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1 DIAGNOSTICS FOR MAPPING A LASER INDUCED PLASMA By DANIEL SHELBY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSO PHY UNIVERSITY OF FLORIDA 2011
2 2011 Daniel Shelby
3 To ThumbWars, 985 5480 and Team Upstairs
4 ACKNOWLEDGMENTS I thank Dr. Nicol Omenetto for being an admirable advisor. He has always kept his door open for questions and his mouth closed when they we re ignorant. He has humbled me by showing me the absolute limits on how much one person can know. Along with Dr. Ben Smith, a graduate student could not desire a better team to show him how little he knows and how far he can go. I thank Dr. Gary Hieftje for making my infancy in the scientific community an inviting one and pointing me to work for a very good and wise group of advisors. I thank my predecessors, Dr. William Wetzel, Dr. Gerardo Gomez, Dr. Benoit Lauly, and Dr. Nicolas Taylor. Their hands on experience gave me the courage and foolishness to dive into instrumentation head on. I firmly believe that I only understand as much as I do now because I had their knowledge and experience to propel me beyond my years. I thank my contempor aries, Greg Bishop, Jonathan Merten, Andrew Warren, Jared Lynch, Warren and Kyle Mino, and Dave and Natasha Pirman Periodic discussions during relieving breaks reassured me that I was not so off track as I had feared. T ravelling with them made it seem n ot so daunting. I thank my family Amanda, Julia, Ed, Sandy, Salah and Rachel for tolerating my moving across the country in pursuit of a continued education. I thank them for being there when I have needed them after not heeding them. I thank them for r eminding me that down in the dumps, I should never go.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 SCOPE OF STUDY ................................ ................................ ................................ 15 Introduction to LIBS ................................ ................................ ................................ 15 Laser Induced Fluorescence ................................ ................................ .................. 17 Instrumentation ................................ ................................ ................................ ....... 19 General Geometry ................................ ................................ ............................ 19 Fluorescence Excitation ................................ ................................ ................... 21 Spectrograph ................................ ................................ ................................ .... 24 CCD Binning ................................ ................................ ................................ ..... 26 Monochromator ................................ ................................ ................................ 27 Timing ................................ ................................ ................................ ............... 28 Absorption Source ................................ ................................ ............................ 30 2 SPATIALLY RESOLVED EMISSION ................................ ................................ ...... 37 Motivation ................................ ................................ ................................ ............... 37 Temperature and Electron Number Density Considerations ................................ ... 38 Experimental ................................ ................................ ................................ ........... 42 Results ................................ ................................ ................................ .................... 45 Conclusions ................................ ................................ ................................ ............ 47 3 SCHLIEREN IMAGING ................................ ................................ ........................... 53 Motivation ................................ ................................ ................................ ............... 53 Premise of Schlieren Imaging ................................ ................................ ................. 55 Sedov Taylor Blast Wave ................................ ................................ ....................... 59 Experimental ................................ ................................ ................................ ........... 60 Results ................................ ................................ ................................ .................... 62 Time Dependence ................................ ................................ ............................ 62 Energy Dependence ................................ ................................ ......................... 63 Density Dependence ................................ ................................ ........................ 64 Conclusions ................................ ................................ ................................ ............ 65
6 4 SPATIALLY RESOLVED LASER INDUCED FLUORESCENCE ............................ 72 Motivation ................................ ................................ ................................ ............... 72 Experimental ................................ ................................ ................................ ........... 74 Results ................................ ................................ ................................ .................... 77 Atomic Fluorescence ................................ ................................ ........................ 77 Ionic Fluorescence ................................ ................................ ........................... 78 Vertically resolved ................................ ................................ ...................... 78 Horizontally resolved ................................ ................................ .................. 79 Conclusions ................................ ................................ ................................ ............ 82 5 TIME RESOLVED LASER INDUCED FLUORESCENCE ................................ ...... 92 Motivation ................................ ................................ ................................ ............... 92 Temperature Measurements ................................ ................................ ................... 94 Experimental ................................ ................................ ................................ ........... 97 Results ................................ ................................ ................................ .................. 100 Temperatures ................................ ................................ ................................ 100 Removing Volumes from Calculated Temperatures ................................ ....... 104 Response Times ................................ ................................ ............................ 106 Conclusions ................................ ................................ ................................ .......... 110 6 CONCLUSIONS ................................ ................................ ................................ ... 122 Completed Project Goals ................................ ................................ ...................... 122 Future Project Goals ................................ ................................ ............................. 123 LIST OF REFERENCES ................................ ................................ ............................. 128 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 14 2
7 LIST OF TABLES Table page 1 1 Properties of the dye lasers used in this study. ................................ .................. 35 2 1 Composition of the D33 aluminum alloy used in this study in mass percent. ..... 49 2 2 Central wavelengths for the nine spectral windows used in this study along with the relevant lines and associated spectroscopic quantities. ....................... 50
8 LIST OF FIGURES Figure page 1 1 General schematic for the proposed instrument. ................................ ................ 33 1 2 Spectral width of dye laser centered at 283.305 nm. ................................ .......... 33 1 3 Absorption profiles of lead in a LIP at several del ays after the plasma formation. ................................ ................................ ................................ ........... 34 1 4 Time profiles of the excimer, dye laser, and doubled dye laser pulses. .............. 34 1 5 Effect of on chip binning for the CCD. ................................ ................................ 35 1 6 MCP response to an LED as a function o f applied voltage. ................................ 35 1 7 Timing schematic for triggers and lasers. ................................ ........................... 36 1 8 Conversion between time and frequency for tuning the diode laser. .................. 36 2 1 Trigonometry for optical emission collection. ................................ ...................... 48 2 2 Diagram of raster across the plasma profile. ................................ ...................... 48 2 3 Map of the T determined from the Saha Boltzmann plot in CF LIBS. ................. 51 2 4 Map of the electron number density from the fitting of the H alpha emission line. ................................ ................................ ................................ ..................... 51 2 5 Maps of the aluminum distribution within the plasma. ................................ ........ 52 2 6 Maps of the silicon distribution withi n the plasma. ................................ .............. 52 2 7 Maps of the magnesium distribution within the plasma. ................................ ..... 52 3 1 Schematic for a generic lens schlieren system working in the dark field. ........... 67 3 2 Comparison between bright and dark field cutoffs for schlieren imaging. ........... 67 3 3 Progression fro m dark to bright field schlieren by moving a horizontally oriented pinpoint cutoff horizontally. ................................ ................................ ... 67 3 4 Progression from bright to dark field schlieren by moving a horizontally oriented pinpoi nt cutoff vertically. ................................ ................................ ....... 68 3 5 Schematic for the optics used in the schlieren imaging for this work. ................. 68
9 3 6 Image taken from WinSp ec32 for measuring the propagation of the shockwave by bright field schlieren imaging. ................................ ...................... 69 3 7 Shockwave expansion by bright field from a LIP formed with 69 mJ/pulse. ....... 69 3 8 Image taken from WinSpec32 for measuring the propagation of the shockwave by dark field schlieren imaging. ................................ ........................ 70 3 9 Shockwave expansion by dark field from a LIP formed with 69 mJ/pulse. ......... 70 3 10 Energy dependence of the shockwave produced by a LIP at atmospheric pressure. ................................ ................................ ................................ ............ 71 3 11 Density dependence of the shockwave produced by a LIP at 49 mJ/pulse. ....... 71 4 1 Examples of the vertical extent of the plasma at two delays. ............................. 84 4 2 ....... 84 4 3 .. 85 4 4 Spatially integrated Pb I emission and fluorescence signals at delays. .............. 85 4 5 Examples of the Pb I parsed emission and fluorescence c urves obtained at three heights within the plasma. ................................ ................................ ......... 86 4 6 Waterfall plot of vertically parsed Pb I emission data. ................................ ........ 86 4 7 Waterfa ll plot of vertically parsed Pb I fluorescence data. ................................ .. 87 4 8 Spatially integrated Ba II emission and fluorescence signals at delays. The spatial integration is along the vertical axis within t he plasma. ........................... 87 4 9 Examples of the Ba II vertically parsed emission and fluorescence curves obtained at three heights within the plasma. ................................ ...................... 88 4 10 Waterfall plot of vertically parsed Ba II emission data. ................................ ....... 88 4 11 Waterfall plot of vertically parsed Ba II fluorescence data. ................................ 89 4 12 Spatially integrated Ba II emission and fluorescence signals at delays from a LIP of 11% Ba by mass. The spatial integration is along a horizontal axis within the plasma. ................................ ................................ ............................... 89 4 13 Spatially integrated Ba II emission and fluorescence signals at delays from a LIP of 0.5% Ba by mass. The spatial integration is along a horizontal axis within the plasma. ................................ ................................ ............................... 90
10 4 14 E xamples of the Ba II horizontally parsed emission and fluorescence curves obtained at three positions within the plasma. ................................ .................... 90 4 15 Waterfall plot of horizontally parsed Ba II emission data. ................................ ... 91 4 16 Waterfall plot of horizontally parsed Ba II fluorescence data. ............................. 91 5 1 Temperature dependence of the precision of the calcula ted temperature from a 10% error within the observed ratio. ................................ .............................. 112 5 2 Separation of energy level dependence of the precision of the calculated temperature from a 10% error within the observed ra tio. ................................ .. 112 5 3 Lens geometry for spatially selecting regions of the plasma. ........................... 113 5 4 Energy level diagram for Ba II. ................................ ................................ ......... 113 5 5 Temporal profile of the excitation pulse at 455.403 nm. ................................ ... 114 5 6 Repeatability of 4 temporal profiles of the 614.171 nm direct line flu orescence each averaged from 500 laser shots. ................................ .......... 114 5 7 Temperatures calculated from the direct line fluorescence at 614.171 nm about 1 mm from the surface. ................................ ................................ ........... 115 5 8 Temperatures calculated from the direct line fluorescence at 614.171 nm grazing the surface. ................................ ................................ .......................... 115 5 9 Temperatures calculated using the conventional Boltzmann plot method on D33 aluminum alloy under the same conditions as the Ba II studies. ............... 116 5 10 Temperatures calculated with errors propagated from interpulse standard deviations. ................................ ................................ ................................ ........ 116 5 11 Temperatures calculated from the direct line fluorescence at 489.997 nm after excitation by 452.493 nm. ................................ ................................ ......... 117 5 12 Temperatures calculate d from the collisionally coupled emission at 389.178 nm after excitation by 455.403 nm. ................................ ................................ ... 117 5 13 Temperature correction for volume ratio between emission and fluorescence . 118 5 14 614.171 nm emission and fluorescence traces ................................ ................ 118 5 15 389.178 nm emission and fluorescence traces. ................................ ................ 119 5 16 Fluorescence traces for 614.171 and 389.178 nm along with scatter from the excitation laser at 455.403 nm. ................................ ................................ ......... 119
11 5 17 Effect of normalization on a saturated flu orescence signal. .............................. 120 5 18 Response times calculated from difference between the half intensity of the direct line fluorescence at 614.171 nm and collisionally coupled line at 389.178 nm. ................................ ................................ ................................ ...... 120 5 19 Fluorescence traces for 489.997 and 389.178 nm along with scatter from the excitation laser at 452.493 nm. ................................ ................................ ......... 121 6 1 Absorpti on of a diode laser as it is tuned away from the center of an argon metastable absorption profile. ................................ ................................ ........... 127
12 LIST OF ABBREVIATION S CCD Charge Coupled Device CF LIBS Calibration Free Laser Induced Breakdown Spectroscopy ICCD Inte nsified Charge Coupled Device LEAF Laser Excited Atomic Fluorescence LIBS Laser Induced Breakdown Spectroscopy LIF Laser Induced Fluorescence LIP Laser Induced Plasma LOD Limit of Detection MCP Multichannel Plate Nd:YAG Neodymium doped Yttrium Aluminum Gar net OPO Optical Parametric Oscillator PMT Photomultiplier Tube Q switch Quality Factor Switch RELIBS Resonance Enhanced Laser Induced Breakdown Spectroscopy ROI Region of Interest
13 Abstract of Dissertation Presented to the Graduate School of the Unive rsity of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DIAGNOSTICS FOR MAPPING A LASER INDUCED PLASMA By Daniel Shelby August 2011 Chair: Nicol Omentto Major: Chemistry While laser induced br eakdown spectroscopy (LIBS) is an attractive technique because of its portability, ease of execution and built in sample preparation, the technique suffers from poor precision. When compared to other plasma emission techniques, primarily inductively coupl ed plasma (ICP), its higher relative standard deviations increase its limits of detection. So much so that LIBS is primarily used to detect only the major elements of a sample. Depending on the spectroscopic properties of the element, some trace identifi cation is possible, e.g. magnesium. Much of this imprecision stems from the coupling of the sampling, atomizing and exciting processes. For ICP analysis, the sampling is accomplished through digestion and the atomization and excitation occur in an almost static plasma. All three of these processes occur almost simultaneously in the laser induced plasma (LIP) which is complicated by its dynamic nature. Since each plasma lasts only several tens of microseconds, a limited amount of information is available from each interrogation. Accordingly, sometimes thousands of plasmas are formed during a single acquisition of data. As each of these plasmas is slightly different in its evolution, the analytically relevant radiation varies between them.
14 The goal here, as many spectroscopy techniques as is possible Each technique lends more insight into the spatial and temporal structure within the plasma. A spatially selective emission strate gy alongside two laser probe methods are evaluated for the purpose of mapping Moreover, by using a fast detector coupled with fast electronics, an attempt at the direct experimental evaluation of time resolved coll isional rate constants at several delays of plasma evolution is described. This is believed to be the first time such an attempt has been made within a LIBS plasma.
