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DESIGN AND CHARACTERIZATION OF AN INTENSITY
MODULATED OPTICAL MEMS MICROPHONE
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA
I wish to give my love and gratitude to my friends and family for all the love and
support I have received during the many years of my college career. I would never have
succeeded to the extent that I have without them. I especially appreciate the love and
support from my fiancee, Ms. Lisa Sewell, and for her ability to see through my
"preoccupied graduate student" exterior and find that which lies beneath.
I would also like to express my gratitude to my advisor, Dr. Toshikazu Nishida,
for recruiting me into IMG and giving me the educational tools and support needed to
complete a difficult project. Thanks also go to Dr. Mark Sheplak, Dr. Lou Cattafesta, and
Dr. Peter Zory for the excellent work they have done in teaching the classes that provided
the foundation for my research, and also for their guidance during the process. I also
wish to thank my friends and colleagues in the Interdisciplinary Microsystems Group
who have provided support. Special thanks go to Karthik Kadirval for his support in the
beginning of my work on the optical microphone project, and to Stephen Horowitz and
Robert Taylor for timely assistance when I needed it.
Financial support for this project is provided by DARPA (Grant #DAAD19-00-1-
0002) through the Center for Materials in Sensors and Actuators (MINSA) and is
monitored by Dr. Paul Holloway.
TABLE OF CONTENTS
A C K N O W L E D G E M E N T S ............................................................................................... iii
A B STRA C T ............... ....................................... .............. ................. x
1 INTRODUCTION ...... .............................. ............ ........ 1
1.1. Optical M icrophone Transduction Schemes....................... ............................. 1
1.1.1. Intensity M odulation ................ ................................ .... .. .. ...... 2
1.1.2. Polarization M odulation............................................. ........................... 5
1.1.3. Phase M odulation. ............................ ..... .. ... ............. .. .. ................ 6
1.1.4. Suitability of Transduction Techniques for MEMS Implementation ............... 9
1.2. M icrophone Structure .. ...... ................................................. .............. 12
1.2.1. Overview ......................................... ............ 12
1.2.2. M EM S Chip .................. .......................................... .......... 14
1.2.3. O optical Fibers ................................................. ......................... ....... 15
1.2.4. L eight Source .......................................................................... 18
1.2 .5 D election E electronics ........................................................................... .... 18
2 MICROPHONE SYSTEM PARTITIONING AND PERFORMANCE METRICS... 21
2 .1. Sy stem P partition in g ........................... .......................................... .................. 2 1
2.1.1. A cousto-M mechanical Stage ........................................ .................. ...... 21
2 .1.2 M echano-O ptical Stage............................................................................ ... 2 1
2 .1.3 O pto-E electrical Stage ........................................................................... .... 22
2.2. System Perform ance M etrics ........................................................ ......... ..... 22
2.2.1. System Sensitivity. ............................................. .. ............. .............. .. 23
2.2.2. System Linearity ...... .............................................................. 39
2.2.3. System Frequency R esponse................................ ............... ... ................. 44
2.2.4. System Electronic N oise ........................................................... ......... .... 46
2.2.5. System M minimum Detectable Signal ....................................... ........... ... 51
2.2.6. Optical Reference Path Losses and System Performance Metrics ............... 55
2.2.7. Summary of Predicted System Performance ............................................... 57
3 DESIGN OF THE OPTICS FOR THE MEMS OPTICAL MICROPHONE ............ 59
3 .1. Selection of th e O ptics ................................................................. ................ .. 59
3.1.1. Perform ance ....................................................... ............ ... 59
3.1.2. System Connectivity ................... ................ ......... .............. 61
3.1.3. Ease of Handling and Manufacturability ................................................... 61
3 .1 .4 C o st ................................................................................................. 6 2
3 .2 Selection of the T ubing ................................................................................. 63
3.3. Alignm ent Issues. .................................................... ............... 64
3.3.1. M EM S Chip Cavity A lignm ent issues.................................. .................... 64
3.3.2. Fiber Bundle G eom etry Issues.................................................... ................. 67
3.3.3. Application of Alignment Theory to Fiber Bundle Selection........................ 68
4 FABRICATION OF THE OPTICAL MICROPHONE ......................................... 70
4.1. M E M S E change P rocess............................................................ .................... 70
4.2. Packaging Process................... .......... .................... ...................... .. ................ 71
5 EXPERIMENTAL SETUP AND RESULTS................. ................. 79
5.1. Laser and Photodetector Characterization........................................................... 80
5.1.1. Experimental Setup for Laser and Photodetector Characterization.............. 80
5.1.2. Results of Laser and Photodetector Characterization.................................... 81
5.2. Static C alibration .............. ...... ..... ................... .............. 81
5.2.1. Experimental setup for static calibration ............................................. .. 81
5.2.2. R results of static calibration ........................................................... ... ......... 84
5.3. Dynam ic Calibration........ ... ..................... .................. .............. 87
5.3.1. Experimental setup for dynamic calibration ............................................. 87
5.3.2. Results of the dynamic calibration......................................... ............. 90
6 CONCLUSIONS AND FUTURE WORK ......................................................... 99
6 .1. C o n clu sio n s...................................................... ............... 9 9
6.2. Future W ork ..................................... .............................. .......... 100
A MEMS OPTICAL MICROPHONE DIAPHRAGM PROCESS FLOW.................. 102
B FIBER BUNDLE PROCESS FLOW ................................................. 105
C M ECH AN ICAL D R A W IN G S........................................................ .... .. .............. 117
D PHOTODETECTOR SPECIFICATIONS.......................... .......... .... 118
E SPECIFICATIONS FOR POPPER & SONS STEEL TUBING ........................... 119
L IST O F R E F E R E N C E S ......... ............... .................................................................. 120
B IO G R A PH IC A L SK E T C H ........................................ ............................................124
LIST OF TABLES
1-1 Summary of Intensity-Modulated Optical Microphone Designs ............................ 10
1-2 Summary of Phase Modulated Optical Microphone Designs ............................... 11
2-1 Acousto-Mechanical Lumped Element Parameters ............................................ 45
2-2 Summary of Configuration Settings for Theoretical Performance Metrics ............ 57
2-3 Summary of Theoretical System Performance Metrics.................................... 58
3-1 Error Analysis of Different Fiber Bundle Configurations..................................... 69
4-1 Wafers Used for Optical Microphone Fabrication ............................................... 70
5-1 Experim ental H P 8168B N oise....................................................... ... ................. 81
5-2 Comparison between Theoretical and Experimental Static Calibration................ 86
5-3 Experimental Results of Unreferenced Output Microphone Dynamic Calibration 98
5-4 Experimental Results of Referenced Output Microphone Dynamic Calibration.... 98
LIST OF FIGURES
1-1 Optical Microphone Classification Based on Transduction Mechanism ............. 2
1-2 Radiated Wave Intensity-modulating Microphone Types.................................... 3
1-3 Evanescent Wave Intensity-modulating Microphone Types.................................. 4
1-4 Polarization M odulating M icrophone Types.................................. .................. ... 6
1-5 Grating-Type Phase Modulating Microphone Types......................................... 7
1-6 Interferometric Phase M odulating M icrophone Types.............................................. 8
1-7 Block Diagram of the Optical Microphone. ......................... ...................... 13
1-8 Cross Section of the Fiber Bundle in the MEMS Chip. .......................................... 14
1-9 Cross Section of the MEMS Chip. .............................................. ................ 15
1-10 End View of the Optical Fiber Bundle. ............... .............................. 16
1-11 Optical Fibers in Steel Tubing.................................................................. 16
1-12 Optical Fiber Bundle Drawing. ........................................ ......................... 17
2-1 Side View of Deflecting Plate or Membrane.................................. 24
2-2- Method of Images (View from Side of Fiber Bundle). ................... ................. 27
2-3 R ing A pproxim ation D iagram ................................................................................ 30
2-4 Theoretical Power Coupled with Ideal Fiber Configuration. ................................. 32
2-5 Theoretical Sensitivity with Ideal Fiber Configuration .............. .............. 32
2-6 Block Diagram of the Unreferenced Output Configuration. ............. ................ 34
2-7 Equivalent Circuit for the PDA400 Photodetector ............................................... 35
2-8 Block Diagram of the Referenced Output Configuration................. .......... 36
2-9 Comparison of Unreferenced and Referenced Output Sensitivities..................... 39
2-10 Linearity of Mechano-Optical Stage. ............................... ....................... 41
2-11 -Plot of Acousto-Mechanical Sensitivity as a Function of Radial Position............ 42
2-12 Noise Contributions for the Photodetector Output......................................... 46
2-13 Noise Contributions for the Microphone Output ............................................ 48
2-14 Illustration of the Physics Behind the MO MDS............................................. 53
3-1 Bundle Position Error Illustration. ........................................ ...................... 65
3-2 Angular Misalignment Error Illustration........ ............ ...................... 66
3-3 Radial Position Error Illustration ............................................... 67
4-1 Abeysinghe et al. Packaging Technique............ ............................. .............. 71
4-2 Beggans et al. Packaging Technique. ...................................................... 73
4-3 Kadirval Packaging Technique................ ........... ................. ...... ..... ......... 74
4-4 Proposed Package for the Optical Microphone. .............................................. 76
4-5 Proposed Optical Microphone Array Package. ..................................... ........ .. 77
5-1 Experimental Setup for Laser Characterization...................... .... .............. 80
5-2 Block Diagram of Static Calibration. ...................................................... 84
5-3 Experimental Power Coupled vs. Equilibrium Gap. ............................................. 85
5-4 Experimental Maximum Power Coupled Regression Line Slope .......................... 86
5-5 Unreferenced Output Optical Microphone Configuration...................................... 88
5-6 Referenced Output Optical Microphone Configuration .................................... 89
5-7 Linearity, Unreferenced Output Configuration. .............................................. 91
5-8 Linearity, Referenced Microphone Configuration. .............................................. 92
5-9 Magnitude Response, Unreferenced Microphone Configuration............................ 93
5-10 Magnitude Response, Referenced Microphone Configuration. ......................... 94
5-11 Phase Response, Unreferenced Microphone Configuration............................. 94
5-12 Phase Response, Referenced Microphone Configuration. ................................... 95
5-13 Electrical Noise Floor, Both Microphone Configurations.............. ........... 97
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering
DESIGN AND CHARACTERIZATION OF AN INTENSITY
MODULATED OPTICAL MEMS MICROPHONE
Chairman: Toshikazu Nishida
Major Department: Electrical and Computer Engineering
This thesis presents the design and characterization of an intensity-modulated
optical lever microphone. Microphone noise models from previous works are expanded
to include the light source and all electronics. Physical phenomena responsible for
limiting the microphone minimum detectable signal (MDS) are identified, and an
accurate model developed for use with an LED or laser light source. The sensitivity,
minimum detectable signal, and electronics noise are characterized by a scaling analysis
in which coupled equations for dependence on optical power, membrane radius,
photodetector gain, and optical losses in the reference path are presented. It was
discovered that, in this optical microphone geometry, the laser is the limiting factor in the
microphone MDS and electronics noise, and optical losses in the reference path can
improve microphone sensitivity, MDS, and noise floor for a referenced optical
An unreferenced electronic configuration and a referenced electronic
configuration were experimentally characterized using a laser as a light source. The
unreferenced optical microphone achieved a sensitivity of 0.032 mV / Pa, MDS of 65 dB
(re. 20 [tPa), and dynamic range from 65 122 dB (re. 20 tpPa). The referenced optical
microphone achieved a sensitivity of 1.77 mV / Pa, MDS of 47 dB (re. 20 [tPa), and
dynamic range from 47 122 dB (re. 20 [tPa). Both unreferenced and referenced
measurements were made at 1600 Hz with a bin width of 2 Hz.
Optical microphones vary widely in their construction, but all possess innate
resistance to electro-magnetic interference (EMI) and other harsh environments to which
other types of microphones are sensitive. This innate resistance is derived from the
separation of the optical sensing element from the electronics via optical fibers and
assumes the electronics are remotely located with respect to the test environment. In the
case where the electronics are not remotely located, the microphone package must isolate
the microphone electronics from the test environment.
MEMS technology provides a promising new implementation for optical
microphones. MEMS devices have the capability to be smaller than conventional
microphones, and MEMS microphone chips could be processed by the thousand on
wafers if the market can support this volume. Despite these advantages, Professor Steve
Senturia  notes that MEMS devices have a coupling between the package and the
device, thus requiring them to be designed concurrently, which makes a MEMS
microphone design inherently more complicated than a conventional (non-MEMS)
1.1. Optical Microphone Transduction Schemes
In 1996, Nykolai Bilaniuk first introduced a classification scheme for optical
microphones that relied on the transduction mechanism as the primary sorting criterion
. He also explained the methods of operation of multiple types of devices in each
category, with emphasis on the most promising technologies, and he also discussed
microphone system performance metrics.
Bilaniuk defined three properties of light that could be modulated: the intensity
(or irradiance), the phase, and the polarization . Since electro-optical detectors
respond to light intensity, all modulation schemes must be reduced to an intensity
modulation at the electronics end of the system. The figure below adapted from 
shows a detailed classification scheme for optical microphones.
Figure 1-1 Optical Microphone Classification Based on Transduction Mechanism .
1.1.1. Intensity Modulation
Bilaniuk  describes an intensity-modulated microphone as one which
selectively removes energy from the optical path. As shown in Figure 1-1, an intensity-
modulating optical microphone can be subdivided into two broad categories: radiated
wave and evanescent wave. All of the energy in radiated wave optical microphone leaves
a controlled optical path and partially recaptured or backscattered . Figure 1-2
recreates Bilaniuk's  illustration of the radiated wave transduction strategies.
Figure 1-2 Radiated Wave Intensity-modulating Microphone Types.
