that of traditional bathymetric lidar due to the multi -channel detector and laser pulse rate. Sea Foam Coverage The dependence of system performance on sea surface conditions was investigated by varying the foam fractional coverage from 0% to 60% in 20% increments. Since spatially explicit models of foam coverage were not available, the prevalence of sea foam is viewed as an environmental variable in this work. One can use the simulator to test performance for cases where foam is preval ent and cases where it is not. The resulting number of signal events from the ocean bottom is shown in Table 5 4. Simulations were run using coastal ocean parameters, with a sea depth of 2 m. For nadir

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71 viewing, the number of recorded signal events decr eased by approximately 18% as fractional foam coverage increased from 0 to 60%. For the scanner extrema, the decrease was 21%. Bottom Reflectance Since the reflectance of wet sand varies widely based on material composition, bathymetric performance was evaluated for a range of bottom reflectance coefficients. The results are shown in Table 5 5. As expected, higher reflectances for the Lambertian bottom led to more signal events. For nadir viewing, the number of recorded signal events increased by appr oximately 450% as reflectance was increased from 0.05 to 0.50. Sea Depth Bathymetric performance with regards to sea depth was also evaluated, with results shown in Table 5 6. For very shallow waters (depth less than 3 m), the simulated system demonstrate d the ability to record returns reliably from the sea bottom, even in the presence of turbidity. As depth increased, performance quickly deteriorated due to the high attenuation in the coastal water, with less than 0.10 signal events per channel per footprint at a depth of 5 m. Discussion Current bathymetric lidar systems, such as the Optech, Inc. SHOALS sensor, employ large transmit pulse energies on the order of several milliJoules and pulse widths on the order of several nanoseconds to enable them to measure bathymetric depths up to 50 m or more [ 3 ]. However, resolving depths in shallow water (< 5 m) is problematic because of difficulties in distinguishing surface and bottom returns due to the large transmitted pulse widths necessitated by high pulse energies [ 50]. While the low transmit pulse energies of LSNR lidar systems limit their use in deep water, they offer a potential advantage in the shallow waters near the surf zone because they can use sub -nanosecond pulse widths.

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72 The bathymetric performance of any lidar system is strongly dependent on ocean conditions. The medium properties which govern the attenuation of the beam through the water column will limit the density of signal points in the final point cloud. Likewise, the sea surface structure and depth can affect the ability to extract the bottom elevations. It has been observed in preliminary CATS hardware tests that extremely strong signals can register false events in subsequent ra nge bins. Therefore a specular glint from the ocean surface may cause the receiver to be flooded by return events so that it is impossible to distinguish the return signal from the shallow sea bottom. This is unlikely, however, to affect all beamlets in a given footprint, much less all beamlets in multiple adjacent footprints. The dense spatial sampling provided by LSNR lidar is another improvement over the current generation of bathymetric lidar systems. Even at low signal levels, a significant port ion of channels will register signal returns at shallow depths. The measurement spacing will therefore be much smaller than that of SHOALS (4 -m nominal measurement spacing). The accuracy of bathymetric elevation measurements is also affected greatly by the method of analysis. The mean sea elevation must be carefully estimated so that corrections can be made for the mediums index of refraction, but random wave structure and its effects on the refraction of the laser beam will strongly impact the actual estimation performance in the littoral region. Therefore, spatially explicit simulation of wave structure, along with fractional coverage of sea foam, should be explored to fully model this effect.

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73 Fig. 5 1. Elevation histograms for 200 simulated foot prints over pure sea water. The scan angle is shown at 0 (nadir) in the left column and 15 (extrema) in the right column. X axis values are in meters. Surface and bottom distributions are easily separable, with a significant decrease in surface return intensity at scanner extrema. Fig. 5 2. Elevation histograms for 200 simulated footprints over coastal ocean conditions. Bottom returns at 5 m are difficult to distinguish due to more severe attenuation. Only a few signal events from the sea floor ar e expected per footprint, implying the need to correlate returns both within a footprint and between adjacent footprints.

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74 Table 5 1. IOPs for bathymetric simulations. Parameter Symbol Pure Sea Water Coastal Water Units Absorption coefficient a0.0517 0.179 1/m Scattering coefficient b0.0025 0.219 1/m Volume Scattering Function at 180 bl(180) 2.94E-04 1.03E-03 1/m 1/sr Value Table 5 2. Standard parameters for bathymetric simulations. Parameter Symbol Value Fractional foam coverage W 0.10 Foam reflectance foam0.22 Skewness coefficient 30.20 Mean Square Wave Slope 0.03 RMS wave height h0.2 m Bottom reflectance l0.30 Bottom surface profile variance 0.001 m Solar zenith s90 Table 5 3. Estimated distribution parameters from simulated data over coastal water. 0 15 0 15 Mean 2.96 3.13 5.96 6.13 Std dev 0.23 0.17 0.23 0.16 Mean 0.99 1.07 0.98 1.07 Std dev 0.06 0.05 0.06 0.05 17.5 34.1 110.1 228.1 Distance (Bhatt.) Gaussian1 (Surface) Gaussian2 (Bottom) Depth (m) 2 5 Scan angle

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75 Table 5 4. Mean number of signal events from the ocean bottom per beamlet as foam coverage is varied from 0% to 60% Mean # of Signal Events Foam Coverage Scan = 0 Scan = 15 0% 0.67 0.58 20% 0.63 0.53 40% 0.58 0.50 60% 0.55 0.46 Observations were made using a sea depth of 2 m and coastal water conditions. Table 5 5. Mean number of signal events from the ocean bottom per beamlet as reflectance coefficient is varied from 0.05 to 0.50. Mean # of Signal Events Reflectance Coefficient Scan = 0 Scan = 15 0.05 0.16 0.13 0.10 0.28 0.24 0.30 0.64 0.56 0.50 0.89 0.77 Observations were made using a sea depth of 2 m and coastal water conditions. Table 5 6. Mean number of signal events from the ocean bottom per beamlet as sea depth is varied from 1 m to 7 m. Mean # of Signal Events Depth (m) Scan = 0 Scan = 15 1 1.04 0.98 2 0.64 0.56 3 0.34 0.30 4 0.17 0.15 5 0.080 0.078 6 0.037 0.034 7 0.016 0.015 Observations were made using a bottom reflectance of 0.30 and coastal water conditions.

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76 CHAPTER 6 TARGET DETECTION ALG ORITHM DESIGN AND IM PLEMENTATION Overview Because of high sampling density and path length resolution, LSNR lidar systems are expected to detect targets that would go unnoticed by traditional ALSM systems [ 51]. Rigorous investigation of this potential has not been completed due to lack of widespread experimental deployment of LSNR lidar. The simulator tool suffices to provide sample dat a sets until further experimentation can furnish applicable data. Considering the data structure of LSNR lidar, a target detection classifier based on mapping data points using an intensity measure is inherently flawed. Because the data capture electronic s poll the detector voltage output and record only a binary event (whether the voltage exceeds the threshold), there is no strict intensity measure in the basic LSNR design, as is typically found in a traditional discrete return lidar system. The fundame ntal idea of operating at single photoelectron sensitivity implies that intensity will not be a robust measure, due to shot noise. This notion is compounded by the dimensions of the investigated targets, as the meter -scale size precludes each target from being abundantly sampled by incident beamlets. Additionally, since the focus is on detection performance with no specific designation of target and terrain material types, there can be no assumption that the spectral reflectance characteristics of the tar get and terrain will be distinct. Attempting to discriminate targets through an intensity measure therefore is not sensible in this context. A two -step classifier has been developed: the local spatial correlation of signal events is first exploited to fil ter out noise, followed by classification of target points using a surface based scheme. The discriminant function for the second step is a buffer zone lying above the reconstructed terrain surface [52]. Terrain in the littor al zone is generally slowly varying in

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77 elevation and, due to the high range resolution and dense point spacing of LSNR lidar, signal returns from a given target surface are expected to be numerous and distinguishable in elevation from the surrounding terra in. Spatial Correlation Feature Concept Consider a LSNR lidar point cloud data set nr r r R ,... ,2 1 Without loss of generality, there exists a subset R S of points corresponding to signal events, 1 2 1,... ,ir r r S and a sub set R N of points corresponding to noise events n i i r r r N ,... ,1 An operator g computes the number of data points in a local neighborhood, equivalent to totaling the number of points occurring off the same local surface. The spatial correlation feature therefore depends on the assumption that signal events will occur in close proximity to other signal events (Equation 6 1). 6 1) N r r g P S r r g Pk k k k | 1 | 1 To substantiate this assumption, consider a signal event lr occurring off a small target 0.5 m on a side. With 20 cm groundal spacing, at least three other beamlets are incident on the same local surface. The conditional expression is then given by Equation 6 2. 6 2) 31 | 0 1 | 1sn l l l le S r r g P S r r g P For expected signal strength sn of 1 photoelectron, the probability of a signal event having one or more local neighbors is 95%. Likewise consider the case of an uncorrelated noise event mr distant from any true surface. If the operator g encapsulates return events from b nearby beamlets, with a range tolerance equivalent to r range bins, the conditional expression is given by Equation 63. 6 3) b bn b r b n r m m m me e N r r g P N r r g P 1 1 | 0 1 | 1

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78 Considering 3 r (a span of 1 range bins), 4 b and bn of 1.25e 3 (noise count per range bin for full solar background noise, as derived from Equation 2 12, the probability of a noise event having one or more local neighbors is 1.5%. It is important to note the conditions under which these assumptions break down. The noise is assumed uncorrelated; in areas where this is not the case (e.g. water column backscatter, while not rigorously defined as noise, degrades target detection performance), dense pockets of noise will register as local surfaces. Complementary a pplication of the surface based classifier mitigate s the impact of these errant regions. The ope rator g considers neighboring points based on two criteria (Figure 6 1): A Maximum difference in elevation 6 4) 21D z zl k B. Maximum distance in the XY plane 6 5) 2 2 2D y y x xl k l k ) (k k kz y x are the geo -centric coordinates for point kr These two criteria form a cylindrical volume around the investigated point kr and are tested for every point lr ( k l ) in t he data set R For each point kr the number of points passing both criteria is calculated and used as the feature value. Parameter Selection The inclusion of two separate criteria (rather than a single distance m easure) allows greater flexibility in the filtering procedure; a strict bound on 1D results in a low probability of falsely classifying noise events as signal while a more lenient value for 2D increases the probabi lity that returns from low reflectivity targets are correctly grouped.