15 CHAPTER 1 SCOPE OF STUDY Introduction to LIBS As an analytical technique, LIBS is very straightforward instrumentally; however the physics behind the phenomenon are complex  The basic and most common setup consists of a solid state Nd:YAG laser operating at the fundamental wavelength of 1064 nm. The laser beam is focused through a convex lens to produce a point focus with a power density greater than 0.5 GW/cm 2  A breakdown of this kind on the surface is composed of a mixture of material and ambient atoms and ions as well as their counterparts, free electrons. Plasma formation begins with the intense emission of continuum followed by analytical line emission of ions and atoms as the prior recombines with lower energy free electrons. These plasmas are characterized by electron number densities near 10 17 cm 3 and temperatures beginning near 20000 K and settling to 8000 K [3, 4 ] Emission from the plasma is collected by a lens system, optical fiber or some combination therein. Detection depends on the application, but the most common is a spectrograph equipped with charge coupled device (CCD) array detector. The concept of us ing a focused laser beam for the production of an emissive plasma was made reality very shortly after the production of the first lasers. In 1962, Brech and Cross were the first to present data from such an arrangement, though they did not publish  LIP continued to be a focus of research, although the topics shared more with fundamental physics [6 8] Despite the quick inception, some years passed before the technique developed much stand alone activity in spectroscopy. The name, LIBS, did not surface for twenty years  With the establishment of the technique for
16 analytical chemistry [10, 11] the figures of merit were quickly established and the advantages of LIBS were highlighted, noninvasive  no sample preparation  and field portability  By this time, much was known about the various regimes of laser power density and t heir applications to machining and metal working  however there was not a unified field of researchers using the technique for analytical chemistry. The spectroscopy of these interactions grew with advent of gated detectors. This coevolution stemmed from the continuum emission at the birth of the LIP. Bremsstrahlung from the free electrons emits a strong, short lived continuum which covers the visible and UV spectrum. For this reason, integrating detection such as photographic plates are difficult to apply to LIBS detection. In itially, the gated detector was a photomultiplier tube (PMT) or photodiode array (PDA) with a pulsed power source. A PMT that was saturated by the initial continuum could be made blind at those times. Unfortunately, this still prevented spectrally resolv ed detection. Additionally, PDAs did not have the sensitivity of a PMT which limited their application to strong lines. LIBS found a true partner in CCDs. Once the solid state array detector become widely available in the 199 0s their application to imag ing and spectroscopy was immediate. With the subsequent addition of intensifiers (ICCD), the sensitivity of the detector was sufficient for even weak lines and the array of pixels was 2 dimensional. Not only could the CCD resolve lines spectrally but spa tially in the direction parallel to the grooves of the diffraction grating for a conventional Czerny Turner spectrograph. Throughout this time, laser sources were becoming more reliable and compact. Thorough studies of wavelength and pulse duration proper ties of LIP made the
17 application of LIBS more successful  As with any technique, LIBS is not a panacea  Although the laser properties are better controlled and understood, the interaction between laser pulses and material is strongly dependent on the material and surroundings [16 18] Minimizing this effect with the proper marriage of material and l aser properties ensures that LIBS does not become a pariah. This could very quickly be true if researchers ignore the noise present in all LIBS analyses  Laser Induced Fluorescence Another laser technique, laser induced fluorescence (LIF), had to wait several years before it could be applied to atomic spectroscopy. In this context, it is also referred to as lase r excited atomic fluorescence (LEAF). As the absorption band of atomic states is very narrow, atomic LIF needed a continuously tunable laser  Once this tool became available, study into atomic fluorescence induced by a laser source began [21, 22] At that time, it was stil l known as Selective Excitation Spectroscopy, and what we know as Saturation was named Infinite Temperature Equilibrium. Over the next two decades, atomic fluorescence was applied to most atom reservoirs, flames  furnaces  glow discharges [25, 26] ICP  hollow cathodes  and LIP [10, 29] Diagnostics were thoroughly studied for single and double probe geometries  as well as their application to ionization spe ctroscopy [31, 32] As can be seen from the citations above, some ten years after the first application of tunable dye lasers to atomic fluorescence, a system was developed that used LIP LIF. Kwong and Measures named their technique Trace (Element) Analyzer Based on Laser Ablation and Selectively Excited Radiation (TABLASER)  This early work f ocused on the application of atomic fluorescence in a LIP for the construction of
18 calibration curves. Certainly, using the plume of a LIP as an atom reservoir for atomic fluorescence increases the sensitivity of the measurement over LIBS  Measures continued some LIF work in LIPs [31, 35] but the method wa s dominated by LIF on small molecules as well as atoms by the electronics industry throughout the 198 0s [36 38] As was mention previously, the 199 0s saw a collabo ration form between LIBS applications and CCD detectors. Accordingly, the first resurgence of literature for LIBS LIF frequently uses a camera to image atomic fluorescence from a sheet of excitation [39 41] Primarily these papers are concerned with the spatial distribution of species within the plasma plume. Such information can optimize the analytical use of the plasma. Others obtain the spatial information by setting an observation height and measuring the fluorescence as a functio n of time [42 44] In the late 199 0s a couple of papers surfaced with an interesting application for LIBS LIF. The authors measure isotope ratios from fluorescence shifts in Li and U. The first application to Li uses a dye laser  This is consistent with the bulk of the work done in the field to that date. Applicat ion of this technique to U was accomplished with a diode laser as the excitation source  This appears to be one of the only applications of a diode laser for LIF within a LIP. LIBS is still an analytical technique, so many papers that combine these methods hope to refine calibrati on curves to reduce the LOD for this direct sampling method [47 50] To this point, much of the research had been done in a vacuum chamber where the ambient gas species and pressure had been closely controlled. The turn of the century also saw a rise in the application of this two laser technique to atmospheric conditions for solids [51, 52] aerosols [53 ] and liquid jets  In recent years, the
19 calibra tion curves have been obtained by optical parametric oscillators (OPOs) [34, 55 57] From the literature, it seems these continuously tunable lasers are replacing the conventional dye lasers used in most previous papers. Finally, a distinction should be made for atomic fluorescence within a LIP. There are two other techniques that share the same basic instrumental setup but differ greatly in their physical principles. First, double pulse LIBS contributes energy to the p lasma through the formation of another breakdown within the rarified atmosphere of the first  This is not a tunable or selective technique. Secondly, Resonance Enhanced LIBS (RELIBS) is very similar to atomic LIF within LIBS. The major difference between the work contained herein and RELIBS is the target of the selecti ve excitation [59 61] Enhancement from RELIBS comes from exc iting the major component within the plasma and allowing that deposited energy to distribute to the minor elements  An apparent fluorescence is detected for almost all minor elements. This fluorescence is tunable over the absorption of the major element. While the excitation is selective, the fluorescence is not. The work co mpleted here selectively excites only single atomic or ionic species. Also, RELIBS should be made distinct from Resonant Laser Ablation  Here the ablation la ser is tuned to an electronic transition to an analyte within the matrix. In this schematic, no secondary probe laser is used. Instrumentation General Geometry The goal of this research is to examine a laser induced plasma from as many spectroscopic angle s as is possible. To this end, an experimental setup is required that could accomplish traditional LIBS emission measurements as well as atomic
20 fluorescence and absorption. The overall geometry is shown in Figure 1 1. Each of these experiments also need ed to be completed with spatial or temporal resolution. As was stated above, the setup revolve s around a laser induced plasma. The data presented in this thesis is collected from a laser induced plasma formed by a pulsed, Nd:YAG laser (BigSky Ultra). Thi s ablation laser operate s at a fundamental wavelength of 1064 nm with a pulse width of 7 ns. It i s possible to vary the laser pulse energy up to a maximum value of 78 mJ. The plasma i s formed by focusing the laser through a plano cal length. Emission and fluorescence spectra are collected using plano convex lens pairs to alternately collimate and focus the image onto the slit of the monochromator or spectrograph. This arrangement is necessary over a single lens as the spacing betw een the plano convex lenses is arbitrary so long as the plasma is well placed at 1f of the collimating lens. In this fashion, the monochromator and spectrograph can be placed arbitrarily away from the plasma source. A common alternative to this arrangeme nt is the collection of emission by a single lens. In that configuration, both the object and image would be placed 2f from the lens. If both detectors are restricted to a 4f distance from the source, depending on the lens, proper placement of both detec tion systems would be overly complicated. Additionally, this lens combination gives higher resolution than a single bi convex lens  The plano convex lens pairs arrangement also allows for conve nient filtering in the collimated region. The monochromator and spectrograph are positioned off axis from one another. In other words, both detection systems could have been placed 90 with respect to the fluorescence excitation. However, this orientatio n would preclude the detectors from
21 being used for any absorption measurements. Accordingly, the monochromator is placed at a larger angle away from the incident laser beam used for atomic fluorescence. Because of small changes in the observation regions of the two detection systems, the laser and sample are mounted on an x y z stage. The entire plasma source could be moved to be centered at the focus of either the monochromator or spectrograph. Fluorescence Excitation The optical probe used for the fluo rescence studies is a dye laser (Scanmate 1, Lambda Physik). The cavity of the Scanmate dye laser i s defined by a front mirror and diffraction grating. Wavelength selection by the diffraction grating allows the dye laser to be tunable across the fluoresc ence of the dye. A circulator pump constantly moves the dye through the cell to avoid damage and subsequent burning by the probe laser. Primarily, two laser dyes are used in this study. A green dye, Coumarin 540A (C540A, Exciton), is used within the tun able range of 520 600 nm when diluted in methanol. A blue dye, Coumarin 450 (C450, Exciton), is used within the tunable range of 430 480 nm when diluted in methanol. Alignment within the dye laser determines the spectral purity of the laser pulse. A mplified spontaneous emission is a side effect of the geometry within the dye laser optics. With the proper alignment, this can be minimized, but affects the bandwidth of the dye laser output. The C540A dye output is frequency doubled to reach the 280 nm regime for probing a lead transition. This laser output is used to induce laser fluorescence inside of a hollow cathode lamp at 405.781 nm with excitation at 283.305 nm While the hollow cathode emission is constant, the fluorescence induced by the dye laser is transient, making it easily discernable from the hollow cathode emission. Within the hollow cathode lamp, the dominant broadening is
22 assumed to be Doppler at 600 K. Equation 1 1 predicts a line width of 0.4 pm when M is the molecular mass of lea  When an excitation scan is com pleted across the fluorescence from the hollow cathode lamp, Figure 1 2 shows a width of 4 pm. ( 1 1 ) Therefore, the dye laser output is an order of magnitude wider than the absorption profile of the lead within the hollow cathod e lamp. From this estimation, the real width of the laser is taken to be the 4 pm measured in Figure 1 2. In addition to measuring the spectral width of the dye laser, this work makes a quick investigation into the spectral width of the atomic lead line at 283.305 nm. Figure 1 3 reproduces the laser profile from Figure 1 2 alongside the normalized Gaussian fits of excitation scans of lead within a LIP at several delays. Clearly, the line width decreases with the increase in delay. In contrast to the hollow cathode source, the laser profile is narrower than the atomic transition at 1 s. Since these profiles are not deconvoluted, the profiles at 5 and 10 s cannot be said to be spectrally wider than the laser profile but they are certainly equal. Wh ile we only consider Doppler broadening within the hollow cathode, the LIP will have more contributions such as Stark broadening from free electrons. The trend from 1 to 10 s shows that the reduction in temperature and electron number density between the se delays significantly contributes to the reduction of the line width. One other consideration for the spectral intensity of the laser is the spacing of longitudinal modes within the laser profile. As the dye laser cavity has a set length, different wave lengths of light will coherently interact with themselves at different
23 these integer values become very large. Therefore, small variations in the wavelength value can be compensated by the integer va lue, n, such the the following relation holds. (1 2) where c is the speed of light. This expression defines the frequency spacing between longitudinal modes within the laser output. For a laser output centered on a wavelength, Eq uation 1 2 gives the spectral spacing of the modes that allow lasing within the cavity defined by length, L. So, for a small cavity, the modes are widely spaced and the allowed lasing wavelengths are widely spaced. This corresponds to regions of lower in tensity between the modes. When the cavity length increases, the modes become more closely spaced and the intensity output verses wavelength or frequency has fewer fluctuations. The laser width calculated above, 4 pm, corresponds to a frequency width of 15 GHz. Equation 1 2 predicts a frequency spacing of modes within a 35 cm cavity to be 430 MHz. A simple division shows that there are 3 5 longitudinal modes within the half width of the dye laser. Therefore, no significant intensity variations should oc cur over the spectral width of the dye laser. These two dyes are used in two separate dye laser cavities. The concentration dependence of the focusing and steering optics makes it unrealistic to operate two, alternating dye cells within the same housing. Accordingly, the excimer laser beam had to be split to simultaneously pump both dye lasers. The excimer laser (LPX 200, Lambda Physik) is a xenon chloride excited complex laser with a wavelength of 308 nm. The maximum pulse energy is 110 mJ/pulse with a pulse width of 30 ns. A 50/50 beam splitter coated for 308 nm separated the laser to pump both dye lasers. High reflective mirrors for 308 nm are used to steer the laser beams into the dye laser housings. A