The moving grating approach relies on the motion of a "light gate" to modulate
the light coupled between an input waveguide and an output waveguide. These types of
devices do not make use of diffraction or any structures on the order of the wavelength of
An intensity-modulated lever microphone utilizes one or more waveguides to
deliver light to a vibrating plate or membrane. Reflected light is collected by one or more
waveguides and delivered to a photodetector. Lever microphones may also have
focusing optics to improve light collection.
In a cantilever microphone, the waveguide is discontinuous, and part is free to
vibrate in an acoustic field. This varies the alignment between the fixed segment and the
free segment of the waveguide, causing a modulation of the power coupled.
Macrobend-type intensity-modulating schemes use acoustic waves to deform a
fiber configuration, such as a coil. Optical fibers are chosen that do not completely
confine the light. The deformation modulates the losses in the length of fiber,
subsequently modulating the output power.
Alternatively, the evanescent-wave coupling methods "rely on ... mode coupling
or on absorption from the evanescent field" . Bilaniuk defines two classes of
evanescent wave intensity-modulating microphones: microbend and coupled waveguide.
Figure 1-3 recreates Bilaniuk's  illustration of the evanescent wave intensity
Figure 1-3 Evanescent Wave Intensity-modulating Microphone Types.
The microbend technique uses a microstructure to apply periodic deformations to
a waveguide. The acoustic field modulates the pressure exerted on the waveguide by
these deformations, which in turn causes leakage of power out of the waveguides.
The coupled waveguide technique can work in one of two different ways. In the
first way, the waveguides are fabricated on a membrane structure with a fixed separation
between the two. The membrane deflects in the presence of an acoustic field, and this
deflection changes the index of refraction in the two waveguides. The change in
refractive index modulates the power coupled between the waveguides. Alternately, the
waveguides are fabricated so that one is attached to a structure, while the other is free to
vibrate. An acoustic field will modulate the separation between the waveguides, which
modulates the power coupled between the two.
1.1.2. Polarization Modulation
The second major category of optical microphones as defined by Bilaniuk  is
polarization modulation. Polarization modulation type devices alter the polarization of
the light when in the presence of an acoustic field. Bilaniuk  subdivides polarization
modulation devices into two subcategories, but he notes that alternate schemes are
possible. Figure 1-4 adapted from  depicts the two subcategories.
In the first category, a layer of liquid crystals is subjected to acoustic field
induced shear stresses, which modulate the polarization of the light passing through. A
polarizer is located at the output of the device to isolate the desired polarization axis.
In the second category, "a moveable dielectric plate interacts with the evanescent
field of a waveguide excited with both TE and TM modes, causing a different change in
the refractive index of the two modes, according to Bilaniuk ". A polarizer at the
output isolates the desired polarization axis.
Nematic Liquid Crystal Differential Index Shifter
Figure 1-4 Polarization Modulating Microphone Types.
1.1.3. Phase Modulation
Phase modulated optical microphones are described by Bilaniuk  as a
mechanism that "changes either the physical length or the refractive index of an optical
test path and recombining the result with the signal from a reference path." The reference
path is unaffected by the acoustic field, while the test path undergoes some form of
mechanical deformation. The two defined subgroups for this category of optical
microphones are grating type devices and interferometric devices.
A grating type device is one with a structure machined onto a waveguide with
features on the order of the wavelength of the light. The two different subcategories of
grating devices defined by Bilaniuk  are input coupling gratings and dynamic
refractive gratings. They are shown in the following figure, adapted from Bilaniuk .
Dynamic Photorefractive Grating
Figure 1-5 Grating-Type Phase Modulating Microphone Types.
The input coupling grating device has a grating fabricated on the waveguide.
Incident light at the proper angle, wavelength and with the proper grating spacing will be
coupled into the waveguide. The acoustic field modulates a nearby dielectric structure,
varying the index of refraction of the system and modulating the output.
The dynamic photorefractive grating uses a prism to split light onto two mirrors,
one of which is free to vibrate in an acoustic field. The light reflects off the mirrors to
pass through a grating, and the light from each mirror is captured by a photodetector.
The light from the stationary mirror is used as a reference signal, while the light from the
vibrating mirror is used as the modulated signal.
The second major category of phase modulating optical microphones is
interferometric-type phase-modulating microphones. They typically use one of the three
most familiar types of interferometers: Fabry-Perot, Michelson, or Mach-Zehnder.
Alternately, a two-mode fiber can be used to make a phase modulated microphone. The
figure below (adapted from ) depicts the four interferometric optical microphone
Input Coupling Grating
Mach-Zehnder Two-Mode Fiber
Figure 1-6 Interferometric Phase Modulating Microphone Types.
The Fabry-Perot optical microphone uses an optical cavity formed between two
parallel surfaces. One of the surfaces is free to vibrate in an acoustic field, while the
other is fixed. Typically, the vibrating surface is a plate or membrane, and the fixed
reflecting surface is the face of the fiber, but additional optics may be used instead.
A Michelson optical microphone splits a free-space beam into two paths. The
reference path is reflected of a stationary reflector. The test path is reflected off of a
reflector that vibrates in an acoustic field. The beams recombine and interfere, and the
recombined signal is received by a photodetector.
In a Mach-Zehnder optical microphone, the light enters via a waveguide, which is
split into two paths. The reference path is held constant, but the test path is free to vibrate
in an acoustic field. The light in the two paths is recombined and sent to a photodetector.
Interference effects will modulate the power seen by the detector.
The fourth type of interference optical microphone is a two-mode fiber
microphone. In this design, a section of two-mode optical fiber is spliced at the end of a
single mode fiber. The two-mode fiber is free to vibrate in an acoustic field. Acoustic
vibrations will modulate the index of refraction of each mode differently, and an
interference pattern will be generated at the junction between the two fibers.
1.1.4. Suitability of Transduction Techniques for MEMS Implementation
In general, the simplest type of microphone to analyze and build is an intensity-
modulated device. The simplest intensity-modulated device can be constructed with an
LED, multimode or single mode fibers, a membrane or other vibrating reflective surface,
and a photodetector.
Table 1-1 (see  ) summarizes recent intensity-modulated optical
microphone designs. The results indicate a large variability in performance with the
implementation of the intensity-modulated microphone. While this observation may
seem obvious, it reinforces the importance of optimizing the system as a whole when
designing the microphone and not just an individual stage.
In general, for the intensity-modulated optical microphone, increasing the
diaphragm radius increases the sensitivity and decreases the minimum detectable signal
(MDS). Therefore, intensity-modulated microphone performance is decreased when the
diaphragm is constrained to have a diameter of less than a few hundred microns.
Table 1-1 Summary of Intensity-Modulated Optical Microphone Designs
Author / Year Design Type Source and ,X Sens Noise Freq Linearity MDS
20-22dB 0 20kH
V. P. Klimashin Lever, -w- Support Incandescent 7.5 mV Pa (re -w- 5dB
1979  Optics, non MEMS Lamp 0 fluctuatio
Hu and Cuomo Lever, -w- Mylar LED, 36.5 mV 0-31.5
1992  Membrane, Non 2.4mW Pa kHz
De Raula and Multiple Light 150 W Xenon 5.6 nW
Vinha Source non-MEMS Arc La Hz05
1992  scheme
Lukosz and Evanescent wave, 49 dB t -
Pliska microbend, 6x6 mm2 L6se, n= 0.31 Pa1 (re to 49 dB 95
632.8 nm 10kHz dB
1992  membrane 20pPa)
Suhadolnik, et Lever, fiber bundle to
al and deflecting speckle MO Stage
1995  diaphragm, non- pattern 1500 gm
Kadirvel Lever, fiber bundle 2 t 110 dB 1 kHz 110 dB 110 dB (re
2002  and deflecting 1550 nm Pa (re 6.4 kHz 135 dB 20 gtPa)
The choice of light source and photodetector also plays a large role in the
performance of an intensity-modulated OM. Both affect the device sensitivity and noise
floor. Sensitivity increases as coupled optical power increases, so high intensity light
sources provide higher sensitivities, provided that the photodetector does not saturate.
A disadvantage of all intensity-modulated OMs is the large DC component of the
received signal. The DC component does not contribute to the device sensitivity, but it
does contribute to photodetector saturation. This limits the product of the optical
received power and the detector trans-impedance gain. The maximum intensity of the
light source is limited by the linearity range and gain of the detector.
Table 1-2 (see  ) summarizes recent phase modulated optical microphone
(PM) designs. Since no standard method of reporting the sensitivity of an optical
microphone has been agreed upon, it is difficult to compare the overall performance of
different PM designs. Theoretically, a PM device would be able to provide higher
performance than an intensity-modulated microphone in a MEMS implementation,
especially for membranes constrained to be smaller than a few hundred microns in
diameter. PM devices have a smaller DC component allowing for more flexibility in
selecting photodetector gain settings.
Table 1-2 Summary of Phase Modulated Optical Microphone Designs
Source and Freq Linearity Reouto
Author / Year Design Type Source an Sens SNR Freq Linearity Resolution
o. Response Range
Rao et al. 1997 Bragg Grating w- 12 pm 50dB >kHz
 Fizeau Cavity = l5000ES
0.5mW Varies by Tested
Furstenau et al. t C (after pigtail) r over
1998  Fabry-PerotLED fwreq range B 100Hz to
,-=1300nm 41w34 15kHz
Du et al. 1999 LED @
De Fiber Bragg Grating L o 1.5 pm / E NA < 1200 +/- 29pE
Graywall 1999 Suace-machd LED @ 100Hz to
 Fabry-Perot Cavity, 650n 8.9 mV / Pa > 100 2kHz
__________ theoretical analysis _________ =m
Rao et al. 2000 Fiber Bragg Grating 54020mW
 and Fizeau Cavity o=1 50m
L o 1550nm
Fabry-Perot Cavity LED @ psi 0 -80 psi
Abeysinghe et machined on surface L 80 NA (0- 552
al. 2001  of optical fiber 850n (16 mV kPa)
Wang et al. Non-MEMS Fabry- LED @ 4 nm psi psi 0.02 psi
2001  Perot Cavity =850nm (0.58m NA (0 (1379 Pa)
Despite these advantages, PM microphones present some significant challenges.
The dimensions involved are on the order of tens of optical wavelengths, making static
characterization and packaging very difficult. PM microphones are much more sensitive
to misalignments and phase noise sources than an intensity-modulated microphone.
Because of this, PM implementations require more complicated electronics for signal
demodulation, and they have stricter requirements for the light source. Finally, a PM
microphone has a periodic power coupled curve, constraining the microphone to either a
very small membrane deflection or to a "peak-counting" scheme during demodulation.
Due to the additional complexity involved in implementing a PM microphone and
the mixed results achieved by previous implementations (Table 1-2), an intensity-
modulated lever-type transduction scheme was chosen for this work.
1.2. Microphone Structure
The intensity-modulated optical microphone that is the topic of this thesis can be
divided into four major physical parts. They are the MEMS chip, the optical fibers, the
light source, and the detection electronics.
The following figure shows the block diagram for the optical microphone. In the
steady-state case, light from the light source is coupled into the transmit (Tx) fiber. The
Tx fiber delivers the light to the MEMS chip, where it is reflected and partially coupled
into the receive (Rx) fiber. The Rx fiber then delivers the light to a photodetector, where
it is converted into an electrical signal and processed by detection electronics. When an
acoustic field is present at the MEMS chip, the coupled optical power is modulated. This
allows the transducer to convert acoustic energy into electrical energy, which is the
definition of a microphone.
Detector and Electronics
Figure 1-7 Block Diagram of the Optical Microphone.
There are four energy domains present in this system that carry information. The
first domain is the acoustic domain, where the desired measurement lies. The MEMS
diaphragm converts the acoustic energy into mechanical energy through its displacement.
The mechanical displacement of the membrane varies the power coupled into the Rx
optical fiber, converting the signal into the optical domain. At the photodetector, the
signal is converted into the electrical domain for analysis.
For our design, we have chosen a reflective-type intensity-modulated optical lever
microphone, with the mechano-optical transduction mechanism shown in Figure 1-8.
The dominant reason for this selection is that this type of intensity-modulated optical
microphone is much simpler to design and package than other intensity-modulated
microphones. Details of each component are described in later sections of this chapter.
Figure 1-8 Cross Section of the Fiber Bundle in the MEMS Chip.
1.2.2. MEMS Chip
The MEMS chip is a 2.5 mm x 2.5 mm silicon chip with a micromachined 1 mm
diameter silicon nitride diaphragm. The process flow for the MEMS chip is discussed in
A cross section of the MEMS chip is shown in Figure 1-9. The dominant
membrane material is a 1 |jm thick layer of silicon nitride. A 70 nm thick layer of
aluminum is deposited on the membrane surface to enhance reflectivity. The cavity
formed by the bulk silicon and silicon nitride membrane is fitted over the end of a steel
hypodermic tube containing the optical fibers.
Protective Steel Tubing
Figure 1-9 Cross Section of the MEMS Chip.
1.2.3. Optical Fibers
The optical fibers selected for the optical microphone are the Thorlabs
AFS105/125Y multimode optical fibers. They are used for both transmit (Tx) and
receive (Rx) fibers. The end of the optical fiber that terminates at the MEMS chip is
designated the device end, and the end connected to the light source / photodetector is
designated the Tx / Rx end. One fiber acts as a Tx fiber, and six fibers are Rx fibers.
Figure 1-10 shows the desired shape of the fiber optic bundle as seen from the nitride
membrane into the steel tubing. In this figure, the cores of each fiber are color-coded,
and surrounded by a white ring representing the cladding. The dashed line is a possible
location for the border of the light cone reflected by the membrane. The receive fiber
area inside the dotted ring is responsible for collection of the reflected light.
Aluminum (70 nm)
Nitride (1 !lm)
Oxide (0.7 !lm)
Bulk Silicon (-500 !lm)
Figure 1-10 End View of the Optical Fiber Bundle.