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79 Selection of z -distance 1D is dependent on the target object under investigation. If the object has an irregular shape as viewed by the sensor, then 1D should be the maximum elevation variation expected from adjacent beamlets incident on the target surface. If, on the other hand, the target has a planar local surface or is highly reflective, 1D should be set to a value co rresponding to the spatial equivalent of the approximate receiver dead time or the range difference between adjacent range bins. Choice of 2D is relatively independent of the target or environment, instead depending on the spatial po sitioning of the beamlet groundals. 2D must be large enough to group returns from adjacent beamlets. If the target surface exhibits low reflectivity at the operational laser wavelength, 2D should be increased to enhance the likelihood of grouping returns from the investigated surface. Note that SCF operation in the spatial domain (i.e. not in the strict range bin/footprint structure of the preliminary output data) allows investigation of returns from overlapping swaths, increasing the amount of pertinent information available to the operator. Distribution of Data Constant angular velocity in the optical wedges of the Risley prism scanner results in closer footprint spacing at the swath extremes (Figure 6 2) Due to the combined effects of scanner motion and platform velocity on footprint spacing, there is distinct variation in the density of return points across the lidar swath. The probability density distribution of data throughout the laser swath can be estima ted using Parzen windowing (Figure 6 3) [46]. This non uniform sampling induced by the scan pattern can be compensated for by multiplying the feature values by a corresponding 2D weighting function based off th e inverse of the density estimate. Portions of the swath containing an exceptionally low number of counts are considered inadequately sampled and their respective points are discarded from further analysis

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80 The applied SCF is the value of the neighborhood operator weighed accordingly by the inverse of the data density estimate. Analysis of the SCF feature space for sample topographic data results in a histogram that is clearly bimodal, as desired (Figure 6 4 ). Topographic DTM Generation A digital terrain model (DTM) of the underlying surface is required in order to use elevation difference as a classifier. The algorithm to reconstruct the underlying topography must be robust because of the high sensitivity of LSNR lidar to noise; even with a narrow range gate and spectral filter, LSNR lidar data recorded during day time can be expected to contain more noise counts than signal counts [ 53]. Because the primary goal of this step is to extract information relating to the broad t errain surface, an approach that tracks the surface while eliminating outliers is necessary. CRR Background Based on the unimodal assumption of return pulse shape, all signal returns from a single beamlet are expected to occur within a short span of range bins (i.e. signal returns are temporally coherent). Given the low signal levels expected (e.g. at a signal strength of 1 p.e., 37% of beamlets will result in no registered signal returns), successful discrimination between signal and noise must be achieve d through utilization of information from adjacent beamlet footprints. The concept of temporal coherence can be extended to encapsulate the returns from multiple beamlets, assuming that the elevation of natural terrain varies slowly. Given the number of independent detector channels in the basic LSNR lidar design, the cumulative event histogram from a single shot then provides sufficient contrast for tracking the surface Degnan and McGarry described discrimination by temporal coherence as applied to SL R2000, a ground -based photon-counting laser ranging system intended to track satellites [13]. The correlation range receiver (CRR), as implemented, was responsible for timeof -flight

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81 measurement of return events and discrimi nation of signal from noise. Timing outputs transferred to the ranging computer were used to create a histogram of the bin counts and calculated the maximum likelihood signal bin (Figure 6 5 ). Sliding CRR Concept The CRR method of signal filtering has b een extended for enhanced accuracy and utility. Instead of approaching the CRR algorithm as a strict histogram analysis with fixed bin placement, the accumulated return history is considered a digital signal and a finite impulse response (FIR) filter can be applied to locate the signal window. Filter type is chosen for robustness; although a Hanning window (or similarly shaped filter) may demonstrate superior performance in certain cases, specifying such a filter shape leans heavily on the unimodal assump tion, which fails when considering bathymetric return waveforms (further details on the bathymetric case are discussed in a following section ). The value of a gated boxcar filter in isolating temporally correlated signal returns in the presence of noise has been previously demonstrated [54] and is chosen for its general robustness and adaptability. The location of the maximum output is tentatively labeled as the temporal position of the terrain signal. Validation is performed by checking the separation between the current and the previous signal cells; if their separation exceeds the allowable span, the next maximal output is tentatively labeled as signal and the validation process is repeated. This approach increases accurac y over the traditional CRR due to its independence from fixed bin placement. If signal returns are spread over two adjacent cells, the CRR filter will irrevocably eliminate some returns and discard information content. Figure 6 5 demonstrates an example, where frame 1 n has a significant number of signal returns in a labeled noise cell due to bin placement.

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82 Parameter Selection The described process is repeated for each shot in the data set. Once all signal cells have been acquired, the data is filtered such that only returns in 'signal cells' remain. The surface is reconstructed by interpolating on a regular grid, using the mean projected elevation within each grid cell. Parameters essential to the algorithm are: Filter length Filt er threshold (minimum count for identification of signal bin) Allowable span between signal cells The number of taps in the boxcar filter is analogous to the optimal CRR bin size developed by Degnan [ 11]. A small filter length is desirable to minimize included noise counts; however the filter length must be sufficiently long so that it encompasses the entirety of signal counts from the surface for an entire footprint, considering pulse spread from slope and roughness effects. Considering a scenario where the instrument is ranging to a surface of constant slope the ideal CRR bin duration is given by Equation 6 6 [11]. 6 6) f rms b 4 rms is the approximate width of the distorted return pulse, is the frame stretch factor (spatial stretching of the frame due to platform velocity, scanner motion, and slope effects), and f is the frame interval, which in our case is chosen to correspond to the laser pulse period (1/8000 s). rms depends on the transmit pulse width, beam divergence, and local slope, and is given by Equation 6 7 [11].

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83 6 7) 2 2 0tan c wT rms 0 is the RMS width of the laser pulse off a normal planar surface and Twis the laser spot radius on the ground. 0 can be estimated using our earlier developed equation for pulse distortion (Eq uation 2 14). The frame stretch factor is given by Equation 6 8 [11]. 6 8) c veff g tan4 eff gv is the effective ground velocity of the laser beam. For the particular topographic scenarios of interest (CATS system parameters, low to moderate surface slope, medium surface roughness), Eq uati ons 6 6 through 6 8 imply a CRR bin size of 7.0 ns. Given range bin duration of 0.5 ns, this translates to a filter length of 14 taps. For highly sloped or rough terrain, a larger filter size may be necessary to successfully track the terrain surface. A desirable choice of frame threshold is large enough to limit false positives (noise bins erroneously identified as a signal bin) while small enough to allow for variability in the number of detected counts in signal cells. Instrument contrast is defined by Equation 6 9 [11]. 6 9) b sn n C 1 sn and bn are the mean signal and noise counts per CRR bin per laser fire. Values for sn and bn can be either estimated based on histogram statistics for extensive data sets or selected conservatively (i.e. assume low signal, high noise levels) based on the equations presented in Chapter 2. The latter method was chosen for our purposes, selecting a value of sn corresponding to one signal event per beamlet and a value of bn corresponding to worst -case solar noise.

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84 The optimum frame thr eshold, as determined from Poisson statistics, is given by Equation 6 10 [11]. 6 10) C N N Kbin s opt) ln( sN is the number of expected signal counts per frame and binN is the ratio of range gate duration to equivalent filter length. The exact value of the chosen allowable span between adjacent signal cells is not overly important; this value is significant only in that it relates to the extent of terrain relief generally expected between adjacent laser foot prints. For this context a cons ervative value equal to the length of our filter (14.0 ns) is chosen, equivalent to a range differential of roughly 1 m. Results The reconstruction algorithm was tested ov er a variety of surfaces in order to evaluate its accuracy and robustness with regards to environmental characteristics (terrain shape, reflectivity, etc.) Environmental conditions and system parameters were set as in shown in Table 3 1 and Table 3 2 wit h surface reflectivity varied from 0.15 to 0.30 and simulations run for 12000 footprints (~1.5 s, covering an area of 90 m x 320 m) at full solar background noise. The surfaces w ere reconstructed with a horizontal resolution of 1.0 m in order to ensure co ntiguity. In all cases the algorithm demonstrated the ability to filter out noise and provide a reconstructed surface of sub -decimeter accuracy (Table 6 1 ). A small positive elevation bias was observed in the reconstructed surfaces, likely due to the com bined effects of receiver dead time and range bin quantization. Bathymetric DTM Generation Reconstruction of the bathymetric surface is a more complicated process than in the topographic case. The sea surface must be correctly located so that range values can be

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85 adequately compensated for refractivity effects. The influence of water column returns prevents application of a relatively broad filter such as the sliding CRR as presented. The optical characteristics of different water types, as well as variab le depth, ultimately leads to a large dynamic range over which the algorithm must operate. With these issues in mind, modifications have been made to the surface reconstruction algorithm to provide comparable results. Method: First, all 'signal' returns (i.e. sea surface, water column, and sea bottom) are isolated. Although ultimately interested in only the bottom returns, the entire water column must be isolated to mitigate any skew induced by errant solar background noise and to allow extraction of the sea surface elevation. The sliding CRR is capable of this objective, after adjustment of the key parameters. Filter length is altered to correspond to the maximum operable depth of the system in question (5 m for CATS would translate to a filter length of 67 taps) and the threshold is chosen sufficiently large to prevent false alarms. After the data has been filtered to exclude noise outliers, a histogram of projected elevation values across the entire data set is created. Decomposition of lidar wavefor ms using Gaussian mixture models and the EM algorithm has been previously demonstrated and performs adequately for our purpose [6 ]. The maximum -elevation mode output (given sufficient weight) from the EM GM algorithm is taken as the mean sea surface level [46]. Based on the output distribution parameters, sea surface returns are discarded, allowing continued analysis on a data subset that presumably includes only water column and bottom returns. T his ensemble approach is only appropriate for data sets exclusively focused on the bathymetric environment; for near shore testing where a portion of the d ata may be resultant from the beach, an additional step is necessary to partition topographic and bat hymetric results to prevent skew of the distribution statistics.

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86 Simply searching the remaining filtered data for the global maximum count is inadequate because the quantity of water column backscatter events may exceed the number of returns from the sea b ottom in turbid water. Because of high dynamic range, extraction of the sea bottom requires analysis of the return energy waveform [ 55]. Although digitized waveform data is unavailable, this analysis process is mimicked by es timating the return waveform through application of a low pass filter to the accumulated footprint histograms. By using a two dimensional LPF on a matrix of the accumulated histogram values, information from adjacent footprints can be effectively used to improve the estimate of the return waveform and increase contrast between the bottom and water column components. The standard approach to bathymetric waveform analysis is the decomposition of the return waveform into constituent model components (exponent ially modified Gaussian for the surface, exponential for the water column, and Gaussian for the bottom) (Figure 66 ) [56]. This form of analysis is inappropriate for LSNR data because the estimated pseudo -waveform is gravely u ndersampled and therefore does not closely fit the described distribution models (Figure 6 7 ). Previous work by Wagner, et. al has demonstrated that decomposition techniques (specifically Gaussian decomposition) are problematic for analysis of weak amplit ude lidar waveform data [ 57]. For that reason, a different analysis method is warranted here. An alternative approach is to locate the sea bottom by searching the reconstructed return waveform for the ultimate significant maxi mum. Ignoring the possible influence of errant noise counts, the local maximum occurring last temporally in the return waveform will correspond to the bottom signal. For each footprint, the return waveform is estimated as described and then the local maxi ma are located. A minimum 'intensity' threshold is applied to prevent background noise that

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87 passed through the boxcar filter from falsely registering a bottom return. Once the bottom signal for a given footprint has been located, a validation algorithm s imilar to that described for the topographic case is applied. As in the sliding CR R case, a maximum allowable spa n between subsequent signal locations is specified. If this span is exceeded, the minimum intensity threshold is lowered and the process is r epeated. The multiple threshold process described is necessary due to the high dynamic range of effective attenuation in natural waters. If using only a single noise threshold value set high, only very strong bottom returns are correctly registered; bott om returns from turbid or deep water scenarios will be ignored and a value within the water column will erroneously be selected as the bottom position. Likewise by setting the single threshold low, the algorithm becomes highly sensitive to noise and will have difficulty discriminating true bottom returns from noise effects. By imposing a displacement condition on the position of the bottom signal, the sensitivity of the bottom detection can be dynamically adjusted to compensate for the large dynamic range of return signal intensity. Once the bottom signal has been located for each footprint, surface reconstruction is straightforward. Returns are filtered, processed into geocentric XYZ coordinates, corrected for refractivity effects, an d gridded as before. Results The algorithm was tested for various terrain shapes, water conditions, and water depths. Parameters used for bathymet ric testing are shown in Table 5 2 with bottom reflectivity of 0.15 and simulations run for 12000 footprints (~1.5 s, covering an area of 90 m x 320 m) at full solar background noise. The bathymetric DTM was reconstructed with a horizontal resolution of 1.0 m in order to create a contiguous surface except in the 5 m coastal water case, where a horizontal resolu tion of 2.0 m was necessary to achieve contiguity. In pure sea water, results were

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88 comparable to the topographic case due to high water clarity and the small quantity of w ater column backscatter (Table 6 2 ). In the coastal water scenarios, the RMSE was m uch higher (7.6 cm at 2 m and 15.5 cm at 5 m) due to the skew induced by water column returns and much greater signal attenuation. In all cases, the algorithm was sufficient in reconstructing a DTM sufficient for the target detection procedure Discrimina tion of Target Areas Now that the spatial correlation feature has been calculated and a DTM of the underlying surface has been constructed, data points can be classified as target or non -target. Techniques for identification of target versus bare earth ar e typically based on an assumption of discontinuity in some spatial measure [52]. Classification is performed using a surface -based scheme: the elevation difference between the target and the underlying bare earth (Figure 6 8 ). Due to the path length resolution of LSNR lidar, this characteristic should be sufficient to distinguish the reconstructed surface from target returns for the target types discussed in the outlined objectives. Implementation of this measure is straightforward and is simply the elevation difference between each data point and the reconstructed surface. The decision boundary is heuristically set as a fraction of the expected target height Sliding CRR vs SCF The sliding CRR and SCF are similar conceptua lly, so it is vital to distinguish the two algorithms to avoid confusion and to reinforce their individual contributions to the overall target detection scheme. The sliding CRR operates within the confines of the LSNR data schemata, and performs well in e fficiently retaining a broad window of signal returns while eliminating a majority of noise. Terrain returns are reliably extracted and the bare surface is easily tracked, ideal for DTM generation.