24 significant amount of cell damage was experie nced during the early stages of this work. To avoid this, no more than 20 mJ/pulse is given to either dye laser. Accordingly, the excimer laser is operated with an average pulse energy of 40 mJ/pulse. Since following this guideline, significantly less d ye cell damage has been observed. Figure 1 4 shows how the pulse shape of the dye laser strongly depend s on the temporal behavior or the excimer laser. The dye laser energy also strongly depends on the input pump energy from the excimer laser and the conc entration of the dye circulating through the cell. Given the pump energy stipulation above and a concentration of 1 mM C540A, the output energy at 566 nm is 4 00 J/pulse. With a concentration of 1 mM C450, the output energy at 45 5 nm is 600 J/pulse. Th e properties of the dye lasers are summarized in Table 1 1. Spectrograph Images and spectra are taken with a 500 m m Czerny Turner spectrograph is used to couple the light into th e spectrograph. The entrance slit is variable as well as the grating used. Three gratings are mounted on a turret within the spectrograph. Depending on the desired resolution at the focal plane, the diffraction grating could be changed between 1200, 240 0, and 3600 grooves/mm. For all of the work contained within this document, the 2400 grooves/mm is used. This choice was made based on the trade offs associated with each grating. As the line density increased, the resolution of the spectrograph also in creased. However, this increase in resolution came at a cost to the throughput of the instrument. Additionally, as could be deduced from the increase in resolution, the bandpass of the spectrograph decrease s with the increase in line density. This is ap parent when one consider s that the detector spacing is set by the
25 pixel size. Any increase in resolution must, then, come from a wider physical separation of wavelengths. So, in the UV and blue spectral regions, a 2400 grooves/mm grating may have a bandp ass of 7 nm whil e the 3600 grooves/mm grating would cover 3 nm across the detector. This spectrograph is not equipped with an exit slit coupled to a PMT. Only an intensified charge coupled device (ICCD) (ICCD 576S, Princeton Instruments) is used for detec tion on this system. A CCD is an array detector. It has many thousands of individual detectors organized in a 2 dimensional grid that is well suited to applications in imaging and spectroscopy. Each pixel ha s a square cross section with a side length of 23 m. When used in conjunction with a spectrograph, one dimension retain s spatial information while the other dimension i s used for discrimination of wavelengths. For is reta ined, and the distribution of intensity at a given wavelength represent s the physical distribution of emitters in the observed volume. The intensifier is a multichannel plate (MCP) to allow for fast response times. A voltage i s applied to the MCP when th e signal need s to be collected. At all other times, the MCP ha s no voltage gradient applied across its channels which eliminate s any cascade amplification of electrons. In this fashion, the signal to the CCD c an be gated on or off by the MCP. During the time that the MCP i s gated on, the CCD integrate s the amplified light signal transmitted by the intensifier. Irising of the CCD image result s if the lower limit of the integration time i s approached. At such sort integration times, the center of the MCP never reache s the appropriate voltage to induce cascade amplification within the channels. The outermost
26 channels do have this amplification. The resultant image has a dark center where little or no amplification occurred. To avoid this side effect of short integration times on the MCP, the shortest gate width used in this work is 100 ns. The MCP i s driven by a high voltage pulse generator (PG 200, Princeton Instruments). Any external trigger given to this detection system i s applied to this controlle r. The internal delay, gate width, and MCP voltage a re set on the PG 200. Once the MCP i i s sent to the CCD controller (ST 138, Princeton Instruments). The CCD i s set to integrate for 5 ms, ensuring that all photons generated by th e MCP a re collected. CCD Binning It i s possible to sum the intensity of several pixels in the physical axis (at a given wavelength). This region i s referred to, in the software, as the region of interest (ROI). The extent of this ROI i s specified in the software that control s the camera readout. Summing c an be executed on the CCD chip or within the software after the entire CCD chip had been read. Both binning options ha ve their restrictions. Binning on chip require s that the total summed intensity be less than the well capacity of the shift register (last pixel of each row used to read out the charge to the computer). Since the shift register i s a pixel, it c an hold a charge of 65,000 counts. So, if one column of pixels within the ROI being summed ha s an accumulated charge greater than one pixel or 65,000 counts, that region ha s to be summed within the software after readout. Summation of this sort introduce s noise into the spectrum. When the camera i s set to bin pixels in the software, each pixel i s read out individually through the cable connecting the camera to the camera controller. This is significant as the analog to digital conversion i s done within the camera controller and not within the camera. Therefore, it i s possible for the analog sig nal to pick up noises
27 as it i s transmitted through the readout cable, much like an antenna. As each column i s transmitted, the pixel intensities a re superimposed over the interference picked up by the cable. The problem i s exacerbated when columns a re bi nned by the software and the in phase interference g i ve s the background a ripple. This ripple ha s a peak to peak intensity on the same order of magnitude as some signal peaks. In order to avoid this issue, the amplification of the signal i s controlled in such a way as to avoid completely filling the shift register during on chip binning. Figure 1 5 shows the dramatic increase in signal to noise when the output i s binned on chip. The amplification of the CCD image i s controlled by varying the voltage appl ied to the MCP in front of the CCD chip. There i s an extra controller, PG 200, that applie s t he voltage pulse to the MCP. With this controller, the MCP voltage c an be varied from 500 V to 9 00 V. To quantify the response of the MCP at different voltages, a DC light source is monitored. A light emitting diode i s chosen as the source because of its flat response with respect to time. So, the spectrograph i s set to the zero order, and the intensity reaching the CCD i s measured with respect to the applied v oltage to the MCP. Each response i s normalized to the response at 500 V, the minimum, and plotted against the applied voltage in Figure 1 6 A power series i s fit to the data which c an be used to calculate the relative response for any given voltage. Mon ochromator A crossed Czerny Turner VUV monochromator (Model 218, McPherson) i s used in this work. The system i s not pumped down to vacuum as all of the desired wavelengths a re reachable under atmospheric conditions. The focal length i s 300 m m with an f/# of i s used to couple the light into the
28 monochromator. Resolution within the monochromator i s set by the variable entrance and exit slits and the 1200 grooves/mm diffraction grating. Two detectors a r e used with the monochromator. A photomultiplier tube (PMT) sensitive to the UV \ Visible wavelengths (R955, Hamamatsu) i s used for slower response measurements. The PMT power supply provided voltage up to 1 kV (226, Pacific Power Supply). Signal from thi s detector i s typically read out by a 500 MHz digital oscilloscope (TDS520A, Tektronix). Faster detection i s accomplished with a MCP PMT (R1564U 07, Hamamatsu). A separate high voltage source i s required for the MCP PMT. This power supply (PS350, Stanf ord Research) i s capable of applying steady voltages up to 3 kV. The signal through this detector i s amplified by the much shorter transit time of the multichannel plate. This g ives the MCP PMT a resolution in the sub nanosecond range. Accordingly, a 6 G Hz digital oscilloscope (TDS 6604, Tektronix) i s used to read the signal from this detector. Timing Timing within the components of the setup i s accomplished with a digital delay generator (DG535, Stanford Research) shown in Figure 1 1 The ablation laser i s controlled externally by TTL pulses from the DG535. External triggers for the flashlamp and Q switch a re supplied with an interpulse delay of 165 s. This delay between the firing of the flashlamp and Q switch i s the optimal spacing set by the manufa cturer. The internal delay between the Q switch trigger and the plasma formation i s 185 ns. A third channel i s used to send a TTL pulse to trigger the excimer laser. The internal delay between the external trigger of the excimer laser and the output of laser light i s 885 ns. Therefore, if both lasers are fired simultaneously, the shortest delay
29 between the plasma formation and the fluorescence probe would be 700 ns. Since this setup need s to be as versatile as possible, the excimer laser i s triggered independently of the Q switch within the ablation laser. By this logic, the excimer laser, and subsequently the fluorescence probe could be fired even before the plasma formed. The fluorescence could be probed at any time during the life of the plasma. Unfortunately, this le aves the system vulnerable to the jitter present in the excimer laser. Although the trigger sent to the excimer ha s negligible jitter in the time domain, the output from the excimer laser c an vary up to 50 ns. More simply, the maxi mum time difference between any two observed laser outputs i s 50 ns. These laser pulses all averaged a delay of 885 ns. The delays described in this section are summarized in Figure 1 7 For time resolved data collection on an oscilloscope, a photodiode i s placed in the excimer pump beam to trigger collection. In this fashion, the plasma formation seemed to jump around on the scope up to 50 ns away while the fluorescence signal from the probed atomic or ionic transition remain s stationary in time. Avera ging of the fluorescence signal i s accomplished in this way. Fluorescence work with the time integrated camera i s completed with the intensifier gate time set wider than the maximum 50 ns jitter present in the excimer beam. This restriction coincid s conv eniently, with the minimum gate requirements to avoid irising within the intensifier. From the fourth channel on the DG535, a synchronous pulse i s sent to the PG 200 when the excimer i s triggered. The 885 ns internal delay of the excimer laser is then ma tched within the PG 200 such that the
30 MCP i gate width i s 100 ns. Absorption Source The instrument constructed for this work is also capable of absorption measurements. These are realized using much the same logic as that of Dr. Lauly during his dissertation work  described. Unlike the previous sections, the timing is not dictated by the DG535. While the delays are still regulated by t he delay generator, the master trigger comes from a triangle waveform generator (Meterman FGC3, Wavetek) operating at 10 Hz and a variable peak to peak voltage. Typically, this voltage is kept at 2 V. The triangle waveform is split to trigger the delay g enerator as well as drive the piezoelectric tuning arm of a diode laser (TEC 500, Sacher Lasertechnik). The diode laser is driven by a modular laser drive (MLD 1000, Sacher Lasertechnik) equipped with current, temperature and tuning controls. It is possi ble to tune the central wavelength of diode laser with this controller while the triangle wave input from the waveform generator causes the output wavelength to oscillate about that center. Laser ouput is steered through a cold Cs cell as well as a Ar fill ed galvatron (L2783 82ANE PB, Hamamatsu). The galvatron is a see through hollow cathode lamp. The cathode is mounted sideways between two Brewster angle windows to allow optical access to the discharge. As the diode laser passes through the two atom res ervoirs, atomic absorption can be used to establish a wavelength reference for absorption measurements within a LIP. Laser intensity is monitored by a PMT (R928, Hamamatsu) mounted on a 0.1 m monochromator (H10, ISA America Inc.). The PMT voltage is moni tored by an oscilloscope operated at a 1 M input impedance. Such a high
31 resistance is used to amplify the slow signal coming from the continuous wave diode laser. Figure 1 8 shows an example of these wavelength references. There are two Cs transitions separated by 9.1 GHz. Additionally, the Ar transition is set 8.9 GHz from the nearest Cs transition. Since the frequency spacing of the transitions is well known and the time scale is monitored by the oscilloscope, the trace in Figure 1 8 is a convenient conversion from time to frequency. Also, note the time scale of the tuning in the figure. The triangle wave that drives the tuning of the laser diode is operated at 10 Hz. Therefore, a single ramp of the diode takes 50 ms. From the spacing shown below a scan rate of 1.75 GHz/ms can be calculated. Since the laser diode is continuously scanned, some attention must be paid to the rate at which it will change during a plasma event. Typically, plasmas are investigated on the scale of s. So, by reducing both the numerator and denominator by three orders of magnitude, the laser diode will scan 1.75 MHz/ s Recall that the atomic transitions within the plasma from Figure 1 3 are on the order of 4 pm. That corresponds to 15 GHz at 283.305 nm. Therefore, the diode would need to scan for 5,000 s to reach the half width of the atomic transition. On the time scale of the plasma formation and evolution, the diode laser can be said to be spectrally stationary. When operating the dye laser, the wavelength sele ction corresponds to a physical manipulation of a grating. Such a tuning method is independent of all other instrumental considerations and can be operated asynchronously to all other components. The diode laser tuning is time dependent. Therefore all o ther timing considerations must defer to the triangle wave driving the piezoelectric tuning arm. For this reason, the delay generator is triggered by the waveform generator output. The ablation laser is
32 triggered by the same logic as described above. Os cilloscope acquisition cannot be triggered by the excimer output in this scenario. Since the probe laser is continuous in this operation, the acquisition trigger comes from the plasma formation rather than the probe incidence. So, the trig ger to the Q sw itch of the ablation laser is also sent to the 500 MHz scope. For this preliminary work, no other delays are introduced into the system, and acquisition of absorption data by the PMT is only studied at the onset of the plasma formation.
33 Figure 1 1. General schematic for the proposed instrument. Figure 1 2. Spectral width of dye laser centered at 283.305 nm.
34 Figure 1 3. Absorption profiles of lead in a LIP at several delays after the plasma formation. Profile shapes are taken by monitoring fluorescence at 405.781 nm while the excitation wavelength is scanned across 283.305 nm. Figure 1 4 Time profiles of the excimer, dye laser, and doubled dye laser pulses.
35 Table 1 1. Properties of the dy e lasers used in this study. Exciton Product Name Peak Lasing Wavelength (nm) Concentration (mM) in Methanol Max Pulse Energy ( J) Dye Laser 1 Coumarin 540A 550 1 400 Dye Laser 2 Coumarin 450 450 1 600 Figure 1 5 Effect of on chip binning for the CCD. A) Binning within the software. B) Binning on the CCD before readout. Figure 1 6 MCP response to an LED as a function of applied voltage. Responses normalized to signal at 500 V.
36 Figure 1 7 Timing schematic for triggers and lasers. Figure 1 8 Conversion between time and frequency for tuning the diode laser.