Figure 1-11 Optical Fibers in Steel Tubing.
Figure 1-11 shows the fiber bundle inside the protective steel tubing. The end
view shown is the ideal position, where the transmit fiber is located in the exact center of
the tube. This allows the light to reflect off of the center of the membrane, which has the
maximum acousto-mechanical sensitivity (defined here as change in membrane
deflection per change in acoustic pressure).
Figure 1-12 is a diagram of the fiber bundle in its protective tubing. Connections
to other parts of the system are noted. The dashed arrows indicate the path of light
through the system. Paths three and four contain modulated data.
Steel Hypodermic Needle
3 ""' To Detector
Emitted Light Device A
membrane present) Receive
Figure 1-12 Optical Fiber Bundle Drawing.
Based on the work of He and Cuomo , the mechano-optical (MO) stage
sensitivity, defined as change in coupled optical power per change in membrane
displacement, is maximized when a single transmit fiber is surrounded by a tightly
packed ring of receive fibers (see Figure 1-10). The smaller the radius of the receive
ring, the greater the sensitivity of the MO stage, and the smaller the equilibrium gap,
which is defined as the equilibrium distance between the fiber bundle face and the
It may be possible to increase the sensitivity of the MO stage by adding extra Tx
fibers . The current fiber bundle is designed to sample the displacement of the
membrane at the center (at the maximum displacement). For membranes which are much
larger than the accompanying fiber bundles, all bundles could illuminate areas near the
center of the membrane, where Sam is high and the stage is linear. If the diameter of the
bundle structures is on the order of the membrane, then sensitivity gains will be lessened
and linearity of the stage may become an issue. Sensitivity and linearity are discussed
later in this thesis.
Since the MO stage sensitivity is a result of the displacement of the illuminated
region of the membrane, extra MO sensitivity can be obtained by illuminating additional
portions of the membrane by additional fiber bundle structures. With the assumptions
that adding additional identical bundle structures does not remove any light collection
ability, the same electro-optic sensitivity is available to each bundle structure, and the
region of the illuminated membrane is locally flat, then the MO stage will remain linear
and the system sensitivity would be given by the following equation.
S= SoeSmoZ,, Equation 1-1
1.2.4. Light Source
The light source used by this optical microphone is the HP8168B Tuneable Laser
Source. The maximum output power of the laser at 1550 nm is 0.515 mW. An alternate
laser source or an LED source could be used in place of the HP8168B.
1.2.5. Detection Electronics
There are three schemes considered by this thesis for use as detection electronics.
The first scheme uses a single photodetector and takes the unreferenced output of the
photodetector as the microphone output. This technique is called the unreferenced output
technique. This scheme can be used with an amplifier at the output of the microphone to
increase the gain. The primary advantage of this scheme is simplicity. Fewer optical and
electronic components are required here than for any other configuration (see Section
5.2.1 for details). This greatly reduces the cost of the optical microphone when compared
with the other opto-electronic configurations. The largest disadvantage of this
configuration is the dependence of the unreferenced OE sensitivity on the optical power
(shown in Section 126.96.36.199). This dependence makes the unreferenced optical microphone
much less stable in the presence of laser instability and drift. Also, the overall sensitivity
of the unreferenced OE microphone is less than the referenced microphone configuration.
The second scheme, which was used by Kadirval , is the referenced output
technique. It uses an optical splitter to separate the light source output into two paths.
One path is connected to the Tx fiber for transmission to the MEMS chip. The Rx output
is the modulated data signal, and is taken to a photodetector. The second path is
connected directly to a photodetector for use as a reference signal. An analog divide
circuit is used to divide the modulated signal by the reference signal, and the divided
signal is taken as the microphone output. The largest advantage of the referenced output
configuration is the independence of the sensitivity on light source power. This
minimizes the negative effects of low frequency fluctuations in the light source output
power, such as fluctuations due to temperature changes. Another advantage of the
referenced output configuration is the ability to significantly improve microphone
performance by adding optical losses to the reference signal path (shown in Chapter 2).
Additionally, an amplifier may be used at the output to further increase sensitivity.
Despite the advantages, the referenced optical microphone requires more optics and
electronics than the unreferenced microphone (see Section 5.2.1 for details). This
increases the cost compared to the unreferenced microphone. Another disadvantage is
the increased electronics noise in the output due to the extra electrical components
(Section 2.2.4 for details).
The third scheme, heterodyne modulation, is designed to take advantage of the
flatness of the overall noise floor of the unreferenced optical microphone at high
frequencies. In this scheme, the laser output is modulated by an external sinusoidal
signal to frequencies much higher than the high frequency cutoff of the microphone. The
received optical microphone signal at the photodetector will be contained as a bandpass
signal centered at fo, where fo is much larger than the microphone bandwidth. After
passing through the photodetector, the signal is passed through a lock in amplifier and
demodulated back to the original baseband signal. This will make the noise floor of the
microphone dependant on the high frequency noise floor of the laser, and not the low
frequencies where 1/f noise (and other noise sources) is present. As with the previous
two OE configurations, an amplifier can be used at the output to increase sensitivity. The
major disadvantage of this electronic configuration is the increased electronic complexity
when compared to the other electronic configurations. Additionally, the lock-in amplifier
must be capable of passing frequencies at least 10 times the microphone high frequency
cutoff. Also, even small laser transients will cause the lock-in amp to fail to reproduce
the signal. This scheme was not implemented in this thesis, although it is likely that an
optical microphone system using a laser as the light source would require heterodyne
detection for satisfactory performance.
MICROPHONE SYSTEM PARTITIONING AND PERFORMANCE METRICS
2.1. System Partitioning
The intensity-modulated optical microphone is partitioned into three stages where
transduction between energy domains occurs. The three stages of an intensity-modulated
optical microphone were identified by Bilaniuk . They are the acousto-mechanical
stage, the mechano-optical stage, and the opto-electrical stage. Kadirval  and Bilaniuk
 discuss these stages in detail, and a summary is included below.
2.1.1. Acousto-Mechanical Stage
The acousto-mechanical stage is where the energy in the acoustic signal is
converted into the mechanical domain. This is accomplished when the pressure and
volume velocity of the acoustic signal induce a displacement and restoring force in the
membrane. The unit of sensitivity for this stage is a displacement per unit pressure,
typically given in jtm / Pa.
2.1.2. Mechano-Optical Stage
In the mechano-optical stage, input optical power is reflected by the displacing
membrane and coupled into output (Rx) fibers. Transduction occurs when the
mechanical displacement of the membrane varies the percent of the input power that is
coupled into the output fibers. The unit of sensitivity of this stage is normalized power
per unit displacement, typically given in |jm-1
2.1.3. Opto-Electrical Stage
The third and final transduction stage in an intensity-modulated optical
microphone is the opto-electrical stage. This stage uses one or more photodetectors to
convert the coupled optical power into an electrical signal. The sensitivity units for this
stage are normally written as in volts (V). Occasionally an author will write the OE stage
sensitivity in V/(W/W). Most authors (including Bilaniuk) lump the optical power
dependence of the overall sensitivity of some microphone configurations into the OE
2.2. System Performance Metrics
Kadirval  used the following performance metrics to classify the optical
microphone. They are sensitivity, linearity, frequency response, noise floor and
minimum detectable signal (MDS). These metrics can also be used to describe the
performance of the individual stages. The theoretically determined performance metrics
for the system and each stage are summarized later in this chapter.
In this thesis, a theoretical sensitivity model for the referenced output
configuration is derived for the case where optical reference path losses and a low-noise
amplifier at the output are present. A theoretical model of the electronic noise is derived
for both unreferenced and referenced configurations. This model extends the noise
model derived by He & Cuomo  and used by Kadirval  to include the intensity
noise of the light source and all electronics. The physics behind the minimum detectable
signal equation presented by Kadirval  are explained, and the equation is used with the
improved noise model to predict the minimum detectable signal.
2.2.1. System Sensitivity
The sensitivity of a system is defined as the differential change of the output
quantity divided by the differential change of the input quantity. For a microphone, the
system output is a voltage, and the input is a pressure. The optical microphone is a multi-
energy domain system with three transduction stages, as previously described. The
maximum ideal sensitivity is a product of the sensitivities of the individual stages.
Equation 2-1 is the equation for the system sensitivity in terms of the individual stages.
All reported sensitivities in this thesis are based on a fiber bundle with identical Tx and Rx
fibers having an inner core diameter of 105 |tm and a cladding diameter of 125 |tm.
S = SamSmoSoe Equation 2-1
Section 188.8.131.52 examines the sensitivity of the OE stage in more detail then was
done by Kadirval . It derives theoretical models for the OE sensitivity in the
unreferenced and referenced configurations, and it examines sensitivity limits of the stage
resulting from the finite linearity range of the photodetector.
184.108.40.206. Acousto-Mechanical Sensitivity
The acousto-mechanical stage converts pressure to a displacement. Equation 2-2
gives the sensitivity of the stage, where Wo is the deflection of the membrane at the
center, and p is the acoustic pressure at the center of the membrane.
Sam = Equation 2-2
To derive Sa, first begin with Equation 2-3, the transverse deflection equation for
a plate derived by Sheplak et al. .
12(1- v2 p 4 a2 r
S k 2Eh3 2kl,(k) 4a2
Figure 2-1 Side View of Deflecting Plate or Membrane.
In the case of a membrane where a << kr, Equation 2-3 simplifies to Equation 2-4.
)= 2.78pa4Ehk2 2
w(r)= 1-2 a 2
Letting Wo = w(0) and substituting Equation 2-4 into Equation 2-3 produces the
equation for the sensitivity of the membrane as a function of radial distance from the
W 2.78a4 I r2
Eh3 k 2 L a 2
If we assume that the light spot on the membrane is very small (10% or less) with
respect to the membrane diameter, then the sensitivity of the membrane can be lumped at
the radial center. Equation 2-6 gives the final equation for the acousto-mechanical
sensitivity of the membrane, lumped to the radial center.
Sa = Sm (0) = -a Equation 2-6
If it cannot be assumed that the light spot is small, then the membrane sensitivity
cannot be lumped into the center of the membrane. Sam will become a function of radial
position, r, with respect to the membrane center, and the microphone sensitivity will
In this optical microphone, the light spot illuminates less than 10% of the
membrane. Based on the observed fiber position error (see Section 3.3.1) of less than 50
|tm for the fiber bundle used in this thesis, Sam can still be approximated as a constant for
The tension parameter k is determined by Equation 2-8. The in-plane stress (Go)
of the nitride layer for the nitride deposition process used in the microphone fabrication
was reported to range between 50 MPa and 120 MPa by the MEMS Exchange website.
Special fabrication instructions were given to minimize the in-plane stress in the nitride
layer, so it is expected that the stress will be equal to the minimum reported value for the
MEMS Exchange deposition process, Go = 50 MPa. Using E = 270 GPa (for SixNy), h =
1 jtm, a = 1 mm, and Vo = 0.27 (for SixNy), we estimate Sam = 1.249 x 10-3 tm / Pa.
k = o Equation 2-7
For a discussion of the effects of the observed membrane linearity on Sa, see
Sections 220.127.116.11 and 5.3.2.
18.104.22.168. Mechano-Optical Sensitivity
The mechano-optical transduction stage converts a mechanical displacement to an
optical power coupling factor. The sensitivity of the stage is given by Equation 2-8,
where w is the deflection of the membrane at the center, and r is the coupled optical
power of the stage in W/W.
Sam = Equation 2-8
He and Cuomo  derived a formula for determining the power coupled by
light reflecting off of a deflecting membrane in a microphone similar to that shown in
Figure 1-8. The analysis is valid for multimode optical fibers. Theoretical work by Ruan
and Felson  can be used to derive the power coupled as a function of membrane
displacement for the case of a single mode transmit fiber and a multimode receive fiber,
although that configuration is not analyzed here. Ruan and Felson's work is applicable to
membranes with a finite radius of curvature, however He and Cuomo's work is not. The
analysis here based on  assumes no misalignment errors and no power lost due to
mismatch between fiber numerical apertures (NA). This is a good approximation when
the angular alignment between the fiber surface and the membrane is less than 5 degrees
(for fibers with NA = 0.22 or less). If this approximation does not hold, then the method
of images (explained below) is not valid. Adjusting the method of images to account for
angular alignments is complicated, and as of this writing, no work exists that rigorously
solves the problem. Section 3.3.1 discusses types of alignment errors, methods to avoid
them, and their implications in more detail.
In general, the power coupled into an optical fiber can be determined by
integrating the optical intensity (also known as the irradiance) over the collecting surface,
assuming all light present is entering the fibers at an angle less than the acceptance angle
of the fiber. If this is not the case, then only the irradiance due to rays entering the fiber
at less than the acceptance angle should be integrated in Equation 2-12. The analysis of
He and Cuomo  assumes the former. The reflected intensity profile at the surface of
the fiber bundle is determined in  by the method of images.
Image Plane Reflecting Plane Receiving Plane
Image Receive Fiber Core
Image Receive Fiber Core
Figure 2-2 Method of Images (View from Side of Fiber Bundle).
In the method of images, the reflecting surface is defined to be the reflecting
plane, and the surface of the fiber bundle (as shown in Figure 1-10) is defined to be the
receiving plane. They are separated by a gap, g. The method of images states that the
reflected optical power incident onto the Rx cores is the same as the optical power
incident on the Rx core images, located at a distance of 2g from the receiving plane.
Using the method of images, He and Cuomo derived an equation for the intensity
on the image plane as a function of radial distance from the center of the fiber bundle.
This thesis uses Equation 2-9 through 2-11 from He and Cuomo  as the first step in
determining the power coupled and sensitivity of the MO stage. Without an
understanding of these equations, a microphone designer will not be able to identify
miscalculations due to errors that have been observed in the output of Equation 2-9. This
problem will be discussed in more detail later in this section.