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89 Because coverage in any given footprint (2 m x 2 m) is dominated by the terrain surface, there is no guarantee that returns from small targets will remain after application of the CRR filter. In addition, due to the nature of the sliding CRR (a relatively broad window used to maximize contrast between signal and noise), a significant number of noise events near the terrain surface may pass through the filter. Although the quantity is low relative to the terrain returns and therefore does not affect DTM generation, such noise events would be difficult to discr iminate against small target returns. The SCF functions much slower due to its point -by -point operation on the projected data, but more effectively utilizes information from other footprints (across track neighbors, as well as along track neighbors) to loc ate local surfaces. Because of this focus on local tracking, the SCF is far more sensitive to dense pockets of erroneous returns located far away from the actual target surfaces The SCF (for filtering signal from noise in general) and the sliding CRR (f or DTM generation, which provides discrimination between terrain and target) are therefore applied in a complementary fashion in order to mitigate their respective weaknesses. Summary The complete target detection procedure is as follows: 1 Form the surface truth for the area under investigation, with target objects located throughout (Figure 6 9) 2 Generate realizations of data using numerical sensor simulator (Figure 6 10) 3 Calculate SCF values for each projected data point (Figure 6 11) 4 Extract DTM surface (Figure 6 12) 5 Classify target points using combination of SCF value threshold and distance to -surface measure (Figure 6 13) 6 Evaluate target detection performance by comparing classification results to ground truth

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90 Observed results show that the designe d target detection algorithm is sufficient as a comparative metric of system performance. The procedure consistently detected targets with high probability, even in conditions of worst case solar background noise. Fig. 6 1. Il lustration of the SCF as a neighborhood operation. For each point in the data set, the number of points that fall within the surrounding cylindrical volume is calculated and used as a measure of local spatial correlation. In the illustrated example, the investigated point (white) is associated with two neighbors (grey). Fig. 6 2. Acrosstrack displacement between adjacent footprints across the laser swath. At the swath edges (scan angle extrema), the footprint spacing is at a minimum resulting in highe r data point density. Note that the effect of aircraft motion is not included in the plots to highlight scanner action. X Z Y D 1 D2

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91 Fig. 6 3. Probability distribution function for beamlet footprints, estimated by Parzen windowing simulated returns using a 2D Gaussi an kernel. High density at swath edges is caused by closer footprint spacing due to scan motion. Histogram of Weighted Spatial Correlation Feature Weighted # of Neighbors Noise Signal Fig. 6 4. Histogram of weighted SCF. Noise events are sparse and randomly located through the point cloud, while signal events are spatially correlated in a local neighborhood. Simulation was set for flat terrain (with three 1 m cube targets), 1000 footprints, and full solar background noise.

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92 Fig. 6 5. Illustration of the CRR concept. The range gate is divided into equal duration CRR bins. A frame is a collection of returns from one or more footprints. The event count for each frame is determined and compared to the threshold value. Bins exceeding the threshold are identified as signal bins (gray). Fig. 6 6. Typical bathymetric lidar return waveform. Region I corresponds to reflection off the sea surface wave structure and sea foam. Region II is comprised of photons reflected towards the receiver as the pulse propagates through the water column (water column backscatter). Region III is the reflecti on off the sea bottom. Note that the optical properties of the water determine the relative peak amplitudes of each of these regions.

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93 Fig. 6 7. Estimated return waveform after application of 2D LPF to the footprint event histogram Results are shown fo r a single 96 -channel footprint (solid line) and an average of 1000 footprints (dashed line). High variability from shot to shot is evident. The ensemble waveform closely resembles the expected waveform shown in Figure 6 6. Simulation was performed for coastal water at a depth of 5 m Fig. 6 8. Surface -based detection scheme. Surface points (white) reside within a small buffer zone about the DTM. Points outside this volume are classified as target (black). The extent of th e buffer zone can be specified heuristically, as a fraction of the expected target height. Reconstructed surface Threshold X Z Y

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94 Fig. 6 9 Surface truth for the simulated scene. Three 1 m cube targets were randomly placed on flat level terrain. Fig. 6 10. Resulting point cloud from simul ation of 1000 footprints in the scene depicted in Figure 6 9 Simulation parameters are as specified in Tables 3 1 and 3 2.

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95 Fig. 6 11. Remaining data points after filtering by SCF value. The top plot shows an isometric view while the bottom shows a XZ view. The three target areas are clearly visible in the bottom view. The SCF threshold value for this example was chosen manually by the observer. Fig. 6 12. DTM generated for the point cloud shown in Fig. 6 10. Horizontal resolution was set to 1 m to allow for contiguous reconstruction of the surface.

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96 Fig. 6 13. Overhead ( XY ) view of the classified point cloud. SCF threshold was set manually by the observer. Target areas are plotted in red while surface points are plotted in g reen. The algorithm correctly identified all three targets, with one false alarm. Table 6 1. Error statistics for topographic DTMs with surface reflectivity set to 0.15. Terrain CRR Sliding Window RMSE Reduction Flat 2.49 2.33 6.4% Sloped2.74 2.48 9.5% Random 2.59 2.39 7.7% Random (high) 3.04 2.76 9.2% RMSE (cm) Simulations were run for 12000 footprints over an area 90 m x 320 m. Table 6 2. Error statistics for bathymetric DTMs with surface reflectivity set to 0.15. Depth Terrain Pure Sea Water Coastal water 2m Flat 2.35 7.38 Random 3.45 7.59 5m Flat 2.57 14.5 Random 3.64 15.5 RMSE (cm) Simulations were run for 12000 footprints over an area 90 m x 320 m

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97 CHAPTER 7 QUANTITATIVE ASSESSM ENT OF TARGET DETECT ION PERFO RMANCE Overview Now that the full target detection classifier has been developed, the procedure can be applied to gauge the target detection performance of a fixed LSNR lidar system (CATS). By altering the target characteristics and environmental conditio ns (terrain shape and water clarity/depth, when applicable), the systems robustness can be categorically evaluated. Modifications to the hardware characteristics, namely laser PRF and transmitted laser pulse energy, are then induced to identify technical areas for design consideration in future system development. Comparison between two scan patterns is also presented. Although using a 45 degree line scan reduces the effective swath width by approximately 30%, this rotated scan pattern is expected to pr ovide more uniform coverage in the inner swath and eliminate the small gaps that are present when using the normal linear scan. The targets under investigation are cube blocks of various sizes (0.5 m or 1.0 m on a side). While vehicle obstructions in the littoral zone are of various shape and size, the selected objects are used for ease of computation and generalizability to other target types. Target reflectance values are chosen to be representative of construction materials (Table 7 1 ) [ 58], [ 59]. The terrain reflectivity is of low importance because the algorithm only requires a quantity of terrain returns sufficient to generate a meter -scale DTM; a value of 0.15, representative of wet sand, is used. Terrain shape is varied and presented in three forms: flat, lowly modulated, and highly modulated (Figure 7 1 ). The standard deviations in elevation of the lowly modulated and highly modulated surfaces are 17 cm and 55 cm, respectively. Although data from the entire swath is available for processing, analysis is limited to the inner swath. Dense footprint spacing at the swath edges results in a significantly higher number

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98 of false alarms, especially in bathymetric cases. We therefore limit our t arget detection analysis to data from the inner 75% of the lidar swath. Target detection performance, for a given system specification and environmental setup, is presented as a receiver operating characteristic (ROC). Typically, operating characteristics are used to depict relative classifier performance in discriminating signal from noise; in our context, the curves are used to depict the relative amount of pertinent target information that can be extracted from a scene given a specific system configurat ion. In each operating characteristic, t he number of false alarms is normalized by the number of tested targets; thus a false alarm count of 1.0 is equivalent to having equal numbers of correctly identified targets and false alarms. The control parameter used to create the characteristic is the SCF decision threshold; as the SCF decision threshold is decreased from its maximum value, the number of detected targets and false alarm counts increases, forming the operating characteristic curve. Topographic Res ults Parameters for topographic simulation were set as specified, with scan pattern set to the standard sawtooth scan. For each case, simulations were run at full solar background noise at a laser PRF of 8 kHz for 10000 footprints, unless otherwise specif ied. 100 cube targets were randomly located throughout an area 75 m x 240 m. Target Properties 1 m targets were easily detected, with 90% of targets detected at less than 0.1 false alarms for all three tested target reflectances. With a target size of 0.5 m, detection performance remained satisfactory, with 90% detection at less than 1.0 false alarms (Figure 7 2).

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99 Terrain Shape Target detection performance for the flat terrain and lowly modulated terrain cases were essentially equivalent in all tested case s. In most tested cases, highly modulated terrain had no effect on target de tection performance. Only with very low target reflectivity and small target size were the effects of terrain shape evident; at target size of 0.5 m and reflectance of 0.05, highl y modulated terrain exhibited a drastic performance reduction, with an approximately ten fold increase in false alarm count (Figure 7 3). System Specifications Increasing the laser pulse repetition frequency from 8 kHz (CATS specification) resulted in a si gnificant performance improvement, especially in cases of small target size and low reflectivity (Figure 7 4 ). The impact of increasing transmitted laser pulse energy was also significant in topographic tests; a 5x increase (from 3 J to 15 J) in transmi tted energy resulted in a nearly 40% reduction in false alarm count at 90% detection. As expected, the 45 degree rotated linear scan resulted in denser and more consistent groundal spacing. At 90% detection, the false alarm count was reduced by 68% when compared to the normal linear scan. Bathymetric Results Bathymetric simulation was set up in the same manner as in the topographic case. Values for the ocean environmental model were set as shown in Tables 5 1 and 5 2 The 'pure sea water' values corresp ond to high clarity water (a Secchi depth of ~15 m) while the 'coastal water' values represent more turbid shallow surf zone conditions (a Secchi depth of ~1.5 m). For each case, simulations were run at full solar background noise at a laser PRF of 8 kHz for 10000 footprints, unless otherwise specified. 100 cube targets were randomly positioned

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100 in an area 75 m x 240 m. F loating targets or targets otherwise suspended above the sea bottom were not addressed in this work Water Clarity and Depth Target dete ction performance over pure sea water was effective for a majority of tested target sizes and reflectances. 0.5 m targets of the maximum tested reflectance (0.20) were well detected at all tested depths, achieving 76% detection at a false alarm count of 1 .0 at a depth of 5 m. Targets of low reflectance were difficult to distinguish regardless of target size or water depth, due to the difficulty in discriminating between closely spaced water column backscatter points and target returns (Figure 7 5 ). In coa stal water simulations, high attenuation compounded the problematic effects of water column backscatter. The simulated system was largely ineffective in extracting targets of low reflectance, even at the minimum tested depth of 2 m (Figure 7 6 ). Results were markedly better for targets at the highest tested reflectance, with 65% and 90% detection (at a false alarm count of 1.0) at a depth of 2 m for targets 0.5 m and 1.0 m on a side respectively. Because of the high attenuation in coastal water, only la rger targets could be extracted effectively at further depths (Figure 7 7 ). System Specifications The dense coverage provided by higher pulse repetition frequency (tested up to 16 kHz) resulted in negligible improvement in detection of very low reflectivit y targets. Increasing laser PRF proved beneficial in a majority of other scenarios however (Figure 7 8). In the detection of 0.5 m targets at the highest tested reflectivity in 5 m of pure water, increasing the laser pulse repetition frequency from 8 kHz to 16 kHz resulted in an increase of detected targets from 76% to 96% at a false alarm count of 1.0. Similar tests for coastal water of 2 m depth resulted in an increase from 65% to 92% detection.