37 CHAPTER 2 SPATIALLY RESOLVED E MISSION Motivation When LIPs are simulated, certain symmetries are assumed. Be it cylindrical or spherical, the symmetry of the simulation still requires some basic, rad ial distribution of temperature, electron number density and analyte number density. In many cases, these are taken to be Gaussian [67, 68] parabolic or flat  To establish if these assumptions hold any water, a n emission experiment i s devised to evaluate the distributions within the LIP. Additionally, spatially integrating a plasma has been shown to generate apparent temperatures that do not reflect local temperatures  The LIP transition s from a hot center up to 20 ,000 K to ambient temperature and pressure within a few millimeters. Accordingly, the temperature at any given point within the plasma plume is likely to be very different from a point further from the plasma center. This gradient in temperature affects the atomic and ionic populations and, therefore, the emissive properties of that point within the plasma. Conventionally, the image of the plasma is formed on the slit such that a horizontal slice is selected out of the image [4, 71, 72] In this way, an image is formed on an array device that could be parsed into spatially resolved sections  Based on this work, a toroidal and Gaussian distribution have been proposed for neutral atoms an d [ 70] For this work, the temperature and electron number density are found to mimic the ionic distribution with peak at the center of the plasma plume. The vertical distribution was also studied and shown to be generally higher in the center of the plume There appeared to be some bimodal structure to the are measured to share the
38 tor oidal distribution  Additionally, the temperature distribution was found to be generally Gaussian with a flat top at the plasma center. Since the plasma being imaged onto the slit is an extended source (a source with depth), there are photons imaged on to the slit that may not have come from that verti cal section of the plasma This concern led to the development of a new collection method for the emission spectra. Instead of conventional imaging lenses transmitting the light to the spectrograph slit, two pinholes a re used to select a cylinder within the plasma volume. This light i s transmitted through a fiber optic cable to the spectrograph. Additionally, a shorter delay time i by Aguilera and Aragon  Temperature and Electron Number Density Considerations Tempera tures presented in this work are calculated using a Saha Boltzmann plot. This combines the relative distribution of two, neighboring charge states to generate a plot of intensity vs. upper energy level of the transition. The slope of such a construction gives the temperature that produces the described distribution. Certain benefits accompany using this approach, and these along with the mathematic principles are explained here. The construction of a Saha Boltzmann plot beg ins with the assumption of a l ocal thermodynamic equilibrium that support s a Boltzmann distribution of atoms within their excited states. Such a distribution i s described by ( 2 1 ) where n p i s the number density (cm 3 ) of the atoms in state p, n T i s the total nu mber density (cm 3 ) of the atomic species, g p i s the degeneracy of state p, U(T) i s the partition function, E p i s the energy (eV) of state p, k i s the Boltzmann constant 1 ) and T is
39 the temperature (K) of the plasma  This expression can be combined with th e radiant power (W) emitted by the analyte within the plasma given by ( 2 2 ) where A pq i s the Einstein coefficient for spontaneous emission (Hz) h i constant pq i s the frequency of the transition (Hz) and V is the volume observed (cm 3 ) within the plasma. Combining these expressions for number density of analyte in wavelength (cm), g ives ( 2 3 ) where c i s the speed of light (cm/s) Taking the natural logarithm of both sides g ives Equation 2 4. ( 2 4 ) This equation h olds the obvious symmetry to y = mx + b which represent s a linear relation between x and y. Additionally this relation i s amenable to graphical interpretation of many emission lines of an analyte within a plasma. The slope, which i s proportional to the inverse of the temperature, produce s a good temperature as it i s derived from several emission lines with in the source, and the y axis intercept g ives the number density for that emitter. Using this same logic and the Saha expression for ionization equilibrium, a similar relation can be derived that cover s adjacent ionization states  Beginning with the Saha equation
40 ( 2 5 ) where n 0 n e and n i are the neutral, electron and ion number densities, respectively, m i s the electron mass (g) E IP i IP i s the ionization energy depression. A correction factor must be applied to the ionization energy because the Debye length replac es infinity in its calculation. After substituting in Equations 2 1 and 2 2 from above and r earranging, the combined Saha Boltzmann relation i s ( 2 6 ) i i s ionic. Taking the natural logarithm of both sides after some rearrangements gives ( 2 7 ) The execution of this relationship is more sophisticated than the simple Boltzmann plot as knowledge i s required of the electron number density within the observed plasma region. Again, the slope of the plot g ives the temperature of the pla sma, but as can be seen from the derivation, the relation holds only when comparing ion to neutral emission intensities. However, this allows for a much larger spread in upper state energies which increases the accuracy of the temperature. Since the plas ma easily ionize s metal vapor, several ionic lines appear in the spectra collected for th is study. So, to facilitate the evaluation of temperature from Saha Boltzmann plots the spectrograph i s scanned over nine spectral windows that contain both atomic a nd first ionic lines of several elements The nine windows used are listed in Table 2 2 along with the relevant lines within each.
41 One of these windows covers the emission of the hydrogen alpha line at 656.279 nm. This line is very convenient for the eva luation of electron number density via Stark broadening  Part of the reason that hydrogen lines have found such popularity in electron number density calculations i s their linear Stark effect [65, 77 79] Because of its simple electronic structure, h with the free electrons that induce the Stark broadening used in the calculation. More complex atoms depend quadratically on the distance of the free electron, while the limit to the interaction betwee n a free electron and hydrogen can be taken as the Debye length within the plasma  Additionally, the quadratic Stark effect is asymmetric, making interpretation more complicated. For this work, the equation proposed by Griem and reproduced as Equation 2 8 i s used along with the constants calculated from the oretical hydrogen line profiles  ( 2 8 ) Clearly, this i s not the optimal position in which to be. The Saha Boltzmann plot depends on knowledge of the electron number density and the electro n number density calculation depends on knowledge of the temperature, the constant C being dependent upon both. Fortunately, the dependence upon these two values i s weak. For instance, an initial guess of 10,000 K and 10 17 cm 3 for temperature and electr on number density, respectively, generate a C of 3.61x10 15 3/2 cm 3 If the temperature i s changed to 20,000 K, C change s to 3.88x10 15 and, if electron number density had been changed to 10 18 cm 3 C bec o me s 3.23x10 15 3/2 cm 3 This weak dependence m a kes the first assumption less critical, and the value of 3.61 x10 15 3/2 cm 3 i s typically used as it i s derived from common LIP properties.
42 Experimental A i s mounted 210 mm in front of a fiber optical cable. The fiber optic cable i s a bund ha s a diameter of 1.3 mm. Finally, the plasma i s positioned 8 mm away from the front aperture. This is all summarized in Figure 2 1 A From these figures, some simple trigonometry g ives w hat will be referred to as the angle of acceptance. This angle i s the largest that would be accepted into the optical train and be detected. For a lens, this angle is easily calculated from the f/#, the inverse tangent of the aperture radius divided by t he focal length. The two pinhole system ha s no real focus, but there is still an angle described by the relation of the two apertures. Tracing a line from the bottom of the fiber optic cable entrance to the top of the pinhole, an angle is defined that de scribe s how much light is detected from undesired sections of the extended source. So, a direct comparison between these two angles (for the lens and the two aperture setup) gives an idea of how selective the collections methods are For the optical trai n described above and shown in Figure 2 1 B an f/7 lens used with the spectrograph has an angle of acceptance of 0.0714 radians as measured from the optical axis. The two aperture system described above has an angle of acceptance of 0.0036 radians. Obvio usly, the two aperture setup is more discriminating than a conventional lens collection. Given these parameters, it is possible to calculate the diameter of the cylinder whose emission is accepted into the fiber optic cable. This diameter is strongly depe ndent on the distance between the front pinhole and the observed volume. The distance used here is 8 mm. At this separation, the angle of acceptance added an additional 56 m to the diameter of the observed region. Therefore, at the center of the
43 plasma the diameter of the observed area is 256 m. Assuming the plasma had cylindrical symmetry with a diameter of 2 mm, the diameter of the observed area at the front and back of the plasma is also calculated as 250 m and 264 m, respectively. This plasma s ize is taken from previous work done by Benoit Lauly of the Winefordner research group  Taking these values into consideration, the two aperture collection system is y z stage (Encoder Mike Controller 1801 1, Oriel) is used to precisely scan the apertures over the profile of the plasma. Once the first aperture is positioned the set distance away from the plasma, the electronic stage is z plane according to the raster depicted in F igure 2 2. Such steps sizes are well within the stage s limitations as the motors driving each axis are The central point of the plasma, corresponding to point 0x0 in the diagram of the raster is determined by a two step process. For the z axis, a Helium Neon laser is mounted behind the two aperture system. The fiber optic cable is removed and the laser beam passed through the fiber mount to the front, 200 m aperture. The laser is moved vertically, along with the two aperture system, until the beam graze s the surface of the sample and a clear diffraction pattern is visible on the other side. This diffraction pattern result s from passing the laser beam through the restricting aperture. The x axis zero is determined by placing the fiber optic cable back into the mount within the two aperture system. While observing plasma emission at 1 s, the spectrograph is set to 0 order. By scanning the apertures horizontally, the most intense point along the axis is taken to be the plasma center. This reference point is stored as 0x0 within the electronic controller of the x y z stage.
44 The 19 individual fibers are subsequently lined up in a slit for the exit of the fiber. The f/number of these fibers is matched to the SP500 used in this work. The spectrograph slit is entrance slit is used. By selecting such a small region for observation, the ICCD require s an integration time of 500 ns to accumulate adequate signal. A del ay time of 1 s is used to coincide with other data planned to be taken. The spectra a re binned on chip and 300 laser shots a re collected for each spectral window at each spatial point. A fresh sample surface is presented to be analyzed for each group of 300 spectra. An aluminum standard, D33, is used with a well known composition listed in Table 2 1. Taking this known composition, nine spectral windows are selected because they contain atomic and ionic emission lines to be used for the constructions of Saha Boltzmann plots within a program developed as a calibration free methodology for LIBS, LIBS++ software first described by Ciucci [81, 82] The central idea of th e CF LIBS software is to generate Saha Boltzmann plots for several different element s with strong emissivities within the plasma. From these plots, a reliable plasma temperature c an be derived. The software generates Saha Boltzmann plots for every element with identified lines within the spectrum provided. During the final analysis, ce rtain temperatures can be ignored if too few lines are identified or misidentified. This is the case for manganese and iron, respectively. Manganese had too few lines and many lines identified as iron were likely other elements. Therefore, the temperatu res presented here only consider the Al, Si and Mg lines identified within the nine windows collected.
45 Results The raster used in the collection of spectra for this work is limited to one half of the plasma profile. Because of concerns over day to day rep roducibility, a single raster is completed in one day, restricting the profile collection to one half. Therefore, the collection began at 0x0 and moved toward the edge of the plasma. In this way, cylindrical symmetry is assumed and the behavior on the ma ps shown below is extrapolated to the other side. For each point in space, a spectrum is pieced together from the nine spectral windows observed, generating a temperature and electron number density for each point. These are mapped out within the two dime nsional grid that defin s th e two aperture raster. The temperature map in Figure 2 3 shows a hot center 500 m above the sample at 1.28 eV which corresponds to 14900 K. The local temperature near the surface is consistently about 1500 K below the temperat ure at z = 250 m. This depression of temperature agrees with the maps produced by Aguilera and Aragon  Additionally, they observe a lack of symmetry within the distribution of temperature at atmospheric pressure. The observed time window is slightly later than that used here, but the trends are certainly similar. Figure 2 4 shows that the electron number densities a re more sporadic in the ir distribution. Like the temperatures, the density near the surface is consistently lower than the rest of the plume again observed by Aguilera  Additionally, both properties share an apparent hot spot in the top right corner. It is very possible that the plasma does not maintain cylindrical symmetry as the shape of the plasma depends on the laser beam profile  Since the beam profile was not known during this work, it is assumed that this consistent displacement of temperature and electron number density
46 r esults from a real structure within the plasma plume. This asymmetric form likely results from the beam profile as each spatial point is collected at a different point on the sample surface. While the sample surface can affect the propagation of the plas ma, this should not be so structured and repeatable as is observed in the images  The temperatures mapped above come from line intensities generated by the CF LIBS software. These integrated line intensities are easily extracted to map the emission intensity of the major and minor components. For illustration, two major component are mapped, Al at 85 % and Si at 9 % as well as a minor component, Mg at 0.04 % the plasma plume, a mushroom cloud. The two major components, Al and Si, track each other very well in Figures 2 5 B and 2 6 B wit h a very similar structure in their relative emission maps. The lower concentration magnesium ion, shown in Figure 2 7 B shows a much more even spread of intensity over the profile of the plasma. The three elements, aluminum, silicon and magnesium, have very moderate ionization potentials, 6.0, 8.2 and 7.4 eV, respectively. Despite the 2 eV difference between silicon and aluminum, their relative intensities map very well which reflects that no new ionization is occurring at this delay. Additionally, the temperature map shows that the predicted temperatures are well below those necessary to affect that change in ionization state. The atomic populations show the same correlation as the ionic. Aluminum and silicon agree in their distribution about the cent er of the plasma plume in Figures 2 5A and 2 6 A respectively. All three species exhibit a much higher density near the surface of the sample. Again, this agrees well with the temperature distribution which has its
47 lowest values just near the surface. T hese arguments agree that the plume has the mushroom cloud shape with the cold vapor filling in underneath the rising hot vapor. Conclusions While much more spatially selective than imaging, the experimental setup suffered from a limited spectral interroga tion. Each spectral region required so many laser shots, that practical limitations on sample size and interrogation time inhibit the investigation. An obvious improvement to the setup would be the use of an echelle spectrometer. With such a spectrograp h, the CF LIBS functionality could be used to full potential by collecting an entire spectrum for each spatial position. By removing the need to stitch together spectral windows, the number of plasmas required for the raster is reduced by orders of magnit ude. Additionally, at these short delays, the plasma is evolving very quickly. A 500 ns gate width on the ICCD could cause some of the spatial resolution to be lost as the plasma expands through the observation volume. The solution to this issue is be t he addition of an ICCD with more sensitivity than the present model used. With a higher sensitivity, a short gate width would be possible. This would increase the temporal resolution which is tied to the spatial resolution when the plasma plume is expand ing at these short delays. Despite the practical limitations of the setup, good agreement is observed with previous imaging work done to map temperature and electron number density 
48 Figure 2 1. Trigonometry for optical emission collection. A) For the two aperture system proposed. B) For the conventional lens collection. Figure 2 2. Diagram of raster ac ross the plasma profile.
49 Table 2 1. Composition of the D33 aluminum alloy used in this study in mass percent. Element Percent Composition Al 84.92 Si 8.54 Cu 2.89 Fe 1.15 Zn 0.59 Ni 0.5 Mn 0.4 Pb 0.14 Ti 0.055 Sn 0.048 Cr 0.047 Mg 0.038
50 Ta ble 2 2. Central wavelengths for the nine spectral windows used in this study along with the relevant lines and associated spectroscopic quantities. Central Wavelength (nm) Emission Wavelength (nm) Emission Species E k (cm 1 ) A ki (x10 8 s 1 ) 263.0 258.588 Fe II 38660.04 0.810 259.373 Mn II 38543.08 2.680 259.940 Fe II 38458.98 2.200 260.569 Mn II 38366.18 2.700 261.187 Fe II 38660.04 1.100 261.382 Fe II 39109.31 2.000 261.801 Fe I 45913.49 0.400 262.567 Fe II 38458.98 0.340 262.829 Fe II 39 013.21 0.860 263.132 Fe II 38660.04 0.600 265.248 Al I 37689.41 0.133 266.039 Al I 37689.41 0.264 281.5 277.930 Fe II 62322.43 0.760 278.369 Fe II 62083.11 0.700 279.553 Mg II 35760.88 2.600 279.827 Mn I 35725.85 3.600 280.270 Mg II 35669.31 2.600 281.619 Al II 95350.60 3.830 283.951 Fe II 79439.47 0.990 285.213 Mg I 35051.27 4.910 303.0 302.063 Fe I 33095.94 0.402 305.007 Al I 61843.54 0.321 305.468 Al I 61747.56 0.449 305.714 Al I 61843.54 0.750 306.429 Al I 61691.46 0.820 306.602 Mn I 49888.01 0.160 325.0 324.725 Cu I 30783.69 1.370 327.376 Cu I 30535.30 1.361 360.0 356.537 Fe I 35767.56 0.380 358.656 Al II 123423.40 2.496 361.876 Fe I 35611.62 0.730 388.0 385.637 Fe I 26339.69 0.046 385.991 Fe I 25899.99 0.097 386.259 Si II 81191.34 0.280 390.068 Al II 85481.35 0.005 390.552 Si I 40991.88 0.118 466.0 466.368 Al II 106920.56 0.530 656.5 656.279 H I 97492.30 0.441
51 Figure 2 3. Map of the T determined from the Saha Boltzmann plot in CF LIBS. Note th at the scale is eV. Figure 2 4. Map of the electron number density from the fitting of the H alpha emission line. Note that the scale is x10 17 cm 3
52 Figure 2 5. Maps of the aluminum distribution within the plasma. A) Atom. B) Ion. Both scales sh ow integrated line intensity in counts. Figure 2 6. Maps of the silicon distribution within the plasma. A) Atom. B) Ion. Both scales show integrated line intensity in counts. Figure 2 7. Maps of the magnesium distribution within the plasma. A) Atom. B) Ion. Both scales show integrated line intensity in counts.