1A (ko -1)-At1an' i -111, If (1k, <2)&(0
A 7 Atan A+tan (1-k)-Altan (A(1- II+ In fj (k >2)&(O
-A 7- Atan 'A+tan (1-k) Atan (A(1- +II+In f~l( 1 (,k >2)& (02
2(1-)14 80, 1+A(k+l
1 (r) A 4 tan (k -l)-tan (k-l)+Atan (A(k -))- Atan ( li -111, f (1< k, <2)& (
S J + Altan' -tan (k -1)+ tan -(A(k -1)) + In ] f (k >2)&(1!k< 2)&(k -k>2)
2 4 F8, 1+ (k4+1)0
A nl .,i (L_+1)2),)] if (k(>2)&(k>2)&(k2)2)
S2(1-A )4 (8k, L++Ak+l
A I1L(k+ I+A2(k I) if (k > 2)&(k > 2)(k k > 2)
nL(k 1)J 1+ -+ 1)2
80, )(k-;1)1+A4(k +1)
The quantity, A, used in Equation 2-9 is defined by Equation 2-10. In Equation 2-
10, rtx core is the radius of the transmit fiber core, and g is the equilibrium gap.
A = -- Equation 2-10
The quantity k used in Equation 2-9 is defined by Equation 2-11. In Equation 2-
11, rtx core is the radius of the transmit fiber core, and r is the radial coordinate measured
from the center of the Tx fiber axis.
k = r Equation 2-11
The quantities Oc and kc are the critical angle of the Tx fiber and the critical value
of k associated with that angle. For more details on the variables, see He and Cuomo's
Some sets of input parameters with a gap, g, on the order of the Tx fiber diameter
were observed to produce non-intuitive intensity profiles. For example, using Equation
2-9 at a gap of 50 |tm with a Tx fiber core diameter of 105 |tm resulted in I(r) = 0 at all
values of r. Therefore, for the theoretical power coupled and sensitivity to be accurate, an
optical microphone designer must plot Equation 2-9 for equilibrium gaps of the desired
value. If the plots are erroneous, then the power coupled and sensitivity analysis will be
invalid. The Mathcad code used to generate the intensity curves was carefully examined
for errors, and none were found. It is possible that Equation 2-9 does not accurately
predict the intensity at small gap distances.
The power coupled into the receive fibers is determined by using a ring
approximation with a power correction factor. The ring approximation used in He and
Cuomo  approximates the face of the receive fibers as an annular ring. The power
coupled is determined by integrating the normalized intensity (Equation 2-9) over the
ring area. Figure 2-3 shows the ring approximation. The actual light collection surfaces
are shaded gray, and the integrated area of the ring approximation is shown by the dashed
ring. Note that the relative sizes of the core and claddings are not necessarily to scale.
Figure 2-3 Ring Approximation Diagram.
The power coupled and sensitivity equations for the mechano-optical (MO) stage
are given by He and Cuomo . These were the equations used by Kadirval  to
predict the performance of the MO stage in his optical microphone. This thesis has
modified the power coupled equation from  (referred to as the ideal power coupled
from this point) to include the effects of radial position errors in the receive optical fibers,
and also to correct for overestimation of the power coupled by the ring approximation.
Radial position error, RPE, is defined and discussed in Section 3.3.2. The power
coupled correction factor, cf, is calculated by taking the ratio of the actual surface area of
the receive fibers to the area of the ring in the ring approximation. The ideal power
coupled is then multiplied by this correction factor (which is a function of the optical
fiber geometry and the RPE) to calculate the corrected power coupled. In this thesis,
ideal power coupled and sensitivity refers to the case where cf = 1, meaning that the ring
approximation area exactly matches the surface area of the receive fibers. Since this can
never happen in practice, the ideal situation will occur only when the area mismatch is
neglected, as is done by  and . The corrected power coupled and sensitivity
equations are given in Equations 2-12 and 2-13.
P, 2c, (RPE) core (k g)
n(g, RPE=) -= -i-(k, kdk Equation 2-12
nt m-l+RPE/C .
Sm (g, RPE) = dPo (Q(g, RPE)) Equation 2-13
dz I dz
Two theoretical corrected power coupled curves, based on using Equation 2-12
with a fiber bundle constructed from AFS105/125Y multimode fibers as both Tx and Rx,
are shown in Figure 2-4. One of the curves corresponds to an RPE of 0 itm, and the other
corresponds to an RPE of 10 |tm (the observed RPE of the custom fiber bundle). The
corresponding corrected sensitivity curves are shown in Figure 2-5. The horizontal axis
on each plot is the equilibrium gap, g, between the receiving plane and the reflecting
plane in the method of images.
The maximum corrected theoretical MO sensitivity with RPE = 0 |tm is Smo =
1.094E-3 |tm-1 and occurs at g = 230 itm. When the power coupled correction factor is
taken into account, the maximum corrected theoretical power coupled is Smo = 0.784E-3
|tm-1 and occurs at g = 265 |tm.
0 100 200 300 400 500 600 700 800 900 1000
Figure 2-4 Theoretical Power Coupled with Ideal Fiber Configuration.
5 2 .0 0 E -0 4 ------ -------- .--------------
0 100 200 300 400 500 600 700 800 900 1000
Figure 2-5 Theoretical Sensitivity with Ideal Fiber Configuration.
The discontinuities observed in the sensitivity equations are due to transitions in
the power coupled integral. Specifically, each discontinuity corresponds to the edge of
the light cone crossing the boundary of the receive fiber ring. The discontinuity is
present in the power coupled equations, but since it manifests in these plots as an integral
of the discontinuity seen in the sensitivity curves, it is difficult to see on the viewing scale
of the power coupled plot.
22.214.171.124. Opto-Electrical Sensitivity
The opto-electrical stage converts an optical power coupled to an electrical signal.
This is accomplished with the use of a Thorlabs PDA400 photodetector, which consists
of a photodiode and a trans-impedance amplifier with five gain settings. In this thesis,
the photodiode and trans-impedance amplifier are collectively referred to as a
photodetector, and they are treated as one unit.
The sensitivity of the stage is given by Equation 2-14, where r is the optical
power coupled, and V is the output voltage of the sensor.
Soe = Equation 2-14
The output voltage of the opto-electrical stage is a function of the detection
electronics and the detection method used. For the Unreferenced Output detection
technique, shown in Figure 2-6, the output voltage is a function of the photodetector
responsivity and gain, the output amplifier gain, and the laser power.
Lowpass Filter /
Photodetector Output Amplifier
Pot R G Ga -0 Vout
Figure 2-6 Block Diagram of the Unreferenced Output Configuration.
The output voltage of the unreferenced output configuration, Equation 2-15, is
derived by applying Kirchoff s and Ohm's Laws to the equivalent circuit of the detector,
shown in Figure 2-7. Since a voltage amplifier is connected in series with the detector,
the output amplifier gain, Ga, is multiplied by Vdet out to get the microphone output
voltage, Vout. Pout is the received optical power from the fiber bundle Rx fibers. By
equating Pout with q times Pin, Equation 2-15 neglects losses in the fiber bundle other than
those from the power coupling effect. For a real bundle, other losses are present at the
connectors and in the fibers themselves. These losses have not been measured and are
Vo, = RGGP,,, = RGGEP,J7
Figure 2-7 Equivalent Circuit for the PDA400 Photodetector.
Substituting Equation 2-16 into Equation 2-15 gives the equation for the electro-
optical sensitivity of the Unreferenced Output detection technique.
So = RGGP,, Equation 2-16
Equation 2-16 shows a linear relation between the received optical power and the
OE stage sensitivity. This linear relationship only holds when the photodetector is
operated in a linear region. A Thorlabs PDA-400 photodetector, with specs given in
Appendix D, has a peak response of 0.95 A/W at 1550 nm. The minimum trans-
impedance gain setting, G, for the PDA400 is 15,000 V/A. Using the detector response R
= 0.95 A/W and the gain G = 15000 V/A, gives Soe = 14250(V/W)*Pin. If Pin = 0.7 mW,
then Soe = 9.975 V. Since the photodetector saturates at 10 V, the maximum
unreferenced OE stage sensitivity is 9.975 V Ga.
It is very important to observe that the overall sensitivity of the unreferenced
optical microphone is limited by the maximum DC optical power received by the
photodetector due to detector saturation. Ideally, the photodetector would consist of only
a photodiode, and a highpass filter would be placed at the photodiode output. Without
the trans-impedance amplifier, the DC optical power can be removed before
amplification, eliminating the limit of the OE sensitivity due to the DC optical power.
Any sensitivity lost from removing the trans-impedance amplifier can be recovered by
increasing the gain of the output amplifier.
The Referenced Output OE Stage is more useful in a microphone system due to
the invariance of the sensitivity with optical power, which will be proven here. Figure
2-8 is a block diagram for the referenced OE microphone configuration. By using the
equivalent circuit of the photodetectors and by inspecting the block diagram, Equation 2-
17 can be derived for the microphone output voltage, Vout.
S Pm Pmod
Vout = GGd R modGmod = GGad modf -od Equation 2-17
refG,,rPf ref Pref,
Figure 2-8 Block Diagram of the Referenced Output Configuration.
- Ga H- Vout
Highpass Filter /
In Equation 2-17, Pmod is identical to Pout in the unreferenced block diagram, when
the same assumptions are made. If a is the optical losses present in the reference signal
path, then Pref can be represented as (1- a) Pin. By observing that the fiber bundle power
coupled, r, is Pout / Pin, Equation 2-17 can be rewritten in terms of the component gains
and the optical power coupled into the fiber bundle.
Vo = Ga)Gad Gmod Equation 2-18
(1- a)G J
Substituting Equation 2-18 into Equation 2-15 gives the equation for the electro-
optical sensitivity of the Referenced Output detection technique, where Gratio is the ratio
of Gmod to Gdet.
Soe = G d Gmod= G0Gd (Grato) Equation 2-19
(I a) Gref 9 (- a)
Equation 2-19 varies directly with the ratio of the modulated detector gain to the
reference detector gain (Gmod / Gref), with the built-in gain of the analog divide circuit
(Gad), and with the gain of the output amplifier (Ga). Also, increasing optical losses in
the reference path, a, increases the sensitivity of the OE stage and decreases the optical
power incident on the photodetector. Later in this chapter, it will be shown that optical
reference path losses will improve the electronics noise and microphone minimum
detectable signal under some conditions.
Using two PDA-400 photodetectors, an analog divide circuit hardwired for a gain
of 10 V, and the minimum and maximum values of Gratio (based on available PDA400
gains settings), the sensitivity of the OE stage can range between Soe min = (0.10 V)*Ga /
(1-a) and Soe max = (1000 V)* Ga / (1-a). If we take the ratio of the sensitivity of the
referenced to the unreferenced OE stage, we can see how the stage sensitivities compare
at varying input power levels. This is done in Figure 2-9 for Gad = 10 V and Ga = 1 V /
From Figure 2-9, it can be concluded that the unreferenced microphone will have
a lower sensitivity than the referenced microphone unless the laser is operated at the
maximum power for which the photodetector remains linear, no reference path losses are
present, and the photodetector gain ratio is one. When this occurs, the two stages will
have identical sensitivities. Increasing Gratio and a will increase the sensitivity of the
referenced OE stage. These values are physically limited by the photodetector range of
linearity for Gratio and c, and also by the analog divide circuit for a. Specifically, the
input to the analog divide circuit must never drop below a certain threshold, and the
output of the analog divide circuit can never saturate. This limits a to less than 0.9 for
the AD circuit used in this thesis. In practice, the PDA400 detectors are not useful when
the gain is set higher than 47,000 V/A. An additional constraint is the fixed gain-
bandwidth product limiting the maximum gain for a minimum bandwidth.
0 100 200 300 400 500 600 700
Laser Power (gW)
Gratio = 1, Gdet = 15000 V/A, Alpha = 0
Gratio = 3 1, Gdet = 15000 V/A, Alpha = 0
-Gratio = 1, Gdet = 15000 V/A, Alpha = 0 5
Figure 2-9 Comparison of Unreferenced and Referenced Output Sensitivities.
2.2.2. System Linearity
The linearity of the optical microphone is determined by the linearity of the
individual stages. The acousto-mechanical stage linearity is governed by the nitride
membrane. The linearity of the mechano-optical stage is dominated by the assumptions
that the membrane curvature is negligible, and by the local flatness of the sensitivity vs.
equilibrium gap curve. The linearity of the opto-electrical stage is governed by the
linearity range of the photodetector and additional electronics. The following sections
establish the conditions for linearity of each stage, and therefore the whole device.
126.96.36.199. Acousto-Mechanical Linearity
The theory for the range of linearity of the membrane was investigated by
Sheplak and Dugundji . Using this theory, Sahni et al.  determined that the
diaphragm is linear over the region from 0 2000 Pa (160 dB re. 20 [tPa). Sheplak et al.
 present Equation 2-20, which relates the membrane aspect ratio to the in-plane stress
and the maximum linear pressure (3% linearity).
h max Pmax E
By substituting the maximum linear pressure and the microphone membrane
dimensions into Equation 2-20, the in-plane stress, co, of the membrane can be estimated.
The experimental linearity range of the microphone (see Chapter 5) is reached at 122 dB
(re. 20 tjPa). This results in the AM sensitivity increasing by a factor of 15. This effect
is considered when predicting the microphone performance in Section 2.2.7.
188.8.131.52. Mechano-Optical Linearity
The linearity of the mechano-optical stage is based on two factors: the linearity of
the power coupled curve (flatness of the sensitivity curve), and the assumption of the
membrane curvature being negligible.