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101 In pure water scenarios, no performance improvement was observed when increasing the transmitted pulse energy, by a factor of up to ten over the CATS specification. Increasing pulse energy often resulted in worse performance; any advantage to increasing the return signal strength was offset by the high occurre nce of water column events. Unlike in pure water, target detection performance in coastal water was often limited by diminished signal strength and the resulting inconsistency of target returns due to high attenuation. Increasing the transmitted pulse e nergy was found to be beneficial in offsetting the high attenuation found in these waters (Figure 7 9), at sufficient depths where the water column backscatter was no longer prevalent Discussion Simulations have shown that the CATS system can be expected to provide robust target detection of meter -scale targets over land, even during day time operation. Ground-based field testing has shown CATS to reliably and accurately register returns from concrete and dry sand at nominal range (98% and 99% of beamlets incident on concrete and dry sand registered at least one return, respectively). These experimental results reinforce the notion that CATS is capable of robust detection of vehicle obstructions and like targets in the beach zone. In clear waters, CATS ca n be expected to detect small targets of sufficient reflectivity to an operational depth of at least 5 m. Experimental data from CATS field testing has shown that 97% of beamlets incident on concrete registered at least one return in 50 cm of pure water. Extrapolating the expected return statistics to 2 m and 5 m, this amount of stability is sufficient for the target detection algorithm and is consistent with CATS expected performance in waters of high clarity. Similarly, CATS can be expected to detect me ter -scale targets of moderate to high reflectivity in turbid waters of very shallow depth. Previous simulation work to evaluate

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102 SHOALS target detection capability showed an inability to reliably extract small (1 m or less in height) targets in depths shal lower than 10 m [ 61]. In these scenarios CATS shows a decided advantage over SHOALS due to dense groundal spacing and short pulse length. Performance in submerged target detection was often limited by return signal strength due to high attenuation in turbid water. High dynamic range is one problem inherent to both the traditional and LSNR lidar paradigm s ; in a given mission, the return signal strength can be expected to vary by at least an order of magnitude due to surface reflectance, water depth and clarity, etc. One solution is to increase the pulse repetition frequency. This approach allows for high density sampling of reflective materials while potentially providing sufficient returns from non reflective targets. Th ere are several drawbacks however; if the target material exhibits very low reflectiv ity, targets may remain occluded by water column backscatter. Secondly, the data throughput will increase proportional to the laser PRF. Costly high -speed receiver elect ronics may then be necessary for on board processing of the return data. Increasing the transmitted laser pulse energy from the CATS specification is also an obvious option. While this solution may be useful in topographic scenarios, bathymetric applicabi lity is hampered greatly by the approximately linear dependence of the quantity of water column backscatter events to transmitted pulse energy. If the detector threshold remains at the single photoelectron level, the increase in water column backscatter e vents will be incommensurate to the smaller increase in target events. In addition, returns from highly reflective surfaces could cause ringing or even damage the sensitive photodetector. Use of a rotated 45 degree line scan generally provides better perf ormance than the standard scan pattern, due to increased groundal density and decreased size of inter -footprint

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103 gaps. Since t he effective swath width is decreased by approximately 30%, the mission budget must be considered accordingly. If an expansive ar ea must be surveyed in a limited number of flights, then the standard sawtooth scan (320 m swath) may be prefer red Fig. 7 1. Representative surfaces for the random terrain shapes. Top plots show lowly modulated terrain ( 2 Z =2.78e 2 m2), while bottom plots show highly modulated terrain ( 2 Z =3.01e 1 m2). Left plots depict zoomed in isometric views of areas containing a single target and right plots show top down views of the entire test region.

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104 Fig. 7 2. Operati ng characteristic curves for CATS parameters over flat terrain. 100 cube targets 0.5 m on a side were randomly positioned in an area 75 m x 240 m for each test. Reflectance was varied from 0.05 to 0.20.

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105 Fig. 7 3. Operating characteristic curves for C ATS parameters. 100 cube targets 0.5 m on a side with reflectivity of 0.05 were randomly positioned in an area 75 m x 240 m for each test. Terrain shape was varied between flat, lowly modulated random, and highly modulated random

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106 Fig. 7 4. Operating characteristic curves for selected laser PRF values. 100 targets 0.5 m on a side with reflectivity of 0.05 were randomly positioned in an area 75 m x 240 m for each test

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107 Fig. 7 5. Operating characteristic curves for CATS parameters over pure sea water of 2 m depth. 100 targets 1.0 m on a side and with varying reflectivity were randomly positioned in an area 75 m x 240 m for each test

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108 Fig. 7 6. Operating characteristic curves for CATS parameters over coastal waters of 2 m depth. 100 targets were r andomly positioned in an area 75 m x 240 m for each test

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109 Fig. 7 7. Operating characteristic curves for CATS parameters over coastal water of varying depth. 100 targets 1.0 m on a side and with reflectivity of 0.20 were randomly positioned in an area 75 m x 240 m for each test

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110 Fig. 7 8. Operating characteristic curves for selected laser PRF values, over 5 m of pure water 100 targets 0.5 m on a side and with reflectivity of 0. 20 were randomly positioned in an area 75 m x 240 m for each test.

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111 Fig. 7 9. Operating characteristic curves for selected transmitted pulse energy values, over 5 m of coastal water 100 targets 1.0 m on a side and with reflectivity of 0. 20 were randomly positioned in an area 75 m x 240 m for each test Table 7 1. Reflect ivity characteristics of common construction materials, at a wavelength of 550 nm. Material Reflectivity Gravel10.32 Concrete10.26 Asphalt10.09 Dark tar10.05 Green paint20.30 Dark blue paint20.08 Black paint20.07 Values obtained from Herold et al.1 and Lavery2.

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112 CHAPTER 8 CONCLUSIONS Research Scope The research reported in this dissertation has focused on t he development and application of a numerical simulator model to predict and assess the performance of the Coastal Area Tactical -mapping System (CATS), developed by the University of Florida with funding by the Office of Naval Research [18]. The simulation program was developed in parallel with design, construction, and testing of a first generation CATS sensor a low signal -to -noise ratio (LSNR) light detection and ranging (Lidar) sensor designed to precisely map shallow coasta l waters and beaches with sufficient resolution to detect obstructions and/or mines 0.5 m larger on a side. The key design specifications for the CATS prototype relevant to simulation are: 1 Operation in a light fixed -wing aircraft flying at ground speeds of 150 to 200 kilometers per hour and altitudes (above local ground level) of 400 to 1000 m 2 Use of a frequency doubled Nd:YAG laser, with an output wavelength of 532 nm (chosen for water penetration), operating at 8000 pulses per second with each pulse havin g 3 J of energy in a pulse length of 480 picoseconds 3 Use of a 100 channel micro-channel -plate PMT to detect return laser signals as weak as a single photo -electron 4 Inclusion of a diffractive holographic element in the laser transmit path to separate the l aser output into a ten by ten array of 100 equal energy beamlets (in combination with a beam expander, this element illuminates a patch of terrain such that contiguous coverage can be achieved at the specified laser pulse repetition frequency through use of the aforementioned multi -channel photodetector)

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113 5 Registration of discrete returns using a multi -channel multi -stop event timer operating at 2 GHz to achieve a range resolution of 7.5 cm 6 Distribution of laser pulses across a swath using a Risley prism scan ner At a minimum, the simulator had to be able to accept the nominal parameters listed above, along with other variable parameters including surface reflectivity, terrain relief, shape and dimensions of potential obstructions or mines, and scanning pattern in order to reliably predict and evaluate the performance of CATS. Simulator Overview The simulator program was developed in the Matlab environment with vectorized code for computational efficiency [18]. The design is modula r to enable it to be easily extended to include features of LSNR lidar units other than CATS. However the current simulator contains only the modules specifically needed to predict and evaluate CATS and would require additional modules for performance pre diction of other sensors with drastically different system characteristics, such as operation at high altitude or integration of a different type of optical mechanical scanner. Risley prism scanners have been used in other lidar units, such as the MIT Jigs aw system, and present a wide selection of scan patterns through operator specification of the angular velocities (rate and direction) of the two optical wedges. Computing the precise location of each of the 100 laser beamlets transmitted for each laser p ulse, for the selected scanning pattern, is handled through repeated application of Snells law. In combination with the laboratory measured angular offsets of the diffractive holographic element and the platform altitude and attitude as provided by estab lished GPS and IMU signals, the scanner module calculates the pointing vector for each transmitted beamlet.

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114 Nominal range acquisition is accomplished through ray tracing of the beamlet vectors to the virtual ground surface. Calculation of the precise proj ected location of each beamlet centroid (100 per pulse) is computationally intensive; a routine based on volumetric discrimination is executed for each beamlet in order to narrow the search of candidate ground points. The range acquisition module then sea rches the remaining points for the minimum -distance point to the beamlet vector and uses this point as a basis for range calculation. The lidar link equation, modified specifically for the CATS application, is used to predict the expected return signal str ength for each outgoing shot. Noise levels are estimated based on solar irradiance through the atmosphere and backscatter off the virtual surface, combined with the manufacturer -specified photodetector dark noise rate. Variability in the return signal in tensity due to scintillation and speckle are not considered, due to their negligible calculated impact on CATS performance. Additional code is included in the simulator program to efficiently model bathymetric environment effects. Beamlet vectors and nomi nal range values are adjusted for refractive index effects. The bathymetric module considers the return signal divided into three constituent components: sea surface, water column, and sea bottom. Optical properties through the water medium are considere d vertically uniform due to the operational focus on very shallow water and the sea bottom signal intensity being a function of the integrated effect of sediment. Multiple scattering is not considered due to the small receiver field -of -view, such that all small angle forward -scattered light is considered lost. Event realizations are generated through consideration of shot noise as the dominant process in return signal variability. A Poisson -distributed random variable is generated for each range bin and its corresponding time signature is used to determine if a discrete event has

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115 occurred in the given bin. This process is applied to each range bin, with the Poisson distribution parameters given by combining the expected signal and noise levels with the predicted return pulse delay and distortion. Target Detection Analytics : As the primary goal of CATS is to detect obstructions and other small artificial targets in the littoral zone, in order to evaluate target detection capacity a functional target detec tion classifier appropriate for LSNR lidar data is necessary [19]. The designed classifier initially exploits the spatial correlation of signal (terrain and target) returns to collect locally clustered events. The spatial cor relation feature, as described, is a volumetric measure of the number of data points occurring locally to the investigated point; signal points will have a significant number of neighbors (assuming sufficient, reliable returns from the surface) while noise events will be largely uncorrelated. These feature-valued events are then compared to a topographic or bathymetric DTM to discriminate between target and terrain returns. The DTM is generated through application of a temporal coherence algorithm known a s the sliding CRR, which demonstrates 5% or greater reduction in root mean square error over previous existing algorithms. For the bathymetric case, further analysis is necessary to isolate sea bottom returns in the presence of noise. Waveform estimation using application of a 2D filter to the combined footprint histograms provides sufficient information to enable generation of the bathymetric DTM with sub-decimeter elevation error in most cases. Simulation Results This study has shown that even in the pr esence of worst -case solar background noise (overhead illumination), the signal return from the terrain surface is easily located through observation of the ensemble elevation histogram (i.e. integration over XY coordinates in the point cloud). Comparison of the SNR for various surface reflectivities demonstrated a weakness of the binary event implementation in the LSNR lidar design; as the diffuse surface reflectance

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116 increased from 0.05 to 0.50, the number of noise events due to solar illumination backsca tter from the surface increased approximately linearly while the number of signal events was limited by the return pulse width and duration of individual range bins. It was shown that expected topographic measurement performance is robust; manual filtering of returns (through application of a 2 meter window placed about the true surface elevation) showed a standard deviation in elevation values of 12 cm at worst -case solar background and 7 cm at night -time operation. Analysis of bathymetric data via appl ication of the expectation maximization (EM) Gaussian -mixture (GM) algorithm reliably extracted the sea surface level (error less than 5 cm) and corrected for refraction effects through the water column. The bathymetric capability of CATS was investigated with regards to optical water conditions (pure sea water, with a total a ttenuation coefficient of 0.05 per m and coastal water, with a total attenuation coefficient of 0.5 per m). Results showed that, at a sea depth of 2 m, the sea surface and bottom we re easily separated in both tested water types due to short transmitted pulse width and sufficient signal strength The point density from the sea bottom was sufficiently high to imply practical sub meter horizontal resolution bathymetric mapping. At 2 m depth, the maximum observed root mean square errors of the reconstructed surfaces were 3.5 cm and 7.6 cm for pure sea water and coastal water, respectively. At greater depths, horizontal resolution of the reconstructed sea bottom was shown to be limited greatly by water clarity; meter -scale bathymetric mapping was only possible at a sea depth less than three times the Secchi depth. The corresponding increase in elevation error was also highly dependent on water clarity; at 5 m depth, the observed RMSE fo r pure water was comparable to the results for 2 m depth (3.6 cm) while the value for coastal water deteriorated substantially (to 15.5 cm).