53 CHAPTER 3 SCHLIEREN IMAGING Motivation Another important check for any simulation of a LIP in atmosphere is the formation and propagation of the shockwave. This effect is generally om itted for early theoretical work done in vacuum [85, 86] but ambient gas properties become significant at atmospheric pressure  This significance holds for both the ablation process [88, 89] and the excitation process within the plasma  At these higher pressures, the sudden formation of a plasma on the sample surface create s a shockwave that is readily measured optically. For simulations of atmospheric breakdown, this is an easy check for agreement with experimental results. The measurement of shock fronts is much older than the advent of the LIP. Accordingly, there are many well defined methods for imaging the phenomenon [90, 91] The two main camps are shadowgraphy and schlieren. Experimentally, these two techniques are very similar, siblings. However, there are some fundamental differences in their sensitivity that clearly discriminate them. Shadowgraphy is sensitive to the second derivative of the refractive index with respect to space while schlieren is sensitive to the first. Additionally, the experimental application of schlieren requires the addition of a cut off within the system. This requirement will be explaine d more. Clearly, schlieren is a more sensitive technique as it responds to smaller gradients, however, the gradients found within shockwaves are large enough that they lend themselves very well to shadowgraphy  Within the LIBS community, shadowgraphy and variants therein are more common than schlieren applications. The most basic form of shadowgraphy, unfocused, has
54 been used to calculate shock ve locities, plume temperatures and electron number densities and the behavior of shockwaves within a cavity [84, 93, 94] A focused shadowgram images a plane some millimeters in front of the perturber. This technique has been used to acquire sharper shadowgrams of shock waves under different atmosph eres [95, 96] Shadowgraphy also shares quite a bit with interference techniques I t is essentially one arm of a two beam interferometer. This logic has been used for papers that study both number densities and shockwave expansion with the same setup. Th e shadowgrams are acquired by blocking the reference arm of the interferometer. Michelson interferometers have been used by Schittenhelm and Vogel [97, 98] and Mach Zehnder interferometers have been used more recently by Sobral, Hauer and Thiyagarajan [99 101] Schlieren applications are more difficult to come by as many times the author still refers to the method as shadowgraphy [102, 103] Despite this common confusion, there are still some applications using schlieren to investigate LIBS [104 106] Cristoforetti investigated the pre ablation scheme of double pulsed LIBS using schlieren to study the coupling of the two plasmas and shockwaves  Vogel conducted a fundamental study of schlieren cutof f techniques for the imaging of laser ablation on tissues. These schlieren images have the highest contrast and resolution of any LIBS application to date  With all of the evidence that an imaging system can give useful insight into the LIP, it is desired to apply this method to this multidisciplinary setup. However, the schlieren system sh ould no t interfere with the regular workings of the emission and fluorescence setups. Therefore, a design for the schlieren system is attempted that
55 leave s the emission optics untouched. Only two optical elements and a probe laser are introduced. Once the tech nique was refined, the probe laser was removed and a dye laser used for LIF served as the probe laser, eliminating the extra instrumentation. Premise of Schlieren Imaging Schlieren imaging is a technique that can measure the density gradient of some pertur bing volume when interrogated with collimated light. Practically, the angle of deflection for a refracted beam of light is directly proportional to the gradient of refractive index within the perturber. These two physical properties, density and refracti ve index, can be easily related for gases by ( 3 1 ) GD is the Gladstone Dale coefficient. For air at standard temperature and pressure, k GD is 0.23 cm 3 g 1 for visible wavelengths  The refractive index change measured is a result of the density change that originates, in this case, from a laser induced plasma. To better describe the phenomenon, begin by defining a three dimensional frame of reference where z is axis of propagation of the light, parallel to the geometric beam of light. The x and y axes are, then, the horizontal and vertical axes perpendicular to the direction of travel for the light beam. In one dimension, if there exists a gradient in the that point in space is defined by ( 3 2 )
56 al axis and n 0 is the refractive index of the surroundings. A similar equation holds for the y axis. So density disturbances must be in the plan e perpendicular to the optical axis. Any refractive index gradients along the optical axis do not affect the beam in this way. There are two, basic classifications of schlieren systems, lens and mirror. For both systems, the fundamental concept is the same, but their implementations differ. The obvious appeal of a mirror system is its freedom from chromatic abe rrations and large scale applicability. Many executions of this technique have used flash lamps that produce a short, continuum pulse of white light to be used as the light source for interrogation. Chromatic aberration within a schlieren system can fund amentally undermine th at instrument ion as will be shown later. Also, large telescope mirrors are much easier to procure for schlieren imaging on the human scale. Lens systems suffer from the aforementioned chromatic aberration, but they are much easier t o setup and align than their mirror counterparts. Additionally, for the application described in this work, a schlieren imaging system with lenses is very similar to certain emission collection optics. Accordingly, a lens system is assembled for this wor k as there are simple ways to circumvent the chromatic aberration issue. A lens schlieren system is summarized in Figure 3 1 and begins with the light source being collimated by a lens. In a perfect world, this light source would be a point source. Howev er, as that is a difficult approximation to make for most lamps, a point source can be improvised by imaging the lamp onto a pinhole. The light from that pinhole can, then, be collimated by the first lens within the schlieren system. Next, position the p erturbing volume within the collimated light from the source and position a
57 focusing lens for the collimated light. This second lens also acts as a collimator for the light that is refracted by the perturbing source. Accordingly, it should be placed 1 fo cal distance away from the perturbing volume. Once the source light has been focused behind the second lens, a cutoff is introduced to block either the refracted light that is now collimated or the focused light from the source. Here, chromatic aberratio n from a continuum source can cause problems. If the cutoff is to be placed to block the focused source light, that position is ambiguous for white light. A final lens forms an image of the collimated, refracted light on the detector. The cutoff mentione d is the most important aspect of the optical train for schlieren imaging. Depending on the light source, there are many forms the cutoff can take. Typically, the cutoff edge needs to be perpendicular to the angle of refraction for the light. To describ e it in more detail, imagine a cylindrical lens that will refract light in on direction while leaving the light undisturbed in the perpendicular axis. Now, the lens is oriented with its cylindrical axis vertically, which causes a beam of light that passes through it to be dispersed horizontally. If a cutoff is to be introduced as horizontal knife edge, the vertical displacement of the knife edge would cut off the same amount of intensity regardless of the cylindrical lens existence. However, if the knife edge is mounted vertically, the intensity it blocks with each horizontal displacement varies strongly with the presence of the cylindrical lens. So, for the knife edge to be effective, the direction of displacement needs to be perpendicular to the edge o f the cutoff. This is the major factor that decides the structure of the light source and cutoff in schlieren measurements. The relation between the source and cutoff determines whether the refracted light or unperturbed light is imaged, dark field or br ight field, respectively.
58 To appreciate the difference between the two fields of imaging, bright and dark, Figure 3 2 compares the cutoffs used in each technique with respect to the mask applied to the light source. Bright field imaging will allow the un perturbed light to pass on to the detector. With the described optical train, an image of the source mask should be made at the location of the cutoff. Without any perturbing density gradient, this is true. Therefore, a cutoff that matches the source ma sk should only pass light that is unaffected by any density change and the bright regions of the image plane will correspond to portions without significant density gradient On the other hand, the dark field cutoffs in Figure 3 2 will only allow all oth er light to pass. Light that remains unchanged will hit the dark field cutoff. Only light refracted by the perturbing density gradient will pass on to the detector. So, the bright portions of the image will correspond to the density gradient perturbing the collimated light. In the present work, there is no source image for the collimated light as its source is a laser beam. The image formed at the focus of the first lens is, simply, a point focus. Accordingly, for this work, the cutoff is, generally, a pinpoint for dark field and an iris for bright field. This is also fortuitous for the structure of the perturbing plasma. As the shockwave is a hemisphere, light is displaced at all angles away from the sample surface instead of linearly as in the cylin drical lens proposed above. Therefore, a pinpoint cutoff for dark field imaging allows the refracted light at all angles around the hemisphere to be imaged. The only exception is the light that is displaced toward the mount of the pinpoint. To illustrat e this point, a horizontally mounted pinpoint is moved about the focus of the unperturbed laser light. Figure 3 3 shows the transition from dark field to bright field schlieren imaging. As mentioned previously, the light refracted
59 laterally, hits the pin point and its mount. There are two dark regions on either side of the shockwave image where this absorbed. Alternately, Figure 3 4 shows the transition from bright field to dark field imaging by moving that same pinpoint vertically into the focus of the unperturbed light. Sedov Taylor Blast Wave Point e xplosions have been well studied since the 194 0s and the first experimental data used to check the theoretical expansion of a strong shock wave into atmospheric conditions were from nuclear test explosions  Since this early work on atomic bombs, Sedov Taylor blast waves stud ies have been done on phenomena as large as supernovae rem nants and as small as LIPs. For those studying and modeling Taylor model is useful in describing the density and temperature profiles behind the shockwave as well as its motion through space  For the present work, the aspect of most concern within this model is the expansion speed of the shock wave. This relation, given by ( 3 3 ) 0 as is commonly assumed, the constant becomes 0 .96  So, any work done to measure the shockwave using a schlieren setup should show three relations: The radius should grow as a power function of exponent 0.4 with respect to time; the radius should grow as a power func tion of exponent 0.2 with respect to deposited energy; and
60 the radius should decay as a power function of 0.2 with respect to the density of the surrounding gas. Experimental Successful schlieren images are collected in two ways. Both setups used the Big Sky Ultra for the formation of the LIP, DG535 for timing and the SP500 set to 0 order. Schlieren images are detected by the ICCD coupled to the spectrograph. In this configuration, the spectrograph bec omes a glorified turning mirror for the imaging laser and a bandpass filter is required to spectrally select the imaging laser and reject plasma emission. The collection lenses for conventional emission and fluorescence studies remain in their same configuration. A cutoff is placed at the focus of the fir st lens, the collimating lens near the plasma source. The cutoff in this experiment is simply a hex wrench mounted such that the tip of the wrench blocked the focused probe beam. A micrometer controlled x y z stage enabled the cutoff to be moved into and out of the focus to optimize the schlieren images. The first iteration of this work was completed along with the spatially resolved emission measurements described above. The motivation for this is to have two sets of data that corresponded to the same l aser pulse energy, sample irradiance, temperatures and electron number densities. Therefore, the expansion of the shockwave measured correlates exactly to the plasmas that generate the emission profiles. A nitrogen laser is triggered by the delay generat or such that the delay between the plasma formation and the probe laser is very well controlled. The timing jitter on the nitrogen laser output is 75 ns. Accordingly, the gate width of 100 ns for the ICCD is wider than the jitter expected from the probe laser. Jitter in the probe laser also necessitated single shot measurements. No averaging is done to generate the
61 schlieren images, so each image came from a single LIP. The probe laser beam is large enough that no beam expander is necessary for it to i nteract completely with the plasma shockwave. Here the laser replaces the source and the first two lenses shown in Figure 3 1. As their sole purpose is to form a cylinder of collimated light, the laser is an adequate replacement for those first few optic al components The simplified optical setup for the present schlieren imaging is illustrated in Figure 3 5. In the second iteration, the coumarin 450 dye laser is used as the probe laser. With the change in wavelength from the 337 nm nitrogen laser, a ba ndpass for 460 nm is installed in place of the 337 nm bandpass. As the dye laser is tunable over this range, the central wavelength is scanned to the maximum transmission of the bandpass filter at 460 nm. Since the dye laser is pumped by the excimer, the dye laser output suffers from the same fluctuations as the excimer. The jitter quoted previously, 5 0 ns, for the excimer required a trick for the timing. For the nitrogen laser, the delay displayed on the DG535 is taken as the time difference. However, this is not the best solution when using an excimer as the probe. To account for this, an extra measurement is taken simultaneously by the monochromator equipped with the PMT. The monochromator is set to the wavelength of the dye laser output. Then, th e PMT voltage is monitored on an oscilloscope during each image collection. The plasma formation is indicated on the PMT voltage trace by the spectrally ubiquitous continuum, and scatter from the probe laser appear s as a second peak. It is a small thing to measure the delay between these two pulses on the PMT voltage trace. So, for each schlieren image taken of an individual LIP, a measured delay is recorded. These delays are used to construct the curves of growth for the shockwave. Additionally, a sli t cutoff
62 is introduced in place of the pinpoint cutoff used previously. The slit is mounted horizontally which allows for light refracted towards the sample surface to be imaged. In this configuration, the top of the shockwave is very clearly imaged for measuring its displacement from the sample surface. Results Time Dependence First, the time expansion of a shockwave is verified using the schlieren setup. A LIP is formed with the ablating laser set to 69 mJ/pulse. The time between the plasma formation and probe laser is shockwave is measured from the sample surface to the top of the shockwave normal to the surface. A single pixel column is selected for measurement, and the shockwave peak or dip is recorded for that pixel column. The peak or dip depend s on the use of dark field of bright field imaging. Figure 3 6 shows a typical image used in the bright field configuration. The red circle highlights the dip in intensity that marks the shockwave Using these measured values along with the delay time, a curve is constructed. Figure 3 7 shows the time evolution of a shockwave created by a laser power of 69 mJ/pulse under atmospheric conditions. Clearly the general trend is acceptable with respect to the growth of the shockwave, but the exponent is too large to agree with theory. The power of 0.45 should be at 0.4 for a perfect marriage to the Sedov Taylor blast wave theory. However, there is evidence that the shockwave from a LIP does not exactl y mimic this theory  Rather, the exponent of time should be l arger, ~0.42 in the work by Wen
63 As can been seen from Figure 3 6 this first expe riment is done using the bright field arrangement. To confirm that the choice of field would not affect the expansion measured with the schlieren technique, another set of images are collected in dark field. Figure 3 8 shows a typical dark field image wi th the intensity peak of the shockwave highlighted by the red circle. The work done in dark field, in Figure 3 9 shows the same time dependence as that done in bright field. In fact, the data overlap when plotted together as can be seen from their fitte d trendline equations. Energy Dependence The second dependence investigated is the relation with deposited energy. From Equation 3 3, it is apparent that the radius of the shockwave should grow as a power function of exponent 0.2. This relation holds onl y if the delay is fixed at a value. Therefore, the delay chosen must be large enough that the jitter within the probe laser is less significant while remaining small enough that the shockwave is easily measured on is chosen, and the actual delays of the schlieren images are recorded in the event that scaling is necessary. Figure 3 10 shows the proper growth with respect to deposited energy, but the theoretical scaling disagrees at low energies. This behavior was also reported by Callies  Pulse energies that approach the breakdown threshold have a significant fract ion of their energy deposited before the plasma formation, or breakdown. Because this energy deposition occurs before the plasma formation, and subsequent shock wave formation, it is lost to sample heating. For the present experimental setup, no plasma f ormation occurred for a pulse energy of 5.7 mJ/pulse. Therefore, the threshold lies between 5.2 and 9.7 mJ/pulse.