The point of interest for the linearity analysis is about the point of maximum
sensitivity. Figure 2-10 shows a plot of the sensitivity from an equilibrium gap of 240
|tm to 290 |tm using Equation 2-13. The vertical axis of the curve is highly magnified,
and the thin horizontal lines denote the region that is within 3% of the maximum
sensitivity. It is evident from Figure 2-10 that the MO stage sensitivity is linear within
+/-10 |tm of the optimal gap. Since the largest maximum membrane deflection, at Pmax =
2 kPa, allowed by the variability in the nitride stress of the MEMS chip process is +/-2.49
|tm, the sensitivity of the MO stage will be constant within 3%. The large window for
linearity holds at equilibrium gaps out to 400 |tm. This means that if the equilibrium gap
is set at a value larger than the best case equilibrium gap, then the sensitivity will still be
constant to within 3% over the range of the diaphragm motion.
2 7.00E-04 -
240 245 250 255 260 265 270 275 280 285 290
Figure 2-10 Linearity of Mechano-Optical Stage.
The second criterion for establishing the linearity of the MO stage is the flatness
of the membrane over the illuminated region. An alternate way of viewing this
requirement is to look at the acousto-mechanical sensitivity of the membrane over the
illuminated region as a function of radial distance from the center. For linearity, the MO
sensitivity of the membrane should vary by no more than 3%. It is important to note that
the method of images used in Section 184.108.40.206 requires a flat membrane in the illuminated
area. This means that the membrane must be within 3% of planar over the illuminated
region, and must be parallel to the fiber bundle face.
Figure 2-11 shows the normalized acousto-mechanical sensitivity, using Equation
2-6, of the membrane as a function of the radial distance from the membrane center. This
plot shows that the sensitivity is within 3% of the maximum when the illuminated area is
within 93 ptm of the membrane center. For optical fibers with an NA = 0.22, the spot
radius is less than 93 jtm when the gap is less than 430 jtm.
0 10 20 30 40 50 60 70 80 90 100
Radial Distance from Membrane Center (pm)
Figure 2-11 Plot of Acousto-Mechanical Sensitivity as a Function of Radial Position.
It has been determined that the MO stage sensitivity varies by no more than 3%
over the equilibrium gap range of 200 |tm to 400 |tm. It has also been determined that
the acousto-mechanical sensitivity at every illuminated point on the membrane is within
3% of its maximum value when the equilibrium gap is less than 430 jtm. Therefore, the
MO stage of the optical microphone is linear when the equilibrium gap is between 200
|tm and 400 |tm. Since the ideal equilibrium gap is 230 itm, the OM stage of the optical
microphone is linear at the equilibrium gap of 230 |tm with a maximum deflection of +/-
2.49 tm at Pmax = 2 kPa.
This analysis does not include the effect of misalignments on the linearity. They
are discussed in Chapter 3.
220.127.116.11. Opto-Electrical Linearity
The linearity of the opto-electrical stage is effectively limited by the linearity of
each electronics component in the system. The PDA-400 photodetectors are linear up to
an output voltage of 10 V. The AD734 analog divide chip is linear over the input range
of +/- 12.5 V. Therefore, the photodetectors are the limiting factor in determining the OE
stage linearity. As long as the detectors are operated below saturation, the opto-electrical
stage is linear.
The maximum voltage that can be output in the linear range of operation for the
electronics serves to limit the maximum sensitivity of the unreferenced output
configuration when the output amplifier is held at a fixed gain. To illustrate, consider
Equation 2-21, the equation for the photodetector output in terms of the optical power for
the unreferenced OE configuration.
Vot = RGP,,,. Equation 2-21
The maximum Vout that the PDA400 photodetector can output is 10 V. The
responsivity is 0.95 A/W. Substituting these constants into the above equation shows that
the product of the gain and the optical power cannot be larger than the saturation voltage
of the detector divided by the detector responsivity, or 10.5 W*V / A for the PDA400.
This product effectively limits the maximum sensitivity that the unreferenced OE stage
can provide, since increasing Piaser requires G to be reduced if Plaser*G > 10 V. When the
range of linearity of the measurement equipment is considered, then the gain of the
output amplifier is also limited. To ensure the microphone can operate in its intended
environment, the linearity range of the measurement equipment must also be considered.
2.2.3. System Frequency Response
The frequency response of the optical microphone was discussed in depth by
Kadirval . He developed an equivalent circuit for each stage of the optical
microphone. The frequency response of the microphone is the product of the frequency
response of the individual stages.
18.104.22.168. Acousto-mechanical frequency response
The lumped element model parameters used in the acousto-mechanical stage are
shown in Table 2-1. These parameters were given by Sahni . The frequency
response analysis for this optical microphone membrane was presented by Kadirval ,
and it remains valid. Using the lumped element parameters in Table 2-1 and the
equations for the frequency response of the AM stage, the 3 dB frequency for the upper
end of the frequency response was 76.25 kHz. The lumped element approximation ia
limited to below 50 kHz according to Sahni , so the upper limit of the frequency
response will not be accurately predicted by this model.
H,,,, (s) (= eff Equation 2-22
H am nor(s)
H o H,(s) ,, n.(j2"OHz)
Table 2-1 Acousto-Mechanical Lumped Element Parameters
Parameter Formula Value Units
Mmea ph 1316 kg / m4
Cmea 1.963E-15 m3 /Pa
Mrad Pa 5.199E+5 kg / 5
Ca ca 1.246E-15 m3/Pa
fresh 0.39 98.6 kHz
The lower end of the frequency response is governed by the vent channel of the
microphone. Although the optical microphone was not designed with a vent channel, the
steel tube is not an exact fit with the membrane cavity, and allows equalization of the
pressure on both sides of the membrane due to low frequency pressure fluctuations.
22.214.171.124. Mechano-optical frequency response
The mechano-optical frequency response is a constant. This was discussed by
Kadirval  in detail, and will not be reproduced here.
126.96.36.199. Opto-electrical frequency response
The opto-electrical frequency response is determined by the frequency response
of the electrical components in the system. The photodetector has a worst case
bandwidth of 50 kHz at the maximum gain and a bandwidth of 10 MHz at the lowest
gain. The analog divide circuit has a bandwidth of 10 MHz. Therefore, the bandwidth of
the photodetectors is the limiting electrical component for the upper range of the
frequency response for practical gain settings.
The lower range of the frequency response is limited by the cut-on frequency of
the highpass filter. In the highpass filter used by this thesis, the cut-on frequency was set
at 30 Hz.
2.2.4. System Electronic Noise
The electronic noise is defined to be the noise, in volts, seen at the output of the
microphone circuit. Previous works (He & Cuomo, 1991 , ) assume that "the
light source does not contribute significantly to the (noise) background." He and Cuomo
note that these conditions do not always hold, and that voltage fluctuations due to light
source noise may affect the signal. This thesis includes the effects of the detector, the
light source intensity noise, and the electronics to determine the electronic noise at the
microphone output. The noise analysis traces the path of RMS noise signals, in V / Hz ,
through both the referenced and unreferenced electronics.
The goal of the first part of the electronics noise analysis is to identify and derive
equations for the individual noise sources that contribute to the electronics noise of the
Figure 2-12 Noise Contributions for the Photodetector Output.
Photodiode NEP Terms Photodetector Electronics
t N, P R*Gn Vd
Pdet NEP, Plight noise Vdet, Vhlight
Figure 2-12 illustrates the noise sources that produce electrical noise at the output
of the photodetector. Pdet NEP is the noise equivalent power at the input of the photodiode
due to the inherent noise of the photodiode (dominated by thermal and shot noise
... equations presented are referenced to Wilson and Hawkes ). The units for Pdet NEP
are W / Hzl2. From this point on, the photodetector output due solely to Pdet NEP is
referred to as the detector (or photodetector) electronics noise, Vdet, and has the units V /
Hz 2. Thermal noise and shot noise are the dominant noise sources in a photodetector.
The shot noise, Vshot, in V / Hz 2, is given by Equation 2-24, where G is the trans-
impedance gain, R is the diode responsivity, e is the charge of an electron, and Plight is the
incident optical power received by the detector.
V hot = G2eRTPgh Equation 2-24
Thermal noise, Vtherm, is also present in a photodetector, and can be given by the
following equation, where k is Boltzman's constant, T is the mean temperature in Kelvin,
and G is the trans-impedance gain.
thern, = TG Equation 2-25
The total detector noise, Vdet, can be written as the RMS sum of the thermal and
shot noise, shown in the following equation.
Vdet hot2 +therm2 Equation 2-26
The other noise source, Plight noise, represents the noise power fluctuation incident
on the photodetector due to fluctuations in the intensity of the light source integrated over
the diode collection area. The units for Plight noise are W / Hzl2. The voltage fluctuations
at the output of the detector produced by Plight noise are referred to in this thesis as the light
source (or laser) electronics noise, Vlight. The units are the units V / Hz Where
necessary, subscripts will be added to distinguish between referenced and unreferenced
quantities. Since Plight noise is highly dependant on the type of light source and supporting
electronics, a purely theoretical model will not be used (see the end of this section).
Instead, the electronics noise at the output of the photodetector will be measured. The
measured quantity will be equal to the RMS sum of Vlight noise and Vdet. By using
Equations 2-24 2-26 and the experimentally measured noise quantity, Vlight noise can be
determined for the light source detector system. When Vlight noise is known, the
photodetector equivalent circuit can be used to calculate Plight noise. Dividing Plight noise by
the photodiode active area produces an estimate of the light source intensity noise.
Microphone OE Stage
Photodiode NEP Terms Microphone Electronics
Pdet NEP, Plaser noise Vnoise ref, Vnoise unref
Figure 2-13 Noise Contributions for the Microphone Output.
The second part of the electronics noise analysis propagates Vdet through the
unreferenced and referenced configurations to determine the electronics noise at the
output of the microphone. These noise terms are referred to as the "total electronics
noise" or the "microphone electronics noise" terms. The total electronics noise is
determined by the amplification of Vdet by signal amplification components and the
addition of any additional electronics noise sources (see Figure 2-6 and Figure 2-8). For
this work, the analog divide IC used by the referenced configuration was the Analog
Devices AD734 .
The electronics noise analysis of the unreferenced microphone configuration in
Figure 2-6 is not difficult since only one signal path exists. By inspecting Figure 2-6,
Equation 2-27 and 2-28 can be derived for the total noise output at the photodetector,
Vdet total and the unreferenced noise, Vunref. In Equation 2-28, Va is the input noise of the
amplifier, in V / Hz"2
Vdet total =Vdet2 + (RGdet Phght_ noie 2 Equation 2-27
Vnref = Ga Vdet total2 + Va2 Equation 2-28
The analysis of the referenced microphone noise is more complicated. There are
two signal paths into the system, and a time-domain division. To complicate matters, the
optical noise Vlight noise in the modulated and reference signal paths (see Figure 2-8) may
or may not be correlated. In a real microphone system, it is expected that the optical
noise in the modulated and reference signal paths will be correlated to some degree.
Theoretical models are presented here for both uncorrelated and correlated optical noise
in the referenced configuration.
Vlight noise ref and Vlight noise mod are given by Equations 2-29 and 2-30, which are
derived from the power to voltage conversion equations of a photodetector.
Vght nose RGeP re ghtP Equation 2-29
hghte_ o =h fe Equation 2-3 0n
hght noise _mod = RGmod lhght noise Equation 2-30
When Vlight noise ref and Vlight noise mod are uncorrelated, they will not divide in the
analog divide circuit. Instead, they add as shown in Equation 2-31 for the uncorrelated
analog divide circuit output, Vad unorr. In Equation 2-31, Vad is the input noise of the
analog divide circuit.
Iad uncorr = Gad ,2Vdet- l hght l nse ref + light _nose mod2 + 2ad2 Equation 2-31
The total electronics noise at the output of the referenced microphone for the
uncorrelated case can be determined by propagating Vad uncorr through the output
amplifier, with input noise Va, as shown in Equation 2-30.
Vrefncor = Ga ad 2uncorr a2 Equation 2-32
When the optical noise is correlated, then it will be divided by the analog divide
circuit. In this case, Vad cor is given by Equation 2-32.
Vad corr = Gad 2Vdet + 2ad + nosemod Equation 2-33
Vh\ght _noise ref
The total electronics noise at the output of the referenced optical microphone
when the optical noise is correlated can be determined by replacing Vad uncorr with Vad corr
in Equation 2-32. Equation 2-34 gives this result.
Vrefcorr = G ad corr2 + V Equation 2-34
Theoretical models for the intensity noise of a laser are inaccurate in predicting
the performance of a commercial laser, due to the uncertainty in the laser quantum
efficiencies, and the variation in the performance of the electronics controlling and
cooling the laser. Coldren and Corzine  present Equation 2-41 for the relative
intensity noise, RIN, of a laser source at the optical resonance frequency (corresponding
to the laser output wavelength). The dampening factor, y, is defined as Kf2R + Yo, and is
not a parameter provided by a laser manufacturer. Experiments can be performed to
quantify it, but these are not practical to do when the direct measurement of the optical
noise PSD will provide the needed value.
RN 1 sr Equation 2-35
In order to make an accurate estimate of the light source noise, this thesis does not
rely on Equation 2-41. The results of the experimental measurements for Plight noise and
Vdet are given in Chapter 5.
2.2.5. System Minimum Detectable Signal
The minimum detectable signal is the smallest signal that can be resolved by the
microphone. The minimum detectable signal is a function of physical interactions
between noise sources and desired signals in each stage as well as the sensitivities of each
stage. Previous work (He & Cuomo, 1991 ) only considered the OE Stage MDS, and
also ignored the laser noise effect on the total electronics noise. This work takes
additional noise sources into consideration (see Section 2.2.4).