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117 Detection performance of CATS was evaluated with regards to cube targets 0.5 m to 1.0 m on a side. Classification analysis of simulated data showed CATS to be capable of detecting more than 90% of targets, 0.5 m on a side and of low reflectivity (0.05 diffuse reflectance coefficient), over flat terrain at a false alarm count of 1.0. Slowly varying terrain, as would b e expected in operation over the beach zone, demonstrated no significant reduction in performance. Increasing the assumed laser repetition rate was shown to drastically improve the target detection capability of the investigated system; an increase of las er PRF by a factor of 2 (from 8 kHz to 16 kHz) resulted in a 60% reduction in false alarm counts for 90% targets detected, 0.5 m on a side and of low reflectivity. A similar but weaker (about 15% reduction in false alarms) impact was observed for a compar able increase in the transmitted pulse energy. As in the evaluation of bathymetric measurement performance, detection of submerged targets was largely dependent on the inherent optical properties of the underlying water, namely absorptance and scattering c haracteristics. The presence of water column returns hampered detection of targets of low reflectivity, even in water of high clarity. In pure sea water, targets of sufficient reflectivity (diffuse reflectance coefficients of 0.10 or higher) were reliabl y detected up to the maximum investigated depth, 5 m. At 5 m depth, at a false alarm rate of 1.0, 73% of 0.5 m targets (with diffuse reflectance coefficient of 0.20) were detected. Results for 1.0 m targets (with reflectance of 0.20) were excellent, with over 98% of targets detected at a depth of 5 m at a false alarm rate of 1.0. Introduction of turbidity to the water environment reduced target detection performance drastically. At 2 m depth, the investigated system demonstrated the ability to reliably detect only targets of the highest tested reflectivity (reflectance of 0.20), with 65% of 0.5 m targets and 90% of 1.0 m size targets detected (at a false alarm rate of 1.0).

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118 Increasing the laser repetition rate demonstrated compelling performance improvem ent due to the linear relationship between quantity of signal events and laser repetition rate. In pure water of 5 m depth, increasing the laser PRF by a factor of 2 (from 8 kHz to 16 kHz) resulted in an increase from 76% to 96% of 1.0 m targets detected at a false alarm rate of 1.0. The same test, repeated for coastal water of 2 m depth, showed an increase from 65% to 92% targets detected. Modifying the transmitted pulse energy did not result in the same consistent performance improvement as laser repe tition rate. Due to the described limit on the quantity of signal events recorded as a function of return signal strength, pulse width, and range bin duration, the net performance change due to altering the transmitted pulse energy is dependent on the env ironments attenuation and target reflection characteristics. In scenarios where signal strength is the limiting performance factor, such as in turbid waters with high attenuation, higher consistency in target returns is achieved by increasing the transmi tted energy. By increasing the transmitted energy tenfold to 30 J (from 3 J, the CATS specification), 74% of 1.0 m size targets (at the highest tested reflectivity) were detected in coastal water of 5 m depth, at a false alarm rate of 1.0. This is a dr astic improvement over the 9% of targets detected at nominal CATS specifications. One caveat to increasing transmitted pulse energy is the increased prevalence of water column backscatter; employing higher pulse energy while remaining at a single photoele ctron detector threshold introduces a number of problems due to the dynamic range of the investigated environments. Detection performance in high clarity waters, or shallow depths, was found to be worse at higher transmitted pulse energies due to the decr eased contrast between water column events and target returns.

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119 Conclusions The presented research indicates that CATS can be expected to provide robust decimeter scale mapping and sub -meter target detection in topographic scenarios, even in the presence of solar illumination due to daytime operation. Root mean square error in the estimated topographic DTM should be less than 5 cm. Over 90% of targets larger than 0.5 m on a side should be detected in the beach zone. Although bathymetric performance will la rgely depend on water conditions, in optically clear waters (total attenuation coefficient less than 0.10 per m), meter -scale horizontal resolution bathymetric mapping and detection of moderately reflective (e.g. concrete) meter -scale targets should be via ble to a depth of 5 m. The accuracy of estimated elevation values should be comparable to the expected topographic performance. Over 70% of targets 0.5 m or larger on a side should be detected to a depth of 5 m. In turbid waters, the operational depth f or both mapping and target detection will be limited to a few meters. At a sea depth of 2 m, the root mean square error in elevation should be less than 10 cm, with the capability to detect more than 60% of targets 0.5 m or larger. The target detection re sults are a useful guide to the design of future LSNR lidar units. The key to improving the LSNR lidar design is increasing the reliability and consistency of returns while preserving a strong contrast between signal returns and background returns, i.e. n oise and water column events (and to a lesser extent, atmospheric backscatter). Shot -by-shot efficiency is essential to preserving this contrast; that is, a return signal strength of 1 p.e., sampled 10 times (i.e. increasing the laser PRF by a factor of 10) provides far more information than a signal strength of 10 p.e. sampled once (i.e. increasing transmitted pulse energy by a factor of 10) if we record single photon events.

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120 A future LSNR lidar that preserves the binary data scheme (i.e. discrete retur ns with a 1 p.e. detection threshold, with no intensity measure) should therefore rely on maintaining a low transmitted pulse energy (predicted return signal strength near 1 p.e. for intended mission) while increasing the density of groundal points, whethe r through inclusion of a micro laser with higher repetition rate or beam splitting (with multiple multi -channel detectors). This technique largely avoids the loss of contrast information (e.g. simply increasing transmitted pulse energy causes an increasin g prevalence of water column returns while providing no additional information about surfaces which would provide reliable and consistent returns at a lesser incident energy) while increasing data fidelity. The main drawback is in designing the receiver/d ata capture electronics; the necessary throughput to handle the incoming data linearly increases with laser pulse rate and could necessitate integration of costly high-speed electronics. An alternative technique would be to diverge from the binary data eve nt scheme and to instead implement a method of waveform digitization, by recording an intensity measure for each registered event. This could be implemented through a series of voltage comparators (tied to the PMT channel responses) rather than a single t hreshold comparator. By then increasing the transmitted pulse energy, the practical operation of LSNR lidar systems could be extended to additional applications (e.g. waters deeper than 5 m) while preserving the dynamic range information necessary to disc riminate between background (i.e. noise and water column) and signal. The disadvantages to this approach are increased data throughput (a 16 bit intensity measure would introduce a 4 -bit field for every recorded event) and additional complexity in the rec eiver optics and electronics. Future Work : Additional areas of interest warrant extension of the presented simulator program. Topographic mapping and target detection under canopy are areas where LSNR lidar

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121 may provide a significant advantage over tradit ional ALSM; the decimeter -scale beamlet groundal spacing and high detector sensitivity could supply significant returns from penetration through canopy gaps. LSNR lidar implementation on high altitude platforms, including spaceborne applications, induces complications due to the propagation of the laser pulse through several layers of atmosphere. Consideration for stratified cloud layers is therefore a logical extension of this work. Speckle and scintillation could play significant roles in inducing vari ability in the return irradiance and their potential contributions must be considered for the investigated application. Although the target detection classifier was designed to be robust, it has a few key requirements: reliable and numerous returns from ta rget surfaces, as well as high contrast between signal and noise. These requirements fail when investigating submerged targets of very low reflectivity, due to attenuation and the prevalence of water column backscatter. Further research could potentially increase the fidelity of low reflectivity target detection. Rather than searching for the target returns (and causal surfaces), an alternate approach would be to consider the voids in the lidar point cloud where target objects may exist. If the scene is sampled sufficiently, the underwater volume will be populated with representative returns from water column backscatter. Sub -volumes (between the sea surface and bottom) with no enclosed data points may be indicative of low reflectivity targets. Practical application of this algorithm would require a LSNR lidar system with much denser point spacing than CATS, due to the highly variable nature of water column events. The depolarization ratio can potentially be used to discriminate between man -made targets and natural surfaces even in turbid medium [62][63]. Man -made surfaces illuminated with polarized light generally retain the incident polarization (due to specular reflection) while diffuse

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122 sur faces result in depolarization. The Swath Imaging Multi -polarization Photon -counting Lidar (SIMPL), a prototype photon-counting system in development at NASA Goddard Space Flight Center, exploits the wavelength -dependent depolarization ratio to differenti ate between surface types (e.g. broad leaf vs. needleleaf vegetation) [ 64]. Future airborne LSNR lidar systems could potentially use the same concept to discriminate between man -made targets and natural surfaces. The potenti al capacity of polarization information to increase target discriminability in LSNR lidar data warrants further investigation through theoretical analysis and simulation. Another consideration for future LSNR lidar prototypes is in the detector threshold l evel. Although CATS was designed to operate at the single photoelectron level, several field tests have focused on operation of the photodetector at a multi photoelectron threshold. The chief observed benefit is that the resulting data contains far fewer returns recorded from water column backscatter, solar noise, etc. Because atmospheric scatter or water column backscatter are generally single photon events, the quantity of recorded noise events is reduced drastically when operating at the multi -photoel ectron threshold. The simulator model could be adapted to fit this situation, with an end goal of assessing target detection performance using multi -photoelectron threshold detection versus single photoelectron detection.

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123 APPENDIX CATS HARDWARE AND SOFT WARE Introduction The CATS prototype has been designed for two primary goals: to improve detection and identification of anti -vehicle and anti -personnel obstacles and munitions in the coastal zone, and to gain a fundamental understanding of low -energy lid ar phenomenology encountered in mapping near -shore coastal environ ments, including shallow water, beaches, dunes, and coastal vegetation High level system design of CATS was done at the University of Florida (Figure A 1) System construction and compone nt integration were done under contract by Fibertek, Inc. (electronic subsystems) and Sigma Space, Inc. (optics) (Figure A 2) Hardware Design A number of factors must be considered in designing a LSNR lidar system. The inclusion of a micro laser, desirab le for low power and weight, limits the laser pulse rate (8 kHz to 20 kHz for commercially available micro lasers) and therefore necessitates the illumination of a patch of terrain and multiple channel detection to achieve sub -meter horizontal resolution Optical components must be chosen carefully to limit solar background noise while maintaining beam quality. S election and integration of electronic components must focus on limiting noise levels while achieving decimeter level resolution. Optics Design and Implementation An operational wavelength of 532 nm (green) was chosen for CATS to provide shallow water penetration. The illumination source is a low power (~ 30 mW), passively Q -switched, frequency doubled neodymium -doped yttrium aluminum garnet (Nd: YAG) laser produc ing 480 ps (FWHM) laser pulses at a rate of 8 kHz

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124 To achieve the desired horizontal resolution of 20 cm, the outgoing pulse pass es through a beam expander and diffraction holographic element, resulting in a 10x10 array of beamlets of n ominally equal power. The beam expander is a plano-convex lens made of BK 7 lens material with magnesium fluoride coasting, chosen for its compatibility with visible and infrared applications. The holographic element splits the Gaussian -distributed beam output into a 10x10 array with greater than 80% efficiency. By using this approach to achieve uniformity of detection across the multiple channel array (rather than a tophat distribution, e.g.), loss of energy due to the dead space between photodetector a nodes is avoided. The resulting beamlets are then reflected out of the shared afocal telescope through two Risley prisms. The Risley prisms are V-coated wedges made of BK 7 optical glass with precisely known angles (13.58) and refractive indices (1.519) Motion electronics are set to slave the rotation of the two parallel wedges to the leading edge of a synchronization pulse based off the laser fire. The two gear ratios of the wedge motors can be altered by the system operator in direction and angular velocity, to allow for a range of relative rotational speeds. The result is a precise scanner motion system that provides a huge variety of potential scan patterns (conical, sawtooth, rosette, etc.). The laser reflections from a surface which propagate back along the same optical path are reflected off a n annular pick off mirror to a spectral filter. The filter is centered at a wavelength of 532.1 (+/ 0.05) nm with FWHM 0.30 (+/ 0.05) nm. The filter has a temperature coefficient of 0.002 nm / C. Dust particles residing on optical surfaces in the receive path may produce interference patterns due to scatter which may interfere with desired signal information. A simple way to deal with this interference is through a tight spatial filter. Scattered li ght can be blocked by