64 Density Dependence The third relation expressed in Equation 3 3 lies between radius and surrounding gas density. To examine this more closel y, the sample is placed within a gas chamber capable of a modest vacuum, 5 mbar. No positive pressure work is completed in this study. As the other parameters need to be constant for this work, a delay is with a pulse energy of 40 mJ/pulse. At this pulse energy, Figure 3 10 shows a good agreement with the scalar predicted by the Sedov Taylor relation. From Figure 3 1 1 there is good agreement between the observed shockwave radius except at the lowest pressure. It appears that the shockwa ve at 50 mbar is moving faster than the predicted value for this density. If a trend line is fit to the data, the power exponent is 0.23 rather than 0.2. So, it is possible that this is simple experimental err or, or there is some more physical reasoning. There are two other variables held constant for this calculation. Time, most certainly, is not drifting in such a way as to cause this disagreement. As stated in the last section, the breakdown threshold can affect the actual energy deposited which could cause an apparent divergence from theory. If the energy deposited were to increase relative to higher pressures, then the shockwave could travel farther than predicted for the data point at 50 mbar. However it has been shown that for nanosecond laser pulses at 1064 nm, the breakdown threshold slightly increases with a decrease in pressure  This would contradict the reasoning above, as l ess energy would contribute to the point explosion. Perhaps this trend could be more accurately explained if more data points were collected at lower pressures, below 50 mbar. Unfortunately, the density gradients at these lower pressures are more difficu lt for the schlieren system to detect as their absolute magnitudes are being reduced. Because of this, the images of the shockwave
65 collected below 50 mbar do not show a distinct shockwave boundary. Any distance measurement done in this regime would be gu esswork and subject to extreme error. It was stated previously that schlieren imaging is a more sensitive method directly these lower pressures  Therefore, it is proposed that this inability to detect shockwaves below 50 mbar is the result of the optical train used to cap ture the schlieren image. For a lens type schlieren system, the sensitivity is directly proportional to the focal length of what is the first imaging lens in my setup. This lens is the third lens in the optical train from Figure 3 1. ( 3 4 ) respect to refraction angle and a is the height of the source image. Simple trigonometry shows that a longer focal length lens in this position of the optical train results in a greater overall displacement from the optical axis for the refracted beams. Therefore, measurement of smaller angles of refraction is possible with the same cutoff. Conclusions A simple, lens type schlieren system is superimposed over a conventional optical emission setup. Successful schlieren imaging is possible without deconstructing any aspect of the emission collection optics or any alteration to the instrumentation. The only changes made to the optical train are the addition of a cutoff and ba ndpass filter for the probe laser. These components are easily removed to resume the normal operation of emission spectroscopy. The schlieren images of LIP shockwaves agree with the Sedov Taylor expansion and the modifications found in the literature.
66 Th e system could be improved with longer focal length collection optics and a higher resolution CCD detector. Conventional schlieren systems do not use scientific cameras as the time resolutions comes from the probe laser delay. Additionally, the intensifi cation of the CCD image introduces losses to the resolution. However, these two alterations would affect the emission studies done with the system and are not implemented. Using the system as is, a future project could scan the cutoff in the plane that c ontains the focused source image. Knowing the optical geometry of the refracted ray collection, a density map could be constructed by measuring the intensity of the refracted beams as a function of displacement from the optical axis. This displacement, a ssuming the light is well collimated, could generate the angle of refraction which gives the gradient of the index of refraction for that point. By building a map of these angle s a density distribution could be integrated. If changes were to be made to t he schlieren system such that the optical emission setup is to be interrupted, a future investigation using this technique and the process described above to reconstruct density distributions could be done for a magnified image of the plume projected on to a CCD detector. This would give very good insight into the structure of a LIP.
67 Figure 3 1. Schematic for a generic lens schlieren system working in the dark field. Figure 3 2. Comparison betwe en bright and dark field cutoffs for schlieren imaging. Figure 3 3. Progression from dark to bright field schlieren by moving a horizontally oriented pinpoint cutoff horizontally.
68 Figure 3 4. Prog ression from bright to dark field schlieren by moving a horizontally oriented pinpoint cutoff vertically. Figure 3 5. Schematic for the optics used in the schlieren imaging for this work.
69 Figure 3 6 Image taken from WinSpec32 for measuring the propagation of the shockwave by bright field schlieren imaging. The red circle indicates the reduction of intensity by refraction. Figure 3 7 Shockwave expansion by bright fi eld from a LIP formed with 69 mJ/pulse.
70 Figure 3 8 Image taken from WinSpec32 for measuring the propagation of the shockwave by dark field schlieren imaging. The red circle indicates the increase of intensity by refraction. Figure 3 9 Shockwave expansion by dark field from a LIP formed with 69 mJ/pulse.
71 Figure 3 10 Energy dependence of the shockwave produced by a LIP at atmospheric pressure. Figure 3 1 1 Density dependence of the shockwave produced by a LIP at 49 mJ/pulse.
72 CHAPTER 4 SPATIALLY RESOLVED L ASER INDUCED FLUORESCENCE Motivation While mapping emission intensities is a very straight forward method of inve stigating analyte distributions, it only interrogates the excited states. Following 0.1 3% for an excited state with degeneracy of 3 and a resonant emission in the blue, 450 nm. In many cases, t ransitions begin at an even higher energy level such as 35,000 cm 1 Maintaining the degeneracy and atomic identity, for the partition function  the population of this excited state falls to 0. 012 %. Considering there are other levels also populated according to the thermal distribution, the ground state will still have an order of magnitude higher density than excited states. Therefore, it behooves the investigator to probe the ground state as well. There are two attacks for that sort of investigation. First, it is possible to measure the absorbance of an incide nt light source. A fraction of the light is absorbed and represents the density of analyte within the probed volume. In some cases, this absorption will result in the excitation of an emissive excited state. With the appropriate magnitude of spontaneous emission coefficient, the fluorescence from that level is informative in the same way. The magnitude of the fluorescence also represents the density of analyte. From a signal to noise perspective, the fluorescence is a more attractive signal as it is po ssible to conduct the investigation with minimal background given the right conditions. However, absorption is more widely applicable as it does not require the transition to be emissive. Ultimately, fluorescence is chosen for this investigation for its easy comparison to thermal emission and its freedom from artifacts induced by refraction.
73 As was discussed earlier, the application of LIF to LIBS is executed in the late 197 0s The combined method LIBS LIF was known as TABLASER  At that time, it was used to construct working curves for impurities in foodstuffs  In the 198 0s the technique began its function as a diagnostic for LIP [31, 37, 112] By 1990, Planar LIF (PLIF) was established as a spatially resolved diagnostic tool within LIPs. These applications applied to atoms [39 41, 113] ions [114, 115] radicals  and oxide s [41, 117] As an alternative to the spatial resolution given by imaging a plane of excitation, time of flight measurements can be conducted at a set height. The time varying signal of fluorescence for a given position has been used to study the distribution of atoms [42 44, 118 120] and oxides  in LIPs. In accordance with the overall goal of this project, the method of data collection for the spatially resolved LIF need s to be compatible with the existing setup. The ICCD is already coupled to the spectrograph for other emission work. Decoupling the detector from the spectrograph require s si gnificant calibration when the two are subsequently reunited. It would be possible to configure the detection system in much the same way as the schlieren imaging. Unfortunately, this significantly limits the species available for investigation by fluore scence as the bandpass filter needs to be customized to the fluorescence wavelength. Therefore, the configuration for this work is a sort of hybrid between the two historical methods described. Essentially, the volume observed is much like a time of flig ht measurement. It remains fixed in space and observes the changes in time. Like the PLIF experiments r eferenced above, the detector still retains a spatial dimension. The fluorescence is resolved spectrally, but the second dimension of the ICCD detecto r resolves either vertical or horizontal distribution s Also, like the
74 PLIF experiments, the excitation is not a point source. In this way, the detection scheme is easily customizable to any analyte with a strong fluorescence in the visible or ultra viol et regions. In conjunction with the spatially resolved emission measurements described earlier in this document, the spatially resolved fluorescence measurements aim to investigate the distribution of atom and ion species within the plasma plume. Complime ntary to the earlier work, the fluorescence measurement can map the unexcited lower level populations of the analyte. Additionally, the experiment does not stop with the cooling of the plasma. While emission measurements are contingent upon this point, f luorescence investigations can continue well after the plasma temperature falls. This means that the fate of the atoms and ions produced by the plasma formation can be determined even if they cease to emit. Experimental Laser induced fluorescence measurem ents are made within a LIP. The formation of the plasma is consistent with the previous sections of this document. A Nd:YAG laser operating at the fundamental wavelength of 1064 nm with a pulse width of 7 ns form s the plasma. Tunable dye lasers are intr oduced at 90 with respect to the incident ablation laser and collection optics. With this geometry, the probe laser illuminate s the plasma from the side. The extent of the probed volume depend s on the focusing optics of the dye laser. Two foci are used ; a conventional plano convex lens generate s a point focus and a cylindrical lens generate s a plane of excitation. For spatially resolved work, the cylindrical lens excitation is the obvious choice as it enables simultaneous acquisition of fluorescence fr om every height within the plasma. A point focus would limit the vertical range of fluorescence within the plasma.
75 Two excitation schemes are used in this project. First, atomic distributions of lead are studied in a plasma generated on a multi component glass (SRM 1412, NIST) that contain s 4.4% lead by mass. To interrogate lead atoms, an excitation at 283.305 nm probe s the direct line fluorescence at 405.781 nm. Second, ionic distributions of barium are ss (Brill C, Corning) with 11% barium by mass. Excitation is at 455.403 nm and direct line fluorescence is monitored at 614.171 nm. The delay between the ablation pulse and fluorescence pulse is varied from 500 ns up to 30 s. Fluorescence detection for this project is accomplished with the spectrograph equipped with an ICCD. The plasma is imaged onto the slit such that a vertical slice is spectrally resolved for detection by the camera. When horizontal slices of the plasma are imaged, a glass dove pris m is introduced into the optical train at 45. Such an orientation turn s the image of the plasma 90. Therefore, a horizontal slice of plasma is selected. Again, as the jitter in the timing of the probe pulse limits the accuracy of the delay, the ICCD g ate is set to a wide 100 ns. As there is some variability with the dye laser intensity, 49 spectra are collected and averaged to generate a single fluorescence image. This averaging is done by manipulating the data in software. No on chip accumulations are used. Additional post processing is necessary as the time integrated measurements did not distinguish between thermal emission and fluorescence. To remedy this issue, emission spectra are taken and averaged in the same manner for each delay. The two signal magnitudes are then subtracted to generate the fluorescence intensity.