Equation 2-42 gives the System MDS for the optical microphone. Three physical
MDS reducing mechanisms are considered: membrane noise due to the Brownian motion
of the membrane atoms, variations in the coupled laser power due to laser intensity noise
in the MO stage, and electronic noise in the OE stage. Each of these terms will be
discussed in more detail later in this section.
MDS = + ght- +Af Equation 2-36
SP,,ram ,,o S
The first term under the radical in Equation 2-42 is the AM stage MDS due to the
Brownian noise of the membrane, given in Pa2. The second term is the MO stage MDS,
which is due to the variations in the coupled laser power due to laser intensity noise, in
the presence of variations due to desired membrane deflection (from an acoustic signal),
given in Pa2. If the laser intensity noise is close in magnitude to the change in coupled
power in the Rx fiber, then the signal can never be distinguishable from the optical noise,
even with an ideal (no-noise) detector. The third term is the MDS of the OE stage, also
given in Pa2. The OE stage MDS is determined by the total electronics noise and the
measurement bin width. In previous works, the MO MDS was neglected [16, 22]. No
previous work takes the light source electronics noise into account when calculating the
OE MDS; they only consider the photodiode shot noise.
188.8.131.52. Acousto-Mechanical Minimum Detectable Signal
The dominant noise source of the AM stage is the Brownian motion of the
membrane. The silicon nitride membrane atoms, like all atoms above absolute zero,
exhibit Brownian motion. This Brownian motion causes a deflection of the diaphragm in
the same manner that an acoustic signal does. Due to this deflection, pressures which
cause a deflection smaller than the deflection due to Brownian motion are not detectable.
The equation for the mean equivalent pressure fluctuations due to the Brownian motion is
given by Equation 2-43 from Chau and Wise .
2 32kT (x7A +Pl V _P2)
Pr = a2 Af Equation 2-37
Using a = 1, T = 300 K, k = 1.38 E-23 J / K, mi = m2 = 4.78 E-26 kg, p = p2 =
101.4 kPa, and a = 500 itm, the mean equivalent pressure fluctuations due to Brownian
Based on the MDS of the other stages (presented later), it can be concluded that this noise
source is completely negligible in an intensity-modulated optical microphone.
184.108.40.206. Mechano-Optical Minimum Detectable Signal
The dominant noise source in the MO stage is the intensity noise of the light
source. The physical effect is illustrated in Figure 2-14. Power is coupled by light
reflecting into the receive fibers from the membrane. This power can be written as the
sum of three components: the optical DC component (Plight), the acoustically-modulated
optical power signal (Pmodulated(t)), and the optical noise power (Plaser noise(t)).
Time Variance of Coupled Power Components
Plaser + Plight noise(t) + Pmodulated(t)
Rx Fibers (more than one)
Figure 2-14 Illustration of the Physics Behind the MO MDS.
When the membrane deflects due to an acoustic signal, Pmodulated(t) is produced.
Fluctuations in the light power output superimposes Plight noise(t) onto the desired
modulated signal. If the fluctuations in power coupled due to light output noise are larger
than the fluctuations in power coupled due to the acoustic signal (Plight noise(t) >=
Pmodulated(t)), then the microphone will not be able to detect the acoustic signal without the
optical noise removed by the electronics. In the event that the optical noise can be
removed by the electronics (see Section 2.2.4), the MO MDS effect will not be present in
The equation for the contribution (when present) of the MO stage to the MDS is:
MDSm = -P-O e Equation 2-38
The MO MDS will dominate the system MDS if the following equation is
satisfied and if the optical noise cannot be removed from the system by the electronics (as
is done by the referenced optical microphone when the optical noise is correlated):
-s > VE Equation 2-39
220.127.116.11. Opto-Electrical Minimum Detectable Signal
Noise mechanisms in the OE stage are due to the electronics, the shot noise of the
photodetector, and the detected noise power of the laser. Lasers operated in constant
current mode are noisy, and will usually dominate the electronics noise. The equation for
the OE stage contribution to the MDS is the following, where Voe noise is the electronics
noise and Af is the measurement bin width of the electronics noise.
MDSOE = V n-fs Equation 2-40
If the inequality in Equation 2-45 does not hold, then the OE stage MDS will
2.2.6. Optical Reference Path Losses and System Performance Metrics
In this section, the effect of optical losses in the reference signal path in the
referenced OE configuration will be analyzed. The effect of optical reference path losses
on sensitivity, electronics noise, and MDS will be discussed.
18.104.22.168. Sensitivity and reference path losses
In Equation 2-50, the referenced microphone sensitivity is presented, with Soe
expanded to show the dependance on a.
Sp ( = Sm Gmp Gmod Equation 2-41
(1 a) Gre
The losses in the reference path in the referenced opto-electronic stage reduce the
voltage seen by the denominator input of the analog divide circuit. Decreasing the
denominator increases the circuit output, so adding optical losses to the reference path
will increase the sensitivity of the microphone. For the unreferenced microphone, there
is no reference path, so a is undefined.
22.214.171.124. Electronics noise and reference path losses
In Equations 2-29, 2-31, and 2-32, it was shown that the electronics noise for the
referenced microphone is dependant on (1 a) when the optical noise is uncorrelated.
Therefore, increasing a with uncorrelated optical noise will decrease the electronics
noise. If the photodetector noise dominates, then the effect of increasing a will be
negligible, but if the light source noise dominates, then increasing a can significantly
improve the referenced electronics noise. Therefore, when the optical noise in the
reference and modulated signal paths is perfectly uncorrelated, optical losses in the
reference path are desirable.
Equations 2-29, 2-33, and 2-34 show that the referenced electronics noise is
dependent on (1 a)-1 when the optical noise is perfectly correlated. In this case,
increasing the losses in the optical path will actually increase the electronics noise (in the
same manner sensitivity is increased). Therefore, when the optical noise in the reference
and modulated signal paths is perfectly correlated, optical losses in the reference path are
A real microphone system is likely to have some correlation between the optical
noise in the reference and modulated signal paths, but the extent of the correlation in
general is unknown. Therefore, it is possible for losses in the reference path to increase
or decrease the referenced electronics noise. It is expected that a referenced microphone
with a small correlation between optical noise signals will receive some benefit from
reference path losses, while a referenced microphone with a large correlation between
optical noise signals will have its noise floor slightly worsened.
126.96.36.199. Minimum detectable signal and reference path losses
The referenced optical microphone MDS is strongly dependent on whether the
optical noise is correlated or not. If the noise is correlated, then the MO MDS does not
factor into the total MDS, since optical noise fluctuations are completely removed. If a
increases and the optical noise is correlated, both overall sensitivity and electronics noise
will increase at approximately the same rate. Therefore, optical path losses will not affect
the MDS when the REF and MOD optical noise is perfectly correlated.
If the noise is perfectly uncorrelated, then overall sensitivity will increase and
electronics noise will decrease. Therefore, optical path losses will improve the MDS
when the REF and MOD optical noise is perfectly uncorrelated. Note that since the MO
MDS effect is not present for the correlated case, the total MDS can be much lower for
the correlated case than for the uncorrelated case.
2.2.7. Summary of Predicted System Performance
Due to the quantity of theoretical data presented in previous sections of this
chapter, the best realistic device performance metrics will be summarized here. No
design has a problem with the frequency response since the most limiting component is
the photodetector with the maximum gain, which has a bandwidth of 50 kHz. Since the
lumped element model approximates the membrane for f< 50 kHz, this will be used as
the upper limit of the frequency response, even though electronics may be capable of
higher frequencies. The lower limit of the frequency response will be 30 Hz, which is the
cut-on frequency of the highpass filter used in the OE stage. The reference path optical
losses in Table 2-2 were experimentally measured. The performance specifications in
Table 2-3 are those that the optical microphone is expected to have when it is
Table 2-2 Summary of Configuration Settings for Theoretical Performance Metrics
Mod Ref Laser .
Mod Ref Laser TAmplifier Ref Optical
S. Detector Detector Output O i
Configuration eeor Deeor O Gain Path Losses
Gain Gain Power (V / V) (W / W)
(V / A) (V / A) (pW)
Unrefer ed O15,000 N/A 350 1 N/A
Referenced 15,000 15,000 350 1 76%
Table 2-3 Summary of Theoretical System Performance Metrics
Sensitivity MDS Electronic Noise
Configuration ,. ,
Configuratio(mV / Pa) (dB re. 20 iPa) (lV / Hz2)
Unreferenced Amplified Output 0.073 73.8 0.19
Referenced Amplified Output 0.612 64.4 14.3
DESIGN OF THE OPTICS FOR THE MEMS OPTICAL MICROPHONE
This chapter examines the selection process for the optics design for the MEMS
optical microphone. The design of the optics must be done in parallel with the
microphone package. Some optics required by the optical microphone are optical fibers,
a light source, an optical splitter, photodetectors, and opto-isolators. Other miscellaneous
components that are needed are connectors, protective tubing for the optical fibers, and
packaging the MEMS optical microphone. This selection process is vital to the bundle
performance and to the feasibility and robustness of the microphone package.
3.1. Selection of the Optics
There are many factors which were considered in the selection of the optics. The
most important factors are device performance, system connectivity, ease of handling,
Device performance considerations are the most important factor for selecting the
optics used in the optical microphone. Performance specifications for the optical
microphone were listed and a theoretical model was derived in Chapter 2 for the system
sensitivity, minimum detectable signal, frequency response, and dynamic range of
linearity. Assumptions and simplifications were part of the theoretical model of the
device performance. Therefore, the microphone optics must have is the ability to adhere
to the theoretical assumptions under the widest possible range of considerations. Ideally,
the selection of the optical components will guarantee the validity of the assumptions.
Practically, the optical components must be selected to minimize deviations from any
inherent assumptions (discussed in Chapters 1 and 2) and the non-idealities included in
As shown in Chapter 2, MDS (in Pa or dB) is dependent on the individual noise
contributions of the light source, the membrane, and the electronics, as well as the overall
sensitivity and the product of Sa and Smo. Therefore the components should be selected
such that their combined contribution to MDS is equal to or below the desired minimum
detectable signal. To determine this, their effects on the sensitivity and noise floor must
be known in advance! Since sensitivity is dependent on received optical power in some
microphone configurations, light sources with high power are usually more desirable than
sources with low power. However the MDS may not be improved, since using a light
source with more power can cause the laser intensity noise to rise to unacceptable levels.
Increasing the numerical aperture of the optical fibers used for the fiber bundle
increases the MO stage sensitivity. Small core fibers have higher sensitivity than large
core fibers. Focusing optics can also be used to provide large MO stage sensitivity
increases. Misalignments and reflection losses can decrease the sensitivity and also
potentially lead to laser instability. Large core fibers should not be coupled (via standard
connectors) to small core fibers, since large power (and sensitivity) losses will result.
Factors that influence sensitivity and MDS also can affect the device linearity.
Increasing the output of the light source without bound will eventually saturate the
detection electronics. By varying the optical fiber numerical aperature, NA, in Equations
2-9 through 2-13, it was found that using optical fibers with high numerical apertures
compresses the power coupled and sensitivity curves towards zero, reducing the range of
linearity of the MO stage when compared with the linearity using a low NA fiber.
3.1.2. System Connectivity
The issue of system connectivity must be considered when selecting optical fibers
and optical equipment. Specifically, it must be possible for two fibers which are to be
connected to each other to be connectorized with compatible connectors. Free space
coupling mechanisms are possible as a last resort, but they are undesirable since they
allow ambient light to be coupled into the system, are difficult to align, and are sensitive
to vibrations. Finally, a design that requires multiple fibers in one connector must take
into account the available connector sizes when choosing the size and types of fibers that
will be used.
3.1.3. Ease of Handling and Manufacturability
Manufacturability of a device is as important to overall success with the
microphone as the performance. No matter how good the predicted performance of a
device, if it cannot be built efficiently and effectively, then it will not be useful. During
fabrication of the fiber bundle, fibers must be stripped, inserted into a steel tube, and
generally exposed to rough handling. In general, the smaller the diameter of the fibers,
the more difficult any handling with them becomes. The yield of the process for
producing fiber bundles is lower for smaller core fibers, therefore, an improved process
for producing small core fiber bundles is required.
Finally, optical fibers and other optical components are expensive. For an optical
microphone to be competitive with a capacitive microphone, the cost of each component
must be minimized. Components should be chosen such that the least expensive
component that satisfies the specifications is used. Although this is an intuitive
statement, its application is not always easy. Packaged lasers with built in control
electronics and ultra low noise floors are expensive, but they may improve the device
performance significantly. However, if the photodetector noise and MDS cannot match
the laser, then the cost of the optical microphone will be needlessly high.
Alternately, it is possible to buy fiber pigtailed lasers at communications
wavelengths (1550 nm) that are (relatively) inexpensive. If care is not taken to protect
these lasers from static electricity and thermal effects, then the lasers will have a high rate
of failure, and the cost of operation of the optical microphone will again become
Based on the sensitivity, noise and MDS analysis from chapter 2, it is best to
select lasers with the highest signal-to-noise ratio. More output power is not always
better, considering that the MO MDS is based on the laser SNR, while the OE MDS is
based on the laser noise power, and can be worsened by increasing the laser power even
if the laser SNR remains constant. Also, OE configurations are available which eliminate
optical power from the sensitivity equation.
Photodetectors with a high gain-bandwidth product and low noise are desirable.
High photodetector built-in gain is undesirable, since the DC component of the optical
signal will result in detector saturation at low power levels, limiting the sensitivity. Also,
an intensity-modulated optical microphone will have a large dc component, so high gain
detectors will saturate. A low-noise amplifier and a high-pass filter at the output of the
system will recover any gain lost by low gain photodetectors or low power lasers.
3.2. Selection of the Tubing
The protective steel tubing is used to protect and align the optical fibers in the
MEMS chip cavity. It provides mechanical support to the fibers and the mounted MEMS
chip and it isolates the fibers inside the tube from the acoustic field under test.