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125 centering a small aperture at the focal spot of the direct beam, while allowing the direct beam to pass through. The resulting cone of light has a very smooth irradiance distribution and can be refocused to form a collimated beam tha t is almost equally smooth. The filtered beamlets are refocused via a telephoto lens before reaching the MCP -PMT. Receiver Design and Implementation To meet the single photon sens itivity along with the multiple -channel requirement, a 10x10 anode array micro channel plate ( MCP ) photomultiplier tube ( PMT ) is used to detect the reflected laser pulses. The MCP -PMT is a secondary electron multiplier consisting of millions of very-thin, conductive glass capillaries (4 to 25 microns in diameter) fused together and sliced into a thin plate. Each capillary or channel works as an independent secondary electron multiplier to form a two -dimensional secondary -electron multiplier. The ends of the capillaries are covered with thin metal electrode s and a voltage is ap plied between both ends to create an electric field in the direction of the channel axis. After a wall -electron collision, secondary electrons are accelerated by this field and travel along the parabolic trajectories determined by their initial ejection v elocity. As a result of repeated secondary electron emissions the electron current increases exponentially as the output end of the channel is approached. For maximum sensitivity (and to prolong detector life) the photon -counting detector is normally off and gated for data collection. In order for the photon -counting detectors gain to settle, the gate pulse must be sent out prior to the start of data capture. Terminal count values for both the start capture pulse and the detector gate pulse are received from the system controller via a circuit on the range/control board, an electronic component also responsible for maintaining a stable high frequency system clock, providing control for the high voltage of the detector assembly, and supporting communicati on between the data capture components and system controller.

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126 The resulting electrical response then passes to the receiver electronics (Figure A 3) A low pass filter is used to stretch the pulse because the input signal pulse width could be of the same order as the sample period of the threshold comparator. The bandwidth of the low pass filter wa s calculated to achieve greater than 90% counting efficiency for single photoelectron events. The preamplifier is a wide band (DC to 1 GHz) low noise RF gain b lock that amplifies the detected signal to a level suitable for the processing electronics to operate. After the signal is filtered, it passes through an automatic gain control (AGC) amplifier. The AGC amplifier is used to compensate for the non uniform r esponse between detectors across the entire detector array. AGC amplifier settings are voltage controlled via calibration values stored in a FPGA. Next, the signal goes to a threshold comparator. Threshold reference voltage is supplied by FPGA control l ogic, routed through DAC channels. This voltage reference corresponds to the voltage level of a single photoelectron. Sensor data at the input of a serial to parallel converter is sampled every clock cycle. The actual system clock therefore determine s the recorded range resolution. To achieve the desired 7.5 cm resolution, a 2 GHz clock is necessary. Because each serial to parallel converter requires a clock signal the high -speed system clock is buffered with fan -out drivers. Programmable delay chip s are used to match propagation delays so that all signals can be sampled at the same time. Processing and Analysis Tools S oftware tools have been developed for processing and analysis of CATS data. Each CATS session produces a set of binary encoded data files : time tag files for the inner and outer (A and B ) optical wedges, a time tag file for the transmitted laser shots, and a file including the event history for the entire test (Figure A 4)

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127 A GUI (graphical user interface) program has been develope d in Visual C++ that allows for conversion of these files into a suite of text file s that are accessible by algorithm development environments like Matlab. W edge index times are output into two 2 -column text file s (one file for the inner A wedge, one f or the outer B wedge) where the first column contains coarse time tag information (measured in seconds) and the second column contains an offset to the coarse time (measured in microseconds). The shot time tag file contains a list of time s, one for ea ch transmitted laser pulse, relative to the previous A -wedge index mark (the counter resets on encoder detection of the index mark), measured in 4 s increments. This shot time tag scheme allows for reliable synchronization of each shot to the scan period. The event history data is also parsed and output into a 4 -column text file with e ach row corresp onding to a single registered event. T he columns are structured in the following format: 1. shot number, 2. channel number, 3. hit number, 4. range bin numb er. Processing Each Risley prism has an index mark etched at its thickest part; an optical encoder, positioned 50 degrees to the vertical along the scanner assembly, allows time tagging of the scanner wedge motion once every rotational period (Figure A 5 ). By calculating the relative angular velocity of each wedge (and resulting angular position) scan pattern s can be reconstructed automatically by the Matlab processing software. Preliminary analysis of CATS data showed errata in the encoder time tags. In dividual w edge time tag entries were often missing (Figure A 6 ) Modifications were made to the processing software to compensate for the se errors, identifying and correcting these instances where necessary.

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128 The complete procedure for processing the s canner wedge time data is therefore as follows (demonstrated for the inner A -wedge) First, the coarse and fine wedge time series are combined to form the absolute index time -tags (i.e. the absolute time when the index mark passed the optical encoder) (Eq uation A 1). A 1) n t e n t n tfine A coarse A A ,6 1 The difference between consecutive index times is then calculated. A 2) 1 n t n t n dA A A During normal operation, n dA should equate to the rotational period of the A -wedge and should be ne arly constant throughout a single test session In practice, this is not the case, a s shown in Figure A 6; the data output by CATS exhibits erratic spikes in n dA due to missing time entries. To interpolate between entries and fill in these gaps, we first determine the standard rotational period for the wedge. We begin by assuming that corruption of the index time data is exclusively caused by missing entries so that n dAmin is an indisputably authentic value for the r otational period. We then search n dA for values subject to the constraint in Equation A 3. A 3) n d m dA Amin ) 1 ( The values for m are therefore a subset of the indices N 2 1 of n dA is a small constant that allows for some variability in the rotational period (a value of 0.001 is used). By assuming that the rotational period is nearly constant throughout the trial, we then estimate the standard rot ational period using Equation A 4 A 4 ) ] [ m d median TA A

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129 We now identify gaps in n dA and estimate the appropriate number s of missing entries based on the standard rotational period and insert this interpolated data into the ti me series. A p seudo -code description of this process is as follows: gaperrors = find( A AT n d 5 1 ) %Locate gaps while( length(gaperrors) > 0) %While gaps exists, ierr = gaperrors[1] %Locate first gap gap_length = ierr dA % Determine duration of gap num_miss = round( 1 AT length gap ) %Determine # of missing entries N t ierr t T miss num ierr t T ierr t T ierr t ierr t t t tA A A A A A A A A A A 1 2 ], 2 [ 1A %Eliminate gap by inserting interpolated data 1 n t n t n dA A A %Re -calculate time difference gaperrors = find( A AT n d 5 1 ) %Repeat process by locating gaps endwhile This algorithm recursively steps through the time values until all the gaps have been filled with interpolated data The entire procedure is applied to the time series information for both optical wedge s to insure data fidelity Reconstruction of the scan pattern (and relative positioning of the shot footprints) is done by interpolating between scanner time tags on a shot -by-shot basis. Accurate shot times are therefore a precondition to 3D data analysis Preliminary analysis of CATS data showed errors in the recorded shot time s E ntries in the shot time data were often erroneous or missing (Figure

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130 A 7 ). Adjustments made to the processing software allow for automatic removal and correction of the shot time data where necessary. To establish a logical framework we first present an overview of the ideal behavior of the shot time -tags. The times for each transmitted laser shot are recorded relative to the A wedge index times, in 4 s increments. Equat ion A 5 gives the typical value expected between subsequent shot times during normal operation A 5) 31 ) s 10 s)/(4 1/8000 ( | 1-6 normal n s n s E However because the shot times are recorded relative to the A -wedge index times, the time counter should be reset on detection of th e A -wedge index mark. Equation A 6 gives the typical differential expected between subsequent shot times after a reset. A 6) 12500 ) s 10 s)/(4 1/20 ( | 1-6 reset n s n s E Ideal operation of CATS should therefore result in recorded shot times that increment by approximately 31 and then reset after a complete period of the A -index wedge (before the counter value exceeds 12500). We search the shot time series data for entries that obey these conditions. First the difference between shot times is calculated (Equation A 7 ). A 7 ) 1 n s n s n dS This derivative can be used to determine two vital quantities: the average time differential between subsequent shots, calculated using Equation A 8 and the average scan period, using Equation A 9 Note that since we are only using these quantities internally, we do not scale them to compensate for the quadruple increment. A 8 ) ] [ n d median TS S

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131 A 9 ) ] [ n d median TS scan n ds is a subset of n dS including only negative values (i.e. res ets) The process to locate all valid shot entries (i.e. normal shots and reset shots) is described by the following pseudo -code: normal_shots = fin d( S S S ST T n d ) %Locate shots with normal increments reset_shots1 = fin d( scanT n s 5 0 1 ) % Condition #1 for resets: previous entry is large reset_shots2 = fin d( S S ST m n s T m ns T m n s 3 & 2 & 1 ) % Condition #2 for resets: next k entries are small reset_shots = intersect(reset_shots1, reset_shots2 ) %Locate resets constrained to two conditions good_shots = union(reset_shots, normal_shots ) S is a small constant that allows for variability in the shot to -shot time increment ( a value of 0.1 is used). m is an integer used to correctly detect reset s in the presence of missing entries (a value of 5 is used). Now that we have located these specific errors values in our shot time data, we purge the corrupted data and retain the valid entries, adjusting the shot indices as necessary. Another major ti ming error corrupts the shot time tags and must be removed before proceeding to analysis. The A -wedge reset signal is occasionally missed by the timing electronics, causing the shot counter to exceed 12500. If the reset signal is again missed at 25000, t he 15-bit counter will roll over the maximum value of 32768 (215) and begin at 0. We must therefore correct these time values such that they retain their relativity to the A -wedge rotational period. The process to correct the entries is as follows: rollo ver_shots = fin d( K n dS 152 ) % Locate rollover errors

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132 %Locate entries affected by rollover and correct. n s = mod ulus ( n s scanT ) %R estore single -period base Now that we have filtered and corrected our timing data, t he projected location of each shot through the prism assembly can be calculated and used to project our data relative to the sensor frame We begin by finding the index of the shot occurring closest to the first A -wedge index mark. This is done using the following algorithm : min_idx = find( m T n sS ) %Find potential scan period ends max_idx = find( ) 1 (S scanT n s ) %Find potential scan period starts start_idx = max_idx[find(max_idx==min_idx[1] 1)] %Locate index of scan start Since our goal is to interpolate the scanner wedge positions for each shot time, we then determine which A -wedge rotational period corresponds to each shot (i.e. which A -wedge time tags are representative of each shot) for ( M i i i i ;1 ; 2 ) %For each shot in the data set if{ S scanT i s 1 ] 1 [ }&{ m T i sS ] [ } %Check if this shot is a reset numResets = numResets + 1 %Increment period counter endif k_ value[i]=numResets %Store period index for this shot endfor The B -wedge time data must also be aligned to the shot times so that the B -wedge angular position can be interpolated This is accomplished by synchronizing the B -wedge rotational periods with the A -wedge indices.