76 As stated above, the end result is an array with spectral resolution in the x axis and vertical resolution in the y axis. The entire intensity could be integrated over the vert ical range or parsed into smaller regions. Binning the entire vertical limits of the plasma at each delay generate s a trend for the plasma on the whole. By selecting smaller regions of the image to be binned, the spatial distribution of the analyte c an b e deduced. This second assertion relie s on the assumption of saturation. Any variation of a fluorescence intensity in the vertical axis could result from a real analyte density change or a difference in probe laser fluence. A thorough check of this assu mption would require the testing and construction of a saturation curve where the fluorescence intensity is measured as the excitation fluence is varied over several orders of magnitude. This process is approximated by measuring the fluorescence intensity with and without a neutral density filter of optical density 0.3. Such an optical density would half the excitation fluence which would half any linear fluorescence that resulted. If the excitation is strong enough such that saturation is achieved, the fluorescence intensity would remain unchanged and the fluorescence would accurately represent the analyte density. This behavior is checked for the fluorescence studies in lieu of the construction of an entire saturation curve. The selection to be binned is determined from images at early and late stages of the plasma evolution. The vertical extent of the plume examined in this study is summarized by Figure 4 1. Emission at an early delay is juxtaposed with the fluorescence later in the plasma expansion. An integration height is set to 140 pixels which corresponded to 3.22 mm. When studying the plasma plume as a whole, the entire 140 pixel region is summed. Ten pixel segments are binned for vertical resolution
77 which results in 14 spatial points. Each 2 shows how the emission and fluorescence images are Parsing is done in the LabVIEW environment using a virtual instrument written in lab. The front panel of the program is shown i n Figure 4 3. Two functions are served by this program. First, the region of interest ( ROI ) c an be refined using the images which are shown before and after ROI selection. Secondly, it bin s the data from each of the 50 frames and output s the intensity v ersus wavelength for convenient treatment in a spreadsheet. It is more economical to take whole images of the plasma and electronically divide the data later. Experimentally, it is feasible to collect each vertically binned region by resetting the ROI an d collect ing all new spectra, however, this strategy would consume much more sample and time. Results Atomic Fluorescence Before the investigation into the spatial distribution of atomic lea d within the plasma, the integrated behavior of the entire plasm a is evaluated for co mparison to the resolved data. Figure 4 4 shows an obvious relation between the thermal emission and to be already saturated. Very little fluorescence is observable at those earl y delays. However, the fluorescence sharply rises as the excited states begin to depopulate from their thermal background levels near When parsing the emission data, the time of flight is apparent at heights just over 1.5 mm. The first temporal point, 500 ns, is too late within the plume expansion to be
78 more spatially selective for this observation. In Fi gures 4 5 A and B the emissive plume clearly expands over 1 mm within those first hundreds of nanoseconds. As the observation region reaches 3 mm in Figure 4 5C is apparent. Emission behavior at late delays within the plasma are summarized in Figure 4 6. The intensity scale is reduced in Figure 4 6 B to show the long lived emission around 1 mm. The fluorescence traces in Figure 4 7 experience the opposite trend. The fluorescence at 3 mm above the surface peaks wit h the emission and surface, the fluorescence peak moves to later delays. At the limit when it reaches the sample surface, the peak fluorescence seems to be nonexistent. The peak fluorescence is quickly reached and maintained until very late delays. At these delays after the plasma has formed, the plume has run its course, radiatively, but the species within it are still traveling out as a result of the explosion. Theref ore, the loss of fluorescence is likely the result of the lead atoms expanding out of the observed volume. This leads to the conclusion that the analyte is more quickly expelled from the observation regions high within the plasma. Emitters within the hig her volumes likely have greater kinetic energy, as they have travelled farther since the ignition of the plasma. Therefore, their velocity removes them from the probing laser more quickly than those analyte atoms at a lower elevation. These atoms have tr avelled a smaller distance and escape the probe laser at much later delays. Ionic Fluorescence Vertically r esolved On the whole, Figure 4 8 shows the barium ionic emission and fluorescence behave very similar to the lead atomic with some small differences. Figure 4 9 shows
79 three characteristic curves from the parsed data. Similar to the atomic data, the However, unlike the atomic data, emission does not seem to depend on the ve rtical location within the plasma. All points within the height of the plume seem to change at the same rate in Figure 4 10. While their relative intensities may be different, they share the same behavior in time. Figures 4 9 and 4 11 B show the fluores species is only 40% of the emission peak intensity. For the atomic transition, the peak fluorescence achieved 90% of the emission peak intensity. The thermal emission has These shorter lived trends make sense as the ionic species are expected to disappear sooner from recombination within the plasm a  Reflecting the trend seen in the emission data, vertically resolved fluorescenc e within the ionic population of barium is much less dynamic than its atomic counterpart. While there is an obvious vertical distribution difference as evidenced by the intensity change, each region seems to change in the same way with respect to time. Ho rizontally r esolved The ionic barium fluorescence within the horizontal slice has a very interesting temporal distribution shown in Figure 4 12. At first glance, the fluorescence seems to be suffering from some post filtering from the surrounding barium i ons. This concern is quickly checked by the collection of another curve with a much lower concentration of barium, 0.5 % by mass. The temporal distribution in Figure 4 13 corresponds to this concentration. The same structure of fluorescence depression ar is observed
80 even at the much lower concentration. It is believed that this feature is real. Additionally, Figure 4 8 shows that it is shared by the vertically resolved fluorescence. If the depression does not result from a reduction of the fluo rescence at that time, then it is reasonable to account for the intensity rise with a rise in local temperature which ionizes barium to this state. This hypothesis is unlikely as the temperatures at these delays are well below the 5.2 eV required to ioniz e atomic barium. Much higher temperatures are possible from the effects of an internal shockwave; however, Wen predict s that the internal shockwaves have expired by this delay  Another possible explanation for the depression is fluorescence quenching. It is possible that collisions within the plasma are contributing to a significant amount of quenching at these delays. Later delays may be free o f phenomenon as the electron energy distribution shifts to lower energies and collisions become less frequent resulting from recombination with ions When looking at the parsed horizontal data in Figures 4 14, 4 15 and 4 16, the negative numbers indicate t he displacement from the center of the plasma away from the dye laser. Positive numbers indicate moving from the plasma center towards the incoming dye laser. Emission profiles from Figure 4 15 B of these two regions show that the plasma plume is asymmetr ic. There is a steeper intensity gradient towards the incoming dye laser. This reflects the trend seen in the spatially resolved emission from Chapter 2. However, in that context, the perspective is not the same, merely the trend for an asymmetric plasm a holds. The elevation observed for this data is possible. Emission intensities are monitored until they fell to several percent of their
81 peak values to determine the top and bottom of the emissive plasma. The midpoint between these two minima is taken as th e center of the plasma. Again, Figure 4 15 A shows a time of spatial points 1.38 mm. Like the vertically resolved data, there does not seem to be a strong spatial dependence for the time evolution of emission intensities. The fluorescence curves are summarized in Figure 4 16 A The strong depression igat ed here. Like the emission curves, the fluorescence has a much steeper rise on the side near the incoming dye laser. Figure 4 16 B shows this very well. Unfortunately, Figure 4 16 B observed in the individual plots. This could i ndicate that the laser is not saturating and the intensity is being absorbed. However, the fluorescence intensity is being reduced linear ly as is highlighted by the red circle in Figure 4 16 B If the laser intensity is being absorbed, it must decay expon saturating and the intensity is decaying according to this relation, then the fluorescence should respond linearly and decay exponentially as well. A possible explanation for this linear decrease in f luorescence intensity has been proposed by Vidal  Here, fluorescence behavior is modeled under conditions of arbitrary optical depth. When the excitation transition is assumed to not be optically thin and the incident irradiance is large, a deviation from the Beer Lambert Law is predicted. In their model, the incident irradiance is reduced linearly with x rather than the exponential decay of a low incidence irradiance.
82 The trend for the fluorescence to increase at even later delays is likely to due to the decrease in excited state barium as is evident from the emission. This behavior is investigated for the entire plasma and is lower ion ization energy requires that a very low energy electron recombine with the ions. Because of this, the ions persist for tens of microseconds. This observation may raise some concern when comparing with the atomic lead data above. It must be remembered th at this behavior is observed within a horizontal slice of the plasma while the plots above show the vertical distribution of lead. For a proper check of this behavior, the horizontally resolved experiment should be reproduced with the lead sample. It can be inferred that such an experiment would see atomic fluorescence persist much past the ionic fluorescence of barium. Conclusions These experiments give insight into the distribution of atoms and ions within the plasmas at much longer delays and larger sp atial regions than emission. The atomic population tends to shift to lower elevations as time progresses while the ionic fluorescence maintains the same relative distribution of density. In both cases, the fluorescence intensity decays in the tens of mic roseconds. The ionic fluorescence fluorescence. This depression is less substantial at the periphery of the plasma. There is some disagreement between the horizontally resolv ed and vertically resolved curves. At the center of each, they should agree with respect to time as they are, theoretically, probing the same volume. Therefore, the discrepancy between the two, the lasting ionic fluorescence present in the horizontal dat a, must result from a different plasma structure. The most significant difference between the two data sets is the servicing of
83 the ablation laser between their collection. When the laser is serviced for a new flashlamp, the cleaning of the optics requir ed a realign ment of the cavity. Such an optical change can change the beam profile. Future work includes the need to directly compare horizontally resolved atomic data to the ionic data presented above. While the data above is believed to be real and fre e from any artifacts, the long lived ionic fluorescence could be confirmed by longer lived atomic fluorescence.
84 Figure 4 1. Examples of the vertical extent of the plasma at two delays. The scales at the sides indicate the pixel number of the camera. The strong emission in A is Sr II. A) Emission at 0.5 s. B) LIF at 7 s. Figure 4 2. Diagram of the vertical separation of data within the CCD image at 0.5 s.
85 Figure 4 3. LabVIEW VI used resolution. Figure 4 4. Spatially integrated Pb I emission and fluorescence signals at delays.
86 Figure 4 5. Examples of the Pb I parsed emission an d fluorescence curves obtained at three heights within the plasma. A) 0.46 mm. B) 1.61 mm. C) 2.99 mm. Figure 4 6. Waterfall plot of vertically parsed Pb I emission data. A) Entire intensity range. B) Intensity scale limited to 2000 counts to highlight the contour of thermal emission.
87 Figure 4 7. Waterfall plot of vertically parsed Pb I fluorescence data. Figure 4 8. Spatially integrated Ba II emission and fluorescence signals at delay s. The spatial integration is along the vertical axis within the plasma.
88 Figure 4 9. Examples of the Ba II vertically parsed emission and fluorescence curves obtained at three heights within the plasma. A) 0.46 mm. B) 1.6 1 mm. C) 2.99 mm. Figure 4 10. Waterfall plot of vertically parsed Ba II emission data.
89 Figure 4 11. Waterfall plot of vertically parsed Ba II fluorescence data. A) Perspective on the decay of the fluorescence with hei ght. B) Perspective on the persistent dip in fluorescence with respect to time. Figure 4 12. Spatially integrated Ba II emission and fluorescence signals at delays from a LIP of 11 % Ba by mass. The spatial integration is al ong a horizontal axis within the plasma.
90 Figure 4 13. Spatially integrated Ba II emission and fluorescence signals at delays from a LIP of 0.5 % Ba by mass. The spatial integration is along a horizontal axis within the plasma. Figure 4 14. Examples of the Ba II horizontally parsed emission and fluorescence curves obtained at three positions within the plasma. A) 1.15 mm. B) 1.15 mm. C) 0 mm.
91 Figure 4 15. Waterfa ll plot of horizontally parsed Ba II emission data. A) Perspective of the decaying ionic emission. B) Perspective of plasma asymmetry. Figure 4 16. Waterfall plot of horizontally parsed Ba II fluorescence data. A) Perspe ctive of the fluorescence with respect to time. B) Perspective of fluorescence asymmetry.
92 CHAPTER 5 TIME RESOLVED LASER INDUCED FLUORESCENCE Motivation Shortly after the advent of the continuously tunable dye laser, Measures proposed its use for selec tive excitation of atomic transitions  In this paper, Measures also covers some applications for which this method may be applied. Many of the applications require time resolution on the scale of the laser pulse used to excite the atoms. During th is time in the field of atomic spectroscopy, time resolution typically meant the execution of a fluorescence lifetime measurement. Accordingly, Measures proposed methods for plasma diagnostics using LIF of atomic states required the measurement of multip le lifetime decays after the excitation pulse. Measure s derived some math that could be used to evaluate local temperatures and electron number densities based on the observed fluorescence decays of multiple levels. In addition to the theoretical work M easures and Kwong conducted some of the first practical research into time resolved fluorescence inside a laser ablation plume  They propose d a method for determining atomic l ifetimes of chromium within a LIP. This use of the combined techniques for lifetime measurements has continued to today for other atoms  and even oxides within the plume  While Measures proposed to use time resolved LIF to evaluate temperatures and electron number densities, Burgess saw the potential to evaluate basic spectroscopic properties of atoms and ions  Again, using time resolved LIF and a consideration for population and depopulation rates within the plasma, Burgess proposed a method to measure spontaneous emission coefficients within a plasma source. For this work, long pulse lengths approached steady state values after an initial saturation of levels. How
93 the system responded after the initial population equilibrium gave in sight into the energy level environment around the two levels of the transition. A measure of these decay rates allowed for an evaluation of the Einstein coefficient, A. Additionally, this work in plasma LIF accounts for significant collisional coupling between neighboring states within an atoms electronic structure. Since these early considerations of LIF, the technique has been used with success in other atom sources such as flames and ICP  From this continued work, it has become evident that time resolution within the pulse length of the probe laser is i mportant  With this powerful tool, investigations have been made into the use of LIF for temperature measurements that build upon the proposal of Measures  some applications, these two excitation steps need have to a well controlled delay. Keeping the same experimental conditions but changing the goal, two step excitation work was also done in ionization spectroscopy  While complicating the experimenta l setup, it is clear that time resolution on the order of the pulse length for the probing laser allows for some powerful techniques. Looking at the techniques listed by Zizak, such an experimental setup also allows for the investigation of so called a population spike from collisions with the probed transition. Those considerations are also important for this work. Collisional p henomena like this have been studie d bef ore in a LIBS plasma  but investigation stopped at integrated fluorescence intensities. It seems that no research has been done to determine the delays betw een these fluorescence traces, rather just their
94 relative intensities. When comparing the volume of work done with LIBS LIF, it is clear that time resolved studies lack in coverage behind spatial and sensitivity investigations. Here, it is proposed to in  Time resolved atomic fluorescence within the plasma plume will be used to determine temperatures and colli sional coupling within the plume. Temperature Measurements The method proposed for the evaluation of temperature was first introduced by Kunze in 1986  Like m any other methods for temperature calculation, this math depends on the Boltzmann distribution of atoms or ions in their excited states from Equation 2 1. Additio nally, the saturation of an optical transition is essential to the calculation. In the most simple terms, the saturation of a generic transition occurs when the population of the lower s tate is equal to the upper state Reality is rarely so simple, and s aturation in practical terms must account for the degeneracy of states. So, for an optical transition with the degeneracies known for the lower and upper states, saturation is defined by the condition: ( 5 1 ) Here, n 2 is the popula tion of the upper level and n 1 is the population of the lower level, and g 1 and g 2 are the degeneracies of the lower and upper levels, respectively. The populations of the two levels at saturation can also be interpreted from the initial thermal, populat ions, n 1 Th and n 2 Th for the lower and upper states, respectively. ( 5 2 )