The protective steel tubing must protect the fibers, mount the microphone chip,
and properly align the fiber bundle. The fiber bundle is assumed to be tightly packed and
aligned with the center of the membrane. Ideally, a tube with an inner diameter (ID)
equal to the fiber bundle diameter and an outer diameter (OD) equal to the MEMS cavity
diameter is used. This topic is discussed in more detail later in this chapter.
The material selected for the tubing was steel, because acoustic impedance of the
protective covering for the fiber bundles needs to be much larger than the acoustic
impedance of the test medium (air, in this case). If the acoustic impedance of the tube
was not much higher than air, then sound could penetrate the tube and cause a
displacement of the fibers in the fiber bundle. This is undesirable, since the theoretical
characterization of the optical microphone requires the fiber bundle face to be fixed. In
an environment where the acoustic impedances of the tube and the medium are more
closely matched, a more sophisticated model should be used to account for possible
movement of the fibers in the tube.
Another reason for the selection of steel as the tubing material is its ability to
protect fibers from damage. Steel is much harder than other reasonably priced materials
and will be able to provide adequate protection to the fiber bundle.
3.3. Alignment Issues
Thus far, only fiber bundles with the optimal bundle geometry and ideal
arrangement between the fiber bundle and the membrane have been analyzed.
Assumptions about the geometry of the bundle have been made, but if the steel tubing
and fibers are not properly chosen, these assumptions may not hold. This section
attempts to develop criteria for minimizing the errors when geometry assumptions do not
3.3.1. MEMS Chip Cavity Alignment Issues
Ideally, the MEMS chip and fiber bundle are aligned as shown in Figure 3-1.
Four geometric parameters of the device are identified: the membrane diameter (DIA),
the fiber bundle diameter (FiberDIA), the inner diameter of the steel tube (ID), and the
outer diameter of the steel tube (OD). Two types of position errors are also identified:
the distance between the outer edge of the steel tube (Type I Error, ERR1), and the
distance between the fiber bundle and the inner edge of the steel tube (Type II Error,
ERR2). Type II Error also represents the worst case radial position error (see Section
3.3.2). The worst case bundle position error (BPE), defined as the radial distance
between the actual location of the Tx fiber core and the desired location of the Tx fiber
core, is given by the following equations.
BPE = ERR1+ ERR2 Equation 3-1
ERR1 (DIA OD)
RR2 = Fi IA)
ERR2 I (ID FiberDIA)
- I I-
Membrane Diameter, DIA
Type I Error, ERR1
Bundle Diameter, FiberDIA
Steel Tube Inner Diameter, ID
Steel Tube Outer Diameter, OD
Figure 3-1 Bundle Position Error Illustration.
From the equations for bundle position error, it is evident that the bundle position
error is minimized when ID = FiberDIA and OD = MembaneDIA. If a device with zero
error could be fabricated, then the fiber bundle geometry would be perfect and the bundle
would always be perfectly aligned. In practice, packaging issues and the unavailability of
optimally sized steel tubing prevent BPE from being eliminated completely.
The steel tubing (and optical fibers) was chosen to minimize the worst case BPE
(and RPE; see Section 3.3.2). The BPE was analyzed for fiber designs using multiple
different fiber types, from small 50 jtm diameter core, 55 jtm diameter cladding fibers to
200 |tm diameter core, 220 |tm diameter cladding fibers. In the ideal configuration,
smaller fibers improve sensitivity and reduce the equilibrium gap. In practice, it is very
Type II Error, ERR2
difficult to build an ideal fiber bundle with 50/55 fibers, since commercially available
tube gauges allows large BPE (and RPE; see Section 3.3.2) with these fibers. The
105/125 fibers used by this thesis were chosen because they provided the best mix
between ideal device performance, worst case error device performance, and
manufacturability. The tube size that minimizes the RPE with the 105/125 fibers is the
21HW gauge from Popper & Sons. Specs for this tube and other useable tube sizes are
shown in Appendix E.
Another type of alignment problem occurs when the fiber bundle face is tilted at
an angle with respect to the ideal position. This angular misalignment error is illustrated
in Figure 3-2. Typical misalignments encountered are only a few degrees. Figure 3-2
exaggerates the effect for purposes of illustration.
Figure 3-2 Angular Misalignment Error Illustration.
Although the alignment problem shown in the above picture is greatly
exaggerated, it illustrates how size mismatches between the OD of the steel tube and the
MEMS chip cavity can invalidate the parallel surfaces assumption. This kind of
alignment problem is usually dealt with by the packaging. Horowitz  studied this
type of alignment error for a solitary single mode fiber optical microphone, but it is
significantly more complicated to theoretically characterize the effects of angular
misalignments for a multiple multimode fiber structure. A detailed analysis of the effects
of this type of alignment error will not be dealt with here. Minimization of Type I Error
can eliminate this problem. For a package that virtually eliminates this type of error, see
3.3.2. Fiber Bundle Geometry Issues
Thus far, the fiber bundle has been assumed to be tightly packed (all fibers in
contact). In practice, this is difficult to do. A fiber bundle geometry with fiber position
errors is shown in Figure 3-3.
Figure 3-3 Radial Position Error Illustration.
The fiber radial position error (RPE) shown above is modeled for small error
values in Chapter 2 by shifting the ring outward by the amount of the radial position
error. In general, this type of error is caused by Type II errors in the fiber bundle
structure, when the Rx fibers are shifted towards the steel tube wall by a different amount
than the Tx fibers. This reduces sensitivity and increases the optimal equilibrium gap
(see Chapter 2). The observed RPE with the custom fiber bundle is 10 itm. Using RPE =
10 |tm for using the 105/125 bundle, the MO sensitivity is reduced by 28% compared to
the case where RPE = 0 |tm (see Chapter 2 for details). For fiber position errors larger
than 30 |tm, the actual ring area diverges significantly from the assumed ring area, and
other effects such as multiple reflections can become significant. Since the corrected
power coupled and sensitivity equations do not consider multiple reflections, a more
sophisticated model should be used when RPE > 30 |tm. Finally, if all the fibers in the
bundle do not have the same RPE, then the corrected ring approximation theory will be
invalid, since the bundle structure assumption will no longer hold (i.e. Rx fibers
randomly placed with respect to the Tx fiber).
3.3.3. Application of Alignment Theory to Fiber Bundle Selection
In this section, the alignment issues are quantified for specific fiber bundle
geometries, and the optical fibers and steel tubing are selected. Equations 3-1 through 3-
3 were used to determine the gauge and wall thickness of the steel tube that minimizes
the worst case alignment errors in the optical microphone. Table 3-1 shows the worst
case bundle position errors when combining various steel tube gauges from Popper &
Sons  with different Tx and Rx optical fibers. The design selected for this thesis was
the first entry in Table 3-1. This design provided the best balance between minimizing
errors and availability of standard optical connectors.
Table 3-1 Error Analysis of Different Fiber Bundle Configurations
S ID OD FiberDIA ERR1 ERR2 BPE BPE
Design Tubing Nr
g (m) (Gtm) (|tm) (|tm) (|tm) (|tm) Norm
x: 105/125 21HW 457.2 812.8 375 93.6 41.1 134.7 0.2694
x: 105/125 20RW 622.3 901.7 375 49.15 123.65 172.8 0.3456
x: 0/25 21TW 609.6 812.8 575 93.6 17.3 110.9 0.2218
Tx: 105/125 20RW 622.3 901.7 575 49.15 23.65 72.8 0.1456
x:0/25 21RW 533.4 812.8 475 93.6 29.2 122.8 0.2456
x:00/25 20RW 622.3 901.7 475 49.15 73.65 122.8 0.2456
x:200/225 21XXTW 711.2 812.8 675 93.6 18.1 111.7 0.2234
Tx:200/225 20XTW 723.9 901.7 675 49.15 24.45 73.6 0.1472
x:5055 21HW 457.2 812.8 165 93.6 146.1 239.7 0.4794
x:5055 20RW 622.3 901.7 165 49.15 228.65 277.8 0.5556
Tx: 105/125 21HW 457.2 812.8 235 93.6 111.1 204.7 0.4094
x: 105/125 20RW 622.3 901.7 235 49.15 193.65 242.8 0.4856
x:055 21HW 457.2 812.8 305 93.6 76.1 169.7 0.3394
The design used by Kadirval's optical microphone was a Tx: 50/55, Rx: 50/55
design fabricated by Romack. It is evident from Table 3-1 that this design could have
significant alignment issues if special packaging techniques are not used. Romack used a
compound tube structure with a smaller tube containing the fibers and a larger tube
housing the small tube.
FABRICATION OF THE OPTICAL MICROPHONE
The fabrication of the optical microphone consists of two parts: (1) the MEMS
optical diaphragm chip, and (2) the fiber bundle. The MEMS chip containing the silicon
nitride diaphragm was fabricated by MEMS Exchange, an umbrella organization that
combines the processing capabilities of many foundries across the country . The
fiber bundle was fabricated at the University of Florida.
4.1. MEMS Exchange Process
The process flow used in the MEMS Exchange process was a modified version of
the process flow designed by Kadirval . Both mask and wafers were purchased
through the MEMS Exchange. The mask was designed at the University of Florida.
Table 4-1 summarizes the wafers used for fabrication of the optical microphone.
Table 4-1 Wafers Used for Optical Microphone Fabrication 
Number of .
r of 5 Material silicon Diameter 100 mm
double side 500 525
Surface Finish s Thickness Orientation <100>
Doping Type n-type Quality prime Resistivity / c
Q / cm
Initial State virgin Source MX Price per19.95
The process grows the membrane layer out of silicon nitride, and uses a DRIE to
etch the bulk silicon and leave the nitride membrane. Silicon dioxide was used as an etch
stop for the DRIE. The detailed process flow is shown in Appendix A.
Not shown in Appendix A are steps to mount and demount the wafer onto a
handle wafer to provide mechanical support during the DRIE.
4.2. Packaging Process
Different novel packaging strategies for an optical microphone have been
proposed [29,30]. Abeysinghe  notes that "adhesives limit the range of operation of
the sensors." To minimize the amount of adhesives used, the cavity is etched at the end
of the fiber and an anodic bonding process is employed to bond an ultra-thin silicon
wafer to the end of the fiber to serve as a membrane . A diagram of the packaging
technique described in  is shown Figure 4-1.
S IJ-Ultra-thin membrane
Figure 4-1 Abeysinghe et al. Packaging Technique.
This packaging technique provides a compact device with a sensor head that is the
diameter of the optical fiber. It would function as a pressure sensor in the configuration
shown above (no vent channel), but modifications could be made to add a vent channel.
With this design, it is difficult to control the mechanical properties of the membrane.
Another possible drawback of the package is the size of the cavity. Depending on the
dimensions of the fiber, the optimal equilibrium membrane position may have both
intensity and interference modulation effect present. If both these effects are present, the
theoretical analysis of the device performance will be very difficult.
A similar packaging technique is proposed by Beggans et al. . Beggans'
technique is more useful for an intensity-modulated device. First, a cavity is machined in
a glass wafer. Then, a hole with a diameter which can accompany an optical fiber is
drilled at the bottom of the cavity through the glass substrate. An ultra-thin silicon wafer
is anodically bonded to the glass substrate, creating a cavity. An optical fiber is inserted
into the cavity through the hole drilled in the substrate and fixed with a bonding agent.
The resulting device is shown in Figure 4-2.
This package allows more flexibility in membrane diameter and equilibrium gap
position, but it does not provide as much control over the equilibrium gap position. As
the fiber is being positioned, an active measurement technique is required to verify
Both techniques presented thus far do not protect the optical fibers. The ideal
package would provide some mechanical support for the optical fibers to reduce the
chances of device breakage. The packaging technique proposed by Kadirval  provides
protection for the fibers by using a fiber bundle like the type described in this thesis. The
optical fibers are protected by a steel tube and furcation tubing. Multiple MEMS chips
with through-wafer holes (identical to those used in this thesis) are bonded together in the
package. All but one of these chips has the diaphragm removed, and they are used to
make a handle wafer stack. The steel tube containing the fiber bundle is inserted through
the handle wafer stack, and the membrane wafer is placed on the top of the wafer stack.
An illustration of the proposed technique is shown in Figure 4-3.
Figure 4-2 Beggans et al. Packaging Technique.
This technique provides both a compact package and support for the fibers. A
drawback is the potential angular misalignment (other than normal light incidence)
between the fiber and the membrane. The worst-case angular misalignment depends on
the diameter of the steel tube and the thickness of the handle wafer stack. Increasing the
thickness of the handle wafer stack and decreasing the difference between the diameter of
the fiber and the wafer hole will reduce the worst-case angular misalignment.
4 Ultra-thin membrane
__ Machined cavity
MEMS Diaphragm Chip
Handle Wafer Stack
Figure 4-3 Kadirval Packaging Technique.
The technique for packaging the optical microphone design proposed in this thesis
is similar to . In this proposed package, a second steel tube is used in place of a handle
wafer stack. This steel tube (package tube) would have an inner diameter equal to the
outer diameter of the steel tube (bundle tube) used in the fiber bundle construction
(approx 830 [tm). An illustration of this package is shown in Figure 4-4. Standard
available tubing gauges (Popper & Sons ) can provide a flush fit to within tens of
microns for this package configuration. The package tube can be an inch or more long.
Using simple geometry, the worst-case angular misalignment can be calculated.