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133 for ( N i i i i ; 1 ; 2 ) %For each wedge index time in the data set idxB = max(find( ] [ i t tA B )) %Locate the last -occurring B -index ] [ ] [,idxB d i TB sync B %Store the B -wedge period for this A -index ] [ ] [,idxB t i tB sync B %Store the last Bwedge index time for this Aindex endfor Assuming constant angular velocity of the optical wedges within the current rotational period, we interpolate the wedge positions for each shot. The A -wedge angular displacement since t he previous A -wedge index in radians, is given by Equation A 10. A 10) n value k d n s s n AA_ 4 2 With the optical encoder for the inner wedge positioned at 320 degrees (as measured in the plane of the sensor window) the angular position of the A -wedge is then given by Equation A 11. A 11) 180 320 n A nA Likewise, with the optical encoder for the outer wedge at 220 degrees, the angular position of the B-wedge is given by Equation A 12. A 12) n s s n val k t n val k t n val k T nsync B A sync B B 4 2180 220, Projection of the propagation vectors through the optical scanner and into geo referenced coordinates closely follows the procedure detailed in Chapter 2. Analysis Because of the high variability inherent in LSNR lidar results (due to shot noise), data sets were typically analyzed over a collection of at least 10000 shots (1.2 seconds of data) In

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134 general, h istograms of the ensemble data were manually observed to locate the appropriate span of range bins corresponding to the target signal. Whe n appropriate, s ignal strength was estimat ed based on the underlying Poisson statistics If the probability 0P of a channel registering no returns for a given shot can be estimated, then the signal strength estimate is given by Equation A 13. A 1 3 ) ) log( 0P ns 0P can be calculated by determining the proportion of shots which result in no signal events. Note that a MLE estimator of the signal strength, based on the ensemble number of registered signal events, is inappropriate due to the effects of receiver dead time and range bin quantization. Field Testing Scanner Motion and Processing Correct operation of the scanner and processing software was verified in February 2008. Accurate reconstruction of a building face 320 m from the sensor was de monstrated using horizontal and rosette scan s (Figure A 8) Verification was repeated in August 2008, providing a detailed reconstruction of a building face and surrounding elements through occluding vegetation at nominal range (Figure A 9) Channel Orientation Orientation of the transmitted channel pattern was verified in May 2008 by constructing a 12 x 12 wood target, positioning the target 550 m away from the sensor and recording data with the footprint positioned at a known bearing (e.g. only lower half of the diamond footprint positioned on the panels, with the top half aimed off into the sky) (Figure A -10) Channel orientation generally agreed with previous laboratory observations However systematic

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135 inconsistencies between observed and predicted results were indicative of an optical misalignment in the CATS system (Figure A 11) Optical misalignment in the receive path has been confirmed by further testing; in an October 2008 experiment the center four beamlets were aimed at a highly reflective target, with the surrounding channels distributed on a low reflectivity surface at a different distance from the sensor Histograms of the ensemble registered returns from the target surface showed the returns to be displaced by approximately 2 rows in t he vertical (Figure A 12). Range Accuracy Range accuracy was tested i n February 2008 by comparing data retrieved using ILRIS a commercial ground -based lidar, and data retrieved from CATS. Dimensions of the building shown in Figure A 8 were calculated bas ed on the resulting point clouds (Figure A 13). Measurement results were favorable, with a typical error margin of less than 0.5 m. Detector Sensitivity Initial testing of the CATS prototype was done using a maximum applied detector voltage of 2300 V. Te chnical specifications for the installed PMT indicate that this region of operation corresponds to multi -photon detection; application of 2500 V is necessary for single photon detection. Field testing done in February 2009 verified that operation at 2500 V drastically increased detector sensitivity (Figure A 14) and result ed in detection of single photon events, namely atmospheric scatter and water column backscatter (Figure A 15) Water Penetration The ability of CATS to penetrate shallow water was test ed in February 2009. Since the ground -based setup required for field testing introduces significant performance degradation (e.g. high scintillation due to a horizontal propagation path near the earths surface, transmission loss from the turning mirror etc. ), extracted performance estimates likely underestimate airborne

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136 operation. The investigated target was a 55 gallon oil drum, with concrete positioned on the bottom to act as a practical reflecting surface (Figure A 16) A 3 by 3 turning mirror suspended above the barrel was used to point the central four beamlets into the water Ranging through 60 cm of pure water (Figure A 17) resulted in, on average, 97% of beamlets registering one or more signal events. Extrapolating these results to a depth o f 5 m CATS can be expected to register one or more signal events in 90% of incident beamlets. Likewise, for coastal water retrieved from Cedar Key, FL (Figure A 18) on average 12% of beamlets registered one or more signal events at a depth of 50 cm. Al though practical performance will largely depend on water turbidity, CATS can be expected to retrieve sufficient returns from the bottom surface to enable meter -scale bathymetric mapping at shallow depths (2 to 5 m) Return Signal Stability Field tests to estimate the signal strength as a function of water depth indicated that event statistics are not consistent and fluctuate in the short term (i.e. within a single experimental trial) During a single 10-second test, with the central four channels aimed at a uniform black wood surface, signal strength was observed to vary by up to 50% (Figure A 1 9 ). The observed variation exceeds that expected due to shot noise and scintillation. Beam Polarization Polarization of the transmitted laser was investigated usin g gray polarization film (greater than 99% polarization efficiency, 25% transmission) placed in the propagation path. As expected, the transmitted beam was observed to be linearly polarized (Figure A 20). The turning mirror did not significantly affect t he beam polarization. Laser light reflections off various surfaces was found to be largely diffuse (nonpolarized light); only specular returns (e.g. off metal) largely preserved the linear polarization.

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137 Outstanding Issues Although CATS ground -based field testing has been largely successful, a number of outstanding issues remain. The previously discussed issues in the recorded data can generally be mitigated through processing software. The observed optical misalignment requires calibration in an optical laboratory. Data from receiver board 1 has generally been observed to be more consistent and reliable than data from the other receiver boards. R eceiver board 2 has been shown to malfunction in inclement weather (Figure A 2 1 ); at low temperatures (40 d eg Celsius), channels on board 2 no longer recorded valid returns while board 1 continue d correct operation. Airborne testing of the CATS prototype is planned for summer 2009. Night time testing over shallow water will potentially confirm the practical ap plicability of the LSNR lidar concept to near -shore bathymetry. Fig. A 1. Schematic showing the conceptual design of the CATS sensor head.

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138 Fig. A 2. Image of CATS hardware prototype. Fig. A 3. Receiver block diagram for n c hannels.

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139 Fig. A 4 Binary data structure of the event history file output by CATS. This structure is repeated for every shot in the data collection. Fig. A 5. Top down view of scanner with telescoping mounting cover remove d. Index mark, shown in red, is aligned with the thickest part of the optical wedge. The lower wedge is a mirror image of this representation. Encoder Index Mark Flight Direction 50

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140 Fig. A 6. Rotational period of one scanner optical wedge calculated for CATS field data (obtained August 2008). Scan period should be consistent throughout the test, at a value of approximately 0.05 s (20 Hz). Problems in the hardware implementation cause some optical encoder time entries to be missing from the output files, requiring correction in processing s oftware. Fig. A 7. Several errors corrupt the shot time tag entries in CATS data. The shot time tags are recorded using a quad -counter (i.e. an increment of 1 is equivalent to 4 microseconds) synchronized to reset on encoder detection of the A -wedge ind ex mark. The maximum shot time tag value therefore should be ~12000 (0.05 s / 4 s). Rollover and small -scale errors in the shot time tags must be corrected by processing software. Data shown was acquired in August 2008.

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141 Fig. A 8. (Top) Image of inves tigated building, 320 m away from sensor. (Bottom) Isometric view of reconstructed point cloud. Ten seconds of data are shown, acquired in February 2008 using a rosette scan and an applied PMT voltage of 2200 V.

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142 Fig. A 9. (Top) Image of investigated bu ilding, 550 m away from sensor. (Bottom) Topdown view of reconstructed point cloud. 30 seconds of data are shown, acquired in August 2008 using a rosette scan and applied PMT voltage of 2200 V. Fig. A 10. CATS footprint centered on 12 x 12 painted wo od target. Sensor was located approximately 550 m away.

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143 Fig. A 11. Histogram of hits for each channel. The CATS footprint was positioned such that only the top half was distributed on the wood target. Data shown was acquired in May 2008. Fig. A 12. With the central four beamlets positioned on a target of high reflectivity (white painted metal), channels 14, 15, 22, and 23 registered a high number of returns from the target surface. The red box indicates correct optical alignment.

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144 Fig. A 13. Me asured building dimensions, using CATS (left) and ILRIS (right) point cloud data. CATS data was recorded at a PMT voltage of 2200 V, using a rosette scan. Length measurements were generally within 0.5 m. 0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 8 x 104 ChannelNumber of EventsCalibration Test: Signal Strength, Dry Sand, RB 5130-5140, 10k shots 2300V 2400V 2500V Fig. A 14. Number of recorded signal events, at three PMT voltage settings: 2300V (blue), 2400V (green), and 2500V (red). The center four channels in the footprint were aimed at dry sand. Data shown is for 10000 shots, acquired in February 2009.

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145 2300 2400 2500 0 1000 2000 3000 4000 5000 6000 7000 Voltage on PMTNumber of EventsAtmospheric Test: Total Accumulated Events Through Duration of Gate (all chans, 8us, 10k shots) Fig. A 15. Total number of atmospheric scatter events at three PMT voltage settings: 2300V (left), 2400V(center), and 2500V (right). Data shown is for 10000 shots, acquired in February 2009.

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146 Fig. A 16. Target configuration for ground -based CATS water penetration evaluation. The CATS footprint is clearly visible on the black cardboard mask (used for orientation and calibration purposes) and surrounding elements. The green barrel is approximately 1 m tall and holds 55 gallons of water. Fig. A 17. Pure water was used to test CATS penetration through wate rs of high clarity. The bottom surface (white painted metal) is clearly visible to the human eye with the barrel completely full (about 1 m deep). Turbidity of the water was measured to be 0.4 NTU.

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147 Fig. A 18. Sea water retrieved from Cedar Key FL was u sed to test CATS penetration through waters of high turbidity. The bottom surface (white painted metal) is not visible to the human eye with the barrel completely full (about 1 m deep). Turbidity of the water was measured to be 3.4 NTU. Fig. A 19. Sign al strength over a 10 second data set, using a 10000 shot window to estimate the necessary statistics. The four central channels were reflected off the turning mirror onto an extensive wood panel painted black. Although some variation is expected in esti mated signal strength due to shot noise and other phenomenological effects, the high variability observed here is indicative of a systematic issue. Data shown was acquired in February 2009.

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148 Fig. A 20. CATS beamlets incident on white painted wood. (Left ) Reflection without polarization film. (Center) Polarization film placed in propagation path, with transmission axis oriented perpendicular to laser polarization direction. (Right) Polarization film with transmission axis oriented parallel to laser polar ization direction. The film transmission is 25%, with greater than 99% polarization efficiency. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 40 60 80 100 120 Shot NumberTotal Hits Per Shot in Chans 1-16Moving Sum Window of Hits Per Shot on Ranging Board 1 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 40 60 80 100 120 140 Shot NumberTotal Hits Per Shot in Chans 17-32Moving Sum Window of Hits Per Shot on Ranging Board 2 Fig. A 2 1 Moving sum window of hits per shot, as a function of shot number. High shot to -shot variability is indicative of normal operation. Due to temper ature, channels on receiver board 2 malfunctioned and began reporting erroneous returns mid-way through the experimental trial. Data shown was acquired in February 2009.