Assuming a worst case gap of 50 |tm between the bundle steel tube and package steel
tube (a reasonable assumption based on available tube gauges), and assuming the
minimum length of 1 in. (25,400 [tm) for the package steel tube, the maximum angular
misalignment of the bundle tube in the package tube is 0.113. If a 2 in. package tube
were used, then the maximum angular misalignment becomes 0.056 o. Therefore, it can
be concluded that this packaging strategy is capable of virtually eliminating angular
The primary advantages of this package are that it simultaneously provides a
robust package and minimizes the worst case angular misalignment error between the
fiber bundle and the membrane, as demonstrated in the previous paragraph. Also, the
dimensions of the package steel tube can be chosen to either minimize package diameter
or to fit a commercially available calibrator such as the Bruel & Kjaer 4231 Microphone
Calibrator . In addition, the outside of the package steel tube could be threaded to
allow a protective screen to be attached over the membrane, protecting it from damage.
For an example of this type of protective screen, see those used by Bruel & Kjaer
1" , 1/2" , and 1/8"  microphones. Another advantage of this package is the
ability to take multiple packaged optical microphones and easily assemble them into a
microphone array bundle.
N IE IS Diaphragm Chip
Package Steel Tube
Bundle Steel Tube
Figure 4-4 Proposed Package for the Optical Microphone.
In the top view in Figure 4-5, seven packaged optical microphones are shown in a
bundle surrounded by an array package steel tube, whose dimensions would be selected
to make the fit as tight as possible. The cylindrical structure of the individual
microphone packages allows the microphone array geometry to be a scaled version of the
fibers in the individual microphone package. This allows an arbitrary number of "rings"
of packaged microphones to be used in the array, without the individual packaged
microphones interfering (mechanically) with each other. In addition, the cylindrical
structure of the proposed array package would be easy to construct, using only a custom
steel tube and epoxy to hold it together. Due to the steel tubing, this proposed array
package would be very robust.
2.5 mm 1mm
Figure 4-5 Proposed Optical Microphone Array Package.
In Figure 4-5, the membranes have been removed from the square chips to show
the individual microphone cavity positions. This proposed microphone array could
sample the acoustic field on the center 50 utm of the 1 mm diameter diaphragm. Each
diaphragm is 2.5 mm from each of its neighbors. Finally, the performance of the
microphones in the array is independent of the number of microphones in the array
(assuming the array package does not affect the sound field and availability of sufficient
light sources, detectors, etc).
EXPERIMENTAL SETUP AND RESULTS
The experimental characterization of the optical microphone is divided into three
sections. First is the experimental characterization of the laser and photodetector. This
characterization measures the value of Plaser noise(Plaser) (compare to Plight noise in Chapter
2). The experimentally measured value Piaser noise(Plaser) is used as an input to the
theoretical model of the microphone presented in Chapter 2.
Second is the static calibration of the custom fiber bundle. This static calibration
attempts to verify the theoretical power coupled vs. equilibrium gap and sensitivity vs.
equilibrium gap plots. The static calibration curve measured in this experiment is used to
identify the location of the fiber bundle with respect to the membrane in the dynamic
The final experimental step is the dynamic calibration of the optical microphone.
In the dynamic calibration, a plane wave tube (pwt), speaker, and calibrated microphone
are used to determine the optical microphone sensitivity, linearity range, frequency
response, noise floor, dynamic range, and minimum detectible signal. The experimental
results are then compared with the theoretical predictions. The dynamic calibration is
performed for both the unreferenced and referenced output microphone configurations.
5.1. Laser and Photodetector Characterization
5.1.1. Experimental Setup for Laser and Photodetector Characterization
In the characterization of the laser (or other light source), the optical spectrum of
the photodetector was measured for laser outputs of 100 pW through 500 [IW, in steps of
50 LiW. The noise power spectral density of the detector output, in V / Hz", was
recorded by the Pulse system from 0 6.4 kHz with a bin width of 1 Hz and using 500
samples. This value is the RMS sum of the detector noise and detected light intensity
noise, both in V / Hz"2. The optical intensity noise component of the detector noise is
determined by removing the theoretical Vdet from the measured value, leaving Vlight (see
Section 2.2.4 for variable definitions). By dividing Vlight by the photodetector
responsivity and gain, the optical intensity noise of the laser, in V / Hz1/2, can be
ISS-1550 PDA-400 System Ethernet Port
Opto-isolator Photodetector S E
-.......... ......... -- -
Electrical Signal .................. System Input [F[fj
Optical Signal System Output
Acoustical Signal ---- System Component
Figure 5-1 Experimental Setup for Laser Characterization.
The DC optical power was obtained by observing the 0 Hz frequency bin. The
worst-case light source noise recorded at 660 Hz, and the best-case noise (where the laser
noise became constant with respect to frequency) was measured at 1600 Hz. The
experimental setup for the laser noise characterization is shown in Figure 5-1.
5.1.2. Results of Laser and Photodetector Characterization
The experimentally measured value for Plaser noise is given by the last column in
Table 5-1. The HP8168B was observed to have a flat noise floor above 1550 kHz.
Below 1.55 kHz, the noise floor was not flat. Since this system would ideally be used
with a heterodyne detection scheme to operate the microphone in the flat noise range of
the light source, the laser linearity and MDS will be experimentally measured above 1550
Hz. For all laser characterization experiments, Gdet = 15,000 V / A.
Table 5-1 Experimental HP8168B Noise
Measured Noise @ Calculated Laser Laser SNR
1600 Hz Noise @ 1600 Hz @ 1600 Hz
(lW) (uV / Hz1/2) (pV / Hz1/2) (dB)
100 0.741 52.0 53.0
150 1.29 90.2 52.4
200 1.53 108 52.9
250 1.06 74.4 55.6
300 1.98 139 53.6
350 0.774 54.3 58.4
400 1.68 118 55.7
450 3.59 252 52.9
500 3.26 229 53.9
The laser was observed to have a maximum SNR at Plaser =350 |LW. Therefore,
this value will be used to characterize the laser.
5.2. Static Calibration
5.2.1. Experimental Setup for Static Calibration
The static calibration of the optical microphone has two goals. The first goal is to
verify the corrected power coupled model presented in Chapter 2. The second goal is to
obtain a power coupled curve for the fiber bundle under consideration, so that it may be
used to measure the equilibrium gap of the assembled microphone package. The
procedure for this is described further in the dynamic calibration section.
In the static calibration experiment used by Kadirval , the fiber bundle is
placed flush against a metal mirror. To align the fibers normal to the mirror, Kadirval
assumed that the power coupled into the receive fibers was maximum when the fibers
were aligned normal to the mirror. While there may be a range of equilibrium gap
distances that this assumption is valid for, it is not valid in general, and will result in the
proper alignment of the fibers with the mirror. Kadirval used a micropositioner to move
the fiber bundle with respect to the mirror. Due to the way in which the fiber bundle was
mounted, the fibers were able to slip in the mechanical mount as the micropositioner was
moved. Due to these two problems with the previous static calibration experiment in ,
the gap measurements reported by the micropositioner were significantly larger than their
actual values, resulting in an incorrect calibration curve.
In this thesis, these two issues have been fixed. The mechanical mounts for the
fiber and the mirror were aligned normal to each other by cubic blocks, which have
parallel surfaces. The mirror was mounted on the micropositioner and was moved with
respect to the fiber bundle, whose position was fixed. The zero position of the mirror was
set by slowly moving the mirror with the micropositioner until mechanical contact with
the mirror was observed. After mechanical contact has been made, the fiber holder is
closed, fixing the fiber bundle in place. Note: the mirror used in these experiments was
slightly rusted and had scratches on its surface. The method of zeroing used here can
potentially scratch the mirror, so it should not be used with a mirror in good condition.
An electrical contact method could be used instead.
The static calibration setup used for the optical microphone is similar to the setup
used by Kadirval  except as noted in the previous paragraph. The experimental setup
for the static calibration is illustrated in Figure 5-2. In Figure 5-2, the custom fiber
bundle is oriented normal to a reflective mirror, which is mounted on a computer-
controlled micropositioner. The computer-controlled micropositioner is automated by a
Labview application to sample the power output of a reference channel and the output of
the fiber bundle. After taking 30 samples, the micropositioner adjusts the mirror position
relative to the fiber bundle and repeats the measurement. This step-and-sample process
continues until cancelled by the user.
The light source used is the LPS-SMF28-1550-FC laser diode operated in
constant current mode by a Keithley 2400 constant current source. Laser light is passed
through a Newport ISS-1550 optical isolator and is split by a 50/50 optical power splitter.
One output of the splitter delivers light into the Tx fiber of the custom fiber bundle. This
light reflects off of the mirror and is collected by the receive fibers, which transport the
light to a PDA-400 detector (TEST). The second splitter output delivers light directly to
another PDA-400 (REF). A Keithley 2000 multimeter controlled by a Labview
application sampled the TEST and REF detector outputs, and sends the data to a
computer where it is recorded in a file along with the micropositioner position. The gain
of the PDA-400 detectors in the static calibration is 15,000 V / A.
After the experiment is complete, the recorded detector outputs are corrected for
the experimentally measured bias errors of each photodetector. Dividing the bias-
corrected TEST data by the bias-corrected REF data and plotting it with respect to the
measured gaps produces the experimental power coupled curve. The results of the static
calibration are presented in the next section.
Keithley 2400 ISS-1550
Keithley 2000 Photodetector
Figure 5-2 Block Diagram of Static Calibration.
5.2.2. Results of Static Calibration
The output of the static calibration is an experimental plot of optical power
coupled vs. equilibrium gap distance. This plot is shown in Figure 5-3 shows the static
calibration curve for the optical microphone using the custom fiber bundle. The plot also
shows the theoretically predicted curves for an RPE of 0 ptm and an RPE of 10 ptm. The
maximum power coupled is slightly higher than theoretically predicted, and the location
of the peak power coupled is at a larger gap than predicted.
0 100 200 300 400 500 600 700
-RPE =0 um -RPE =100 um r Expenmental
Figure 5-3 Experimental Power Coupled vs. Equilibrium Gap.
800 900 1000
The location and magnitude of the max slope of the experimental curve was
determined by fitting a regression line to points in a 30 |tm window on the experimental
power coupled curve. The location of the maximum slope of the regression line was
assumed to be the gap at the maximum slope, and the maximum slope of the regression
line was assumed to be the peak slope of the experimental power coupled curve. The
regression line at the peak slope is shown in Figure 5-4.
Table 5-2 Comparison between Theoretical and Experimental Static Calibration
Category (RPE = 0 jim) (RPE = 10 m) experimental
Peak Power Coupled 21.6 % 17.2 % 22.1%
Gap @ Peak Power (,m) 500 530 600
Power Coupled @ Max 52 4.2 10.9
Gap @ Max Slope (rtm) 230 260 360
Maximum Slope (tm-1) 1.094 x 10-3 0.784 x 10-3 0.800 x 10-3
200 240 280 320 360 400 440 480 520 560 600
Figure 5-4 Experimental Maximum Power Coupled Regression Line Slope.
The R2 value of the regression line in Figure 5-4 indicates the MO stage is linear
over the gap region from 350 |tm to 380 |tm. Since the membrane deflection is much less
than 30 |tm, the MO stage is linear when operated at the maximum sensitivity.
In both Figure 5-3 and Figure 5-4, the experimental power coupled curve is much
less smooth than the theoretical curve. At some gap values the power coupled seems to
be discontinuous with the surrounding power coupled points. This is believed to be
caused by two phenomena. The first cause is table vibrations. The optical table on which
R 2 0.9948
the experiments were performed was not isolated from the ground by a cushion of
compressed air. This allows acoustic vibrations traveling through the floor of the room to
vibrate the mirror during the measurement. The second cause is the roughness of the
mirror surface. The mirror used in this experiment was observed to have scratches and
rust spots on the mirror surface. Light interacting with the scratches and rust spots can
cause discontinuities in the measured power coupled.
5.3. Dynamic Calibration
5.3.1. Experimental Setup for Dynamic Calibration
The goal of the dynamic calibration is to characterize the sensitivity, minimum
detectable signal, electronics noise, linearity, and frequency response of the unreferenced
and referenced optical microphone configurations, and to compare the experimental
performance of the microphone with the theoretical performance.
In the both unreferenced and referenced output calibration experiments, the cut-on
frequency of the SRS 560 was 30 Hz, the gain of the SRS 560 was 1 V / V, and the trans-
impedance gain of the PDA-400 detector(s) was 15,000 V / A. Data is taken with the
Pulse system from 0 Hz 6.4 kHz with a 2 Hz bin width. All single tone measurements
were made with a sinusoidal input at 1600 Hz. A uniform window was used to measure
single tone signals, and a Hanning window was used for measuring broadband or noise
signals. In all experimental setups (Figure 5-5 and Figure 5-6), a B&K 4138 1/8"
microphone , pre-calibrated with a B&K 4228 pistonphone , is used as a
reference microphone. This microphone is mounted next to the optical microphone at the
end of the plane wave tube, and it connected to an input channel of the Pulse system (not
shown in Figure 5-5 and Figure 5-6). The experimental setups for the optical microphone
dynamic calibration are similar to the setup used by Kadirval .
Pulse System Amplifier JBL Speaker and
m Plane Wave Tube
...... ............. > .....P.a.ub.
Ethernet Port Pulse System
SRS 560 Filter / Amp
Figure 5-5 Unreferenced Output Optical Microphone Configuration.
A "power coupled alignment" technique is introduced for measuring the
equilibrium gap. This technique makes a power coupled measurement as the fiber bundle
and membrane chip are mounted on the custom plane wave tube (PWT) plug and relates
the power coupled measurement to an equilibrium gap by the static calibration curve.
The first experimental setup is the unreferenced output configuration, shown in
Figure 5-5. The optical splitter is not required for operation of the microphone in this
configuration. In the unreferenced output configuration, the system output is taken at the
output of the SRS 560 Filter / Amplifier.
Pulse System Amplifier
JBL Speaker and
Computer Plane Wave Tube
Computer 1 I0*MOD
Ethernet .. .
SRS 560 Filter / Amp Analog Divide Circuit
Figure 5-6 Referenced Output Optical Microphone Configuration.