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149 LIST OF REFERENCES 1 W. M. Kaula, G. Schubert, and R. E. Lingenfelter, Apollo laser al timetry and inferences as to lunar structure, Proceedings of the Fifth Lunar Conference vol. 3, pp. 30493058, 1974. 2 K. C. Slatton, S. Cheung, and H. Jhee, "ReducedComplexity Fusion of Multiscale Topography and Bathymetry Data over the Florida Coast", IEEE Geoscience and Remote Sensing Letters ,vol. 2, no. 4, pp. 389 393, Oct 2005. 3 J. L. Irish and W. J. Lillycrop, Scanning laser mapping of the coastal zone: the SHOALS system, ISPRS Journal of Photogrammetry and Remote Sensing, vol. 54, pp. 123129, 1999. 4 J. E. Means, et al, Use of large -footprint scanning airborne lidar to estimate forest stand characteristics in the western cascades of Oregon, Remote Sensing Environ. vol. 67, pp. 298308, 1999. 5 H. J. Zwally, et al, ICESats laser measurements over polar ice, atmosphere, ocean, and land, Journal of Geodynamics, vol. 34, pp. 405445, 2002. 6 B. Long, A. Cottin, and A. Collin, What Optechs bathymetric lidar sees underwater, Geoscience and Remote Sensing Symposium, 2007. IGARSS 2007. IEEE International pp.31703173, 2007. 7 D. Harding, et al, The Swath Imaging Multi Polarization Photon -counting Lidar (SIMPL): An innovative laser altimeter for mapping ice, water, land and forest cover, Geophysical Research Abstracts European Geosciences Union, vo l. 9, 2007. 8 J. B. Abshire, et al, Pushbroom Laser Altimetry using Fiber Lasers and Photon Counting Detectors, Lasers and Electro -Optics, 2007. CLEO 2007. Conference on pp.1 2, 6 11 2007. 9 R. Dubayah et al, Land surface characterization using lidar remo te sensing, Spatial Information for Land Use Management Hill MJ, Singapore: International Publishers Direct, pp. 25 38, 2000. 10. D. Harding, "Pulsed Laser Altimeter Ranging Techniques and Implications for Terrain Mapping", in Topographic Laser Ranging and Scanning: Principles and Processing, J. Shan and C. Toth, eds., CRC Press, Taylor & Francis Group, 2008. 11. J. Degnan, Photon -counting multikilohertz micro -laser altimeters for airborne and spaceborne topographic measurements, Journal of Geodynamics, vol. 34, pp. 503549, 2002. 12. K. Clint Slatton, William E. Carter, Ramesh L. Shrestha, William Dietrich, Airborne Laser Swath Mapping: Achieving the resolution and accuracy required for geosurficial research, Geophys. Res. Lett ., vol. 34, 2007.

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150 13. J. Degnan and J. McGarry, SLR2000: Eyesafe and autonomous single photoelectron satellite laser ranging at kilohertz rates, SPIE, vol. 3218, pp. 6377, 1997. 14. M. Vaidyanathan, et al, Jigsaw phase III: a miniaturized airborne 3 D imaging laser radar with photon -counting se nsitivity for foliage penetration, Laser Radar Technology and Applications XII vol. 6550, pp. 65500N, 2007. 15. K. L. Albright, et. al, RULLI: A photon counting imager, International Advanced Studies Institute (IASI) Symposium on Detection and Analysis of Sub -surface Objects and Phenomena 1998. 16. J. Degnan, et. al, Design and performance of an airborne multikilohertz microlaser altimeter, International Archives of Photogrammetry and Remote Sensing, vol. XXXIV3/W4, Annapolis, MD, pp. 9 16, 2001. 17. W. E. Car ter, R. L. Shrestha, and K.C. Slatton, Photon counting airborne laser swath mapping (PC -ALSM), IAG International Association of Geodesy Symposia: Gravity, Geoid, and Space Missions vol. 129, pp. 214 217, 2004. 18. T. Cossio, K. C. Slatton, W. E. Carter, K. Shrestha, and D. Harding, Predicting t opographic and b athymetric m easurement p erformance for l ow -SNR a irborne l idar, IEEE Transactions on Geoscience and Remote Sensing, accepted for publication 19. T. Cossio, K. C. Slatton, W. E. Carter, and K. Shrestha, P redicting small target detection performance of low SNR airborne l idar submitted for review. 20. Y. M. Govaerts and M.M. Verstraete, Raytran: A Monte Carlo ray tracing model to compute light scattering in three -dimensional heterogeneous media IEEE Transac tions on Geosciences and Remote Sensing, vol. 36, no. 2, 1998. 21. A. I. Borisenko and I. E. Tarapov, Vector and Tensor Analysis with Applications Dover, 1968. 22. G. Fuller, Analytic Geometry 5th ed., Addison Wesley, 1980. 23. D. Sunday, Intersection of Rays/Seg ments with Triangles softSurfer.com, http://www.softsurfer.com/Archive/algorithm_0105/algorithm_0105.htm#References 2001. 24. C. S. Gardner, Target signatures fo r laser altimeters: an analysis, Applied Optics vol. 21, pp. 448453, 1982. 25. A. Chepurnov, F. Nede oglo, A. Etenko, and A. Sabelnikov, Application of software and hardware components of can technology for accelerator control, Problems of Atomic Science a nd Technology Nuclear Physics Investigations, vol. 43, pp. 75 77, 2004. 26. J W Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomenon, J. C. Dainty, Ed., Springer -Verlag, 1975.

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151 27. E. P. MacKerrow and M. J. Schmitt Measurement of integrated speckle statistics for CO2 lidar returns from a moving, nonuniform, hard target, Applied Optics vol. 36, no. 27, pp. 69216937. 28. Z. Liu, W. Hunt, M. Vaughan, C. Hostetler, M. McGill, K. Powell, D. Winker, and Y. Hu, Estimatin g random errors due to shot noise in backscatter lidar observations, Applied Optics, vol. 45, pp. 44374447, 2006. 29. R. R. Beland, Propagation through atmospheric optical turbulence, in The Infrared and Electro -Optical Systems Handbook F. G. Smith, Ed. ( SPIE Optical Engineering Press, Bellinghan, WA), vol. 2. ch. 2, 1993. 30. R. E. Hufnagel, Propagation Through Atmospheric Turbulence, in The Infrared Handbook W. L. Wolfe and G. J. Zissis, Eds. (U.S. GPO, Washington D.C.), ch. 6, 1978. 31. D. L. Fried, Apertur e Averaging of Scintillation, Journal of the Optical Society of America vol. 57, no. 2, 1967. 32. G. H. Suits Natural Sources in The Infrared Handbook W. L. Wolfe and G. J. Zissis, Eds. (U.S. GPO, Washington D.C.), ch. 3, 1978. 33. R. Levinson, P. Berdahl, and H. Akbari, Solar spectral optical properties of pigments Part I: model for deriving scattering and absorption coefficients from transmittance and reflectance measurements, Solar Energy Materials and Solar Cells vol. 89, no. 4, pp. 319349, 2005. 34. G. Guenther and R. Thomas, System design and performance factors for airborne laser hydrography, OCEANS vol. 15, pp. 425430, 1983. 35. P. Koepke, Effective reflectance of oceanic whitecap s, Applied Optics, vol. 23, pp. 18161824, 1984. 36. E. C. Monahan and G. MacNiocaill, Whitecaps and the passive remote sensing of the ocean surface, Int. J. Remote Sensing, vol. 7, pp. 627642, 1986. 37. C. H. Whitlock, D. S. Bartlett and E. A. Gurganus, Sea Foam Reflectance and Influence on Optimum Wavelength for Remote Sensing of Ocean Aerosols, Geophys. Res. Lett. vol. 9, p. 719, 1982. 38. J. L. Bufton, F. E. Hoge, and R. N. Swift, Airborne measurements of laser backscatter from the ocean surface, Applied O ptics, vol. 22, pp. 26032618, 1983. 39. C. Cox and W. Munk, Measurements of the roughness of the sea surface from the suns glitter, J. Opt. Soc. Am., 1954. 40. J. Wu, Phys Fluids vol. 5, p. 741, 1972.

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152 41. B. M. Tsai and C. S. Gardner, Remote sensing of sea state using laser altimeters, Applied Optics vol. 21, pp. 39323940, 1982. 42. C. Mobley, Light and Water: Radiative Transfer in Natural Waters, Academic Press Inc., 1994. 43. T. J. Petzold, Volume scattering functions for selected ocean waters, SIO Ref. 72 78, Scr ipps Inst. Oceanogr., LaJolla, pp. 79, 1972. 44. W. H. Wells, Theory of small angle scattering, NATO Publication AGARD -LS -61, 1973. 45. H. R. Gordon, Interpretation of airborne oceanic lidar: effects of multiple scattering, Applied Optics, vol. 21, pp. 29963 001, 1982. 46. R. Duda, P. Hart, and D. Stork, Pattern Classification Wiley, pp. 124128, 2001. 47. T. Kailath, The divergence and Bhattacharyya distance measures in signal selection, IEEE Transactions on Communication Technology vol. com 15, no. 1, 1967. 48. B. M ak and E. Bernard, Phone clustering using the Bhattacharyya distance, in ICSLP96, The Fourth International Conference on Spoken Language Processing, vol. 4, 1996. 49. G. Guenther, L. Goodman, D. Enabnit, R. Swift, and R. Thomas, Laser bathymetry for near -s hore charting applications, IEEE Oceans vol. 10, pp. 390396, 1978. 50. S. Peeri and W. Philpot, Increasing the existence of very shallow -water lidar measurements using the red -channel waveforms, IEEE Transactions on Geosciences and Remote Sensing, vol. 4 5, no. 5, 2007. 51. K. C. Slatton, W. E. Carter, and R. Shrestha, A simulator for airborne laser swath mapping via photon counting, Proc. SPIE, vol. 5794, no. 12, 2005. 52. G. Sithole and G. Vosselman, Comparison of filtering algorithms, Proceedings of the ISPRS Working Group III/3 Workshop: 3 D Reconstruction from Airborne Laserscanner and InSAR data October, Dresden, Germany, 2003. 53. J. Degnan, Unified approach to photon -counting microlaser rangers, transponders, and altimeters, Surveys in Geophysics vol. 2 2, pp. 431447, 2002. 54. P. Yang, D. P. Myers, G. Li, and G. M. Hieftjet, Constant -fraction discrimination/boxcar integrator for plasma source time of -flight mass spectrometry, Applied Spectroscopy, vol. 49, no. 5, pp. 660664, 1995. 55. G. C. Guenther, A. C. Cunningham, P. E. LaRocque, and D. J. Reid, Meeting the accuracy challenge in airborne lidar bathymetry, Proceedings of EARSeL -SIG Workshop LIDAR Dresden/FRG, 2000.

PAGE 153

153 56. W. Cheng, W. S. Lu, and A. Antoniou, Efficient waveform composition on airborne laser b athymetry, IEEE Proceeding on Communications, Computers, and Signal Processing 1995. 57. W. Wagner, A. Ullrich, V. Ducic, T. Melzer and N. Studnicka, Gaussian decomposition and calibration of a novel small -footprint full -waveform digitising airborne laser s canner, ISPRS Journal of Photogrammetry and Remote Sensing, vol. 60, no. 2, pp. 100112, 2006. 58. M. Herold, D. A. Roberts, M. A. Gardner, and P. E. Dennison, Spectrometry for urban area remote sensing development and analysis of a spectral library from 350 to 2400 nm, Remote Sensing of Environment vol. 91, pp. 304319, 2004. 59. N. P. Lavery, Mathematical framework for predicting solar thermal build up of spectrally selective coatings at the Earths surface, Applied Mathematical Modelling vol. 31, pp. 16351651, 2007. 60. T. Fawcett, An introduction to ROC analysis, Pattern Recognition Letters vol. 27, pp. 861874, 2006. 61. G. C. Guenther, T. J. Eisler, J. L. Riley, and S. W. Perez, Obstruction detection and data decimation for airborne laser hydrography, Pro c. Canadian Hydro. Conf. pp. 51 63, 1996. 62. J. E. Kalshoven Jr. and P. W. Dabney, Remote sensing of the Earths surface with an airborne polarized laser, IEEE Transactions on Geoscience and Remote Sensing, vol. 31, no. 2, pp. 438446, 1993. 63. G. Lewis, D. Jordan, and P. Roberts, Backscattering target detection in a turbid medium by polarization discrimination, Applied Optics, vol. 38, no. 18, pp. 3937, 3944, 1999. 64. D. Harding, J. Abshire, P. Dabney, A. Seas, C. Shuman, X. Sun, S. Valett, A. Vasilyev, T. Yu T. Huss, J. Marzouk, and Y. Zheng, The Swath Imaging Multi -polarization Photon -counting Lidar (SIMPL): a spaceflight prototype, Geoscience and Remote Sensing Symposium, 2008. IGARSS 2008. IEEE International.

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154 BIOGRAPHICAL SKETCH Tristan Cossio is a Ph D. student in the Department of Electrical and Computer Engineering at the University of Florida. He is a member of the Adaptive Signal Processing Lab under Dr. K. Clint Slatton. He is in his third year of a Graduate Student Researchers Program fellows hip sponsored by David Harding at NASA Goddard Space Flight Center. Tristan completed his undergraduate work at the University of Florida in May 2004, receiving a Bachelor of Science in e lectrical e ngineering. He received his Master of Science in e lectric al e ngineering from the University of Florida in May 2006.