95 With some rearranging, these two equations can be combined in a way that relates the initial upper level population to the increase in population. These two values are selected as they can be readily measured through thermal emission from the upper level and direct line fluorescence. ( 5 3 ) By including the relation between the lower and upper states from the Boltzmann distribution fro m Equation 2 1, a final relation between the fluorescence and temperature is realized. Here, the intensities are directly substituted for number densities according to Equation 2 2, as this is a ratio between the emission and fluorescence from the same t ransition. Typically, the fluorescence intensity would be dependent on the number density of the lower level from which it is excited; however, in this derivation, saturation of that transition is assumed and the fluorescence comes only from the maximum a llowed change in the upper state according to Equation 5 3. The spectroscopic properties of the transition are the same for both quantities and the 2 is the increase in the upper level population and I 2 is the intensity of the thermal emission. ( 5 4 ) Recall that E 21 is the energy difference between the levels involved in the saturation, k is the Boltzmann constant and T is the excitation temperature. In the conversion between nu mber densities and intensity, I 2 and I 2 most constants cancel. However, while the two quantities share the same constant for spontaneous emission and wavelength, they differ in their observed volumes for emission and fluorescence,
96 V Em and V Fl respectively. This consideration has been app arently neglected Kunze in his treatment of mathematics  It has be en included here as these two volumes will differ if the entire plasma is not saturated with fluorescence. Ultimately, an expression for the evaluation of temperature is desired. So, some rearrangements of Equation 5 4 can easily be done to generate such an expression for temperature. (5 5) From this point, the ratio between the fluorescence increase and thermal emission will be called R. If the natural log is taken of each side of Equation 5 4 followed by a derivative, an expres sion for the relative error of the ratio results ( 5 6 ) Applying the chain rule with some rearrangements generates an equation that evaluates the relative error of the temperature calculation based on the relative error within the m easured ratio. ( 5 7 ) This final expression is the one used to calculate the propagated error from the ratio measurement to the final temperature. Besides the obvious dependence on the measured error, there are two clear dependencie s for the temperature error. For the following discussion, the measured error is set at an arbitrary 10 %
97 Figure 5 1 shows that the calculated error increase s with the calculated temperature. From the equation, it is clear that the dependence begins line arly as the ratio of exponentials is insignificant. The range of this linear dependence increases with the energy difference between the levels. At these higher energies, the roll off occurs later as the temperature takes longer to overcome the large ene rgy difference. Eventually, the increase in error ceases to be dependent on the temperature. For the levels used in this study, that maximum error is roughly 9 % but does not occur until unreasonably large temperatures. The second dependence arises from the energy difference between the two levels involved in the saturation and is plotted in Figure 5 2. Similar logic applies to this relation as in the previous discussion. Initially, the two quantities are inversely proportional. This indirect proportio nality rolls off to a minimum value at high energy differences. The rate of this decline to the minimum depends loosely on the temperature as it sets the magnitude of the exponential. By 10 eV, most reasonable temperatures have approached their asymptote between 0.5 and 1.0 % For the energy levels used in this study, that corresponds to a threefold reduction in the relative standard deviation. However, such energies also surpass the ionization potential of barium. Experimental The instrumentation and or ientation for this work shares heavily with the previous chapter. Accordingly, only the differences will be explained here. The plasma formation and probing are the same. As with the previous work, the probe beam is focused into a plane of excitation. Temperatures are investigated at two heights, and the experiments need to be free from any possible systematic error from spatial effects. A smaller region
98 of the plasma is collected for this investigation and a point focus would require that the observat ion volume overlap exactly with the probed volume. These two regions would also have to be moved in unison. Detection of the LIF signal is accomplished through a 0.3 m monochromator equipped with a 1200 grooves/mm grating and MCP PMT. Time resolution wit hin the probe pulse is desired which requires this fast detector. In conjunction with the fast response time of the detector, the scope used is a 6 GHz digital oscilloscope. Typically, 500 LIF traces are averaged on the scope and saved to the internal ha rd drive. To generate an uncertainty for the thermal emission and fluorescence, pixels are averaged within the same trace for the two values. Their standard deviations are taken to represent the noise within the two signals. The scope is equipped with a GPIB (General Purpose Interface Bus, IEEE 488) connection. Through this connection, individual scope traces are collected by the computer for the purpose of analyzing the statistics between plasmas. The volume of the plasma observed in this setup needs t o be restricted as much as is possible. The reasoning for this requirement lies in the proposed temperature calculation. Since the equation depends on the ratio between the thermal emission and fluorescence intensities, the observed volume of both should be equal. Were they not, the ratio of intensities would vary, not because of the induced fluorescence, but as a result of the differing observation volumes. In an attempt to control this limitation, a trick has been introduced into the collection optics shown in Figure 5 3. First, an image of the plasma is formed by a single biconvex lens. The plasma and image are both 2 focal distances away from the lens. An image is formed on an iris which is restricted down to
99 a diameter of 0.5 mm. A second biconv ex lens is used to form an image of the light passing through the iris. This is the image that hits the slit of the monochromator and is used in the time resolved fluorescence studies. Temperatures are calculated using fluorescence waveforms from Ba + Th e same excitation scheme used in the spatially resolved work is used here. The ion is excited at 455.403 nm while emission and fluorescence intensities are monitored at 614.171 nm. It is important that the observed fluorescence is a strong line while not being self absorbed. A strong emission is required for an adequate evaluation of the thermal population of levels, but a very strong line can sometimes be self abosorbed at higher concentrations. The emission line used here is relatively weak. With an Einstein coefficient for spontaneous emission of 4.12x10 7 Hz, the barium ion line falls within this region. In addition to temperature calculations, the time resolved fluorescence measurements lends itself to analyzing the collisional coupling within the p lasma. To investigate these properties two excitation and observation schemes are used. The energy levels and transitions involved are plotted in Figure 5 4. Two excitation wavelengths are used as they are easily tunable and correspond to strong transit ions. Both probes populate levels with strong direct line fluorescence, and both schemes allow for the collisional population of an excited state at 54949 cm 1. Specifically, the first excitation used is that of the previous chapter at 455.403 nm with fl uorescence at 614.171 nm. The second scheme excites at 452.493 nm with the fluorescence 489.997 nm. The collisionally coupled state emits at 389.178 nm. For this part of the study, 500 fluorescence traces are averaged to generate each waveform.
100 Results Temperatures Time resolved fluorescence waveforms are the work horse for th is section These waveforms are induced by the dye laser output tuned to a transition of the analyte, barium, in this work. The specific output of the dye laser at 455.403 nm with respect to time has no clean distribution as shown in Figure 5 5. Rather, it reflects the temporal shape of the excimer laser pumping it. Temperatures calculated with these LIF traces take their fluorescence increase from the fluorescence induced by the initial peak of the dye laser and their thermal emission as the signal present just before the fluorescence peak. There is some concern that the erratic power output of the excimer laser could introduce some drift in the dye laser power. If great enough, this drift could alter the shape of the fluorescence waveforms. While unlikely, as 500 laser shots are averaged, the reproducibility of the method is checked by four repetitions of the experiment with 500 averages of 614.171 nm fluorescence on four diffe rent sample locations. Figure 5 6 shows the overlay between these four trials. Clearly, any drift present in the excimer laser power does not affect the results generated by this experiment. From fluorescence waveforms similar to those plotted in Figure 5 6, temperatures are calculated at several delays within the plasma and plotted in Figure 5 7. This particular set of data is collected with the iris selecting a region about 1 mm off of the sample surface. Accordingly, the temperature at the earliest d elay time, 1 s, is both uncertain and low. This indicates that this spatial region lies at the edge of the emissive plume at that delay. Any measurement taken on the steep gradient of a dynamic system is expected to exhibit this precision decrease. By 2 s, the plume has expanded
101 to encompass that entire region, giving a more reliable temperature measurement. The temperature levels out around 7000 K and maintains that value through the delay of 10 s. Next, the iris is moved to image the region of the plasma just grazing the sample surface. Emission intensities are monitored as the iris is moved down, through the image. Temperatures calculated for this height are plotted in Figure 5 8. The volume observed at this height has the most intense emission and highest temperatures as measured by the two aperture system. As expected, the temperatures at early delays reflect the hotter core of the plasma plume. For the higher elevation, the temperatures settle down to 7000 K by 3 s. At the center of the pl asma, the temperature takes until 8 s to reach that level. To verify that these temperatures make sense for this laser irradiance, a Boltzmann plot needed to be constructed based on Equation 2 4. The Boltzmann plot is taken to be the experimental check a s it is the widely accepted method for temperature calculation within a plasma source [70, 75, 130] Its construction is explained in Chapter 2 for the d erivation of the Saha Boltzmann plot used in the CF LIBS analysis. Sabsabi established the convenient use of a single spectroscopic window for the construction of Boltzmann plots  Centered at 373 nm are 8 iron lines with well known spectroscopic properties. These lines can be used without any calibration of the instrument response as they are all closely spaced and span 8,000 cm 1 or 1 eV, in energy. While the above plots represent temperatures with a measure of spatial resolution, the Boltzmann plot presented in Figure 5 9 is an integration of the entire plasma. Additionally, the sample used for the fluorescence temperatures is a glass with
102 a very low con centration of iron. The window and procedure proposed by Sabsabi would not work as an easy check for this sample  So, a different sample containing more iro n is placed at the focus of the laser. The aluminum D33 alloy is used. Its composition is shown in Table 2 1. While the different physical properties of the silicon glass and aluminum alloy will cause different plasmas to form, this is simply a check th at the temperatures are in the correct order of magnitude and exhibited the same trend. The same ablation laser properties and ambient conditions are used for each measurement. Again, the temperature at 1 s is unreliable. It is believe d that these early delays may not adhere to the local thermodynamic equilibrium necessary to fulfill the requirements of a Boltzmann plot. Later delays, however, show a very similar trend to the fluorescence temperatures. A temperature of 7000 K is approached near the 7 s delay and maintained through 10 s. Since this is an integrated measurement, there will be some overlap between both of the spatially resolved fluorescence temperature measurements. As was described in the experimental section, much of this work is aver aged on the oscilloscope. The model of oscilloscope used in this work does not report the standard deviation of each time pixel when taking the average. As a work around, several pixels are taken in each region, emission and fluorescence, and these value s are used to generate errors. Another approach for the evaluation of noise within the signal is to collect 500 individual traces and average them in a spreadsheet program outside of the oscilloscope. Then, a standard deviation between the 500 traces can be obtained for each point in time. Finally, a calculated temperature can be derived from a
103 single point of emission and a single point of fluorescence. The magnitude and trend of the temperatures in Figure 5 10 agree well with the work done on single t races. The error is obviously much more significant, never dropping below 45 % However, when the same calculation is made on the similar experiment done with 452.493 nm excitation and 489.997 nm fluorescence the error within the temperature is much les s. Figure 5 11 shows the temperatures at delays for this higher energy excited state. Since these two methods should contain the same experimental error, it may hint that some problems may rest with the use of a resonant line. As will be shown in the ne xt section, the 452.493 nm transition is very clearly saturated at all times. With the fluctuations present in the pulse to pulse power of the excimer laser, it is possible that some laser shots may not completely saturate the resonant transition. This c ould introduce significant error into the calculation when propagating error between shots. There is a collisionally coupled state that lies 23,997 cm 1 above the level probed by the 455.403 nm. It is a simple matter to measure the fluorescence from this level the results from the dye laser probe. Since this level is collisionally populated with respect to the probe laser, it is not expected to be a saturated transition. Accordingly, it should not fulfill the requirements of the temperature method used o n the direct line fluorescence at 614.171 nm. A strong radiative transition from this level has the wavelength of 389.178 nm. By monitoring the emission and fluorescence from this level in the same we that the direct line fluorescence is measured, temper atures can be calculated for several delays. Figure 5 12 shows the temperatures calculated from this fluorescence. The temperatures calculated here are larger than those derived from the direct line fluorescence. Such a trend is expected for a transitio n that is not saturated.
104 The observed fluorescence will be interpreted as the increase in population required to equilibrate the two levels. When this value is low as a result of a linear response to excitation, the thermal emission is interpreted as bei ng too large of a contribution. That higher weighting to th e thermal emission results in a falsely high temperature. Removing Volumes from Calculated Temperatures While there is very good agreement between the saturated fluorescence temperatures and the B oltzmann plot method, the issue of observed volumes cannot be ignored. Equation 5 5 shows the volume dependence of the calculations. For the work above, a value of 1 is assumed. Figure 5 13 illustrates the behavior of the calculated temperature as the v olume ratio is increased to a realistic value. The plasma plume can be estimated at 2 mm. This dimension depends on the delay after the plasma formation, but the diameter will be somewhere near this value for most delays considered here. The width of th e excitation plane within the plume is close to 0.1 mm. Therefore, the volume corrected temperature corresponds to 5000 K at a volume ratio of 20 While the observed areas are the same, the depth observed for the emission and fluorescence are different. The optics and iris used to restrict the observed volume only works in two dimensions. The third dimension, depth is controlled only by the volume excited by the dye laser. This issue can be easily avoided experimentally if the dye laser is expanded to induce fluorescence within the entire plasma. In this scenario, the volumes would be equal, and their ratio would reduce to 1. However, for the laser energies and power available with the current dye laser setup, the reduction of laser excitation irradi ance brought about by beam expansion would not maintain saturated conditions over the entire excitation volume The levels would no longer obtain an equal population density, and no te mperature could be calculated.
105 The above correction factor is an estima tion that depends on the delay of observation and plasma structure. A more absolute solution would be a mathematic removal of the volume ratio. An expression for temperature without the volume ratio would be possible if the volume ratio could be cancelle d by executing the temperature measurement twice. A ratio of these two expressions would eliminate the volume dependence since both expressions would have the same emi ssion and fluorescence volumes. These two measurements would have to be at different wa velengths such that a ratio between the two would not simply reduce to 1. Beginning with Equation 5 4, the ratios and the degeneracies for each ratio will be reduced to Therefore, a ratio of two Equations 5 4 gives, (5 8) where V Em = V Em Fl = V Fl s removes the volume dependence and generates Equation 5 9. The equation has been rearranged into this form to show the consequences of possible assumptions. (5 9) The first ass umption is required to use Equation 5 9 as an evaluation for equal. (5 10)
106 From Equation 5 10 it would be possible to calculate a temperature from two measured intensity ratios. The relation is strongly dependent upon the difference between E 21 and E 21 w o energy differences are equal or very close, as in our case. If E 21 = E 21 (5 11a) and (5 11b) This solution requires that there is no transition Such a stipulation contradicts the measurement itself. Therefore, the two saturated transitions, E 21 and E 21 very different ene rgy differences for the mathematics to hold. In the present work, the energy differences are very nearly the same, resulting in the condition of Equation 5 11b An actual temperature can only be calculated in this manner for two saturated transitions tha t are significantly more different than 455.403 nm and 452.493 nm Response Times Evaluating the population dynamics within a plasma which result from a probe laser can shed light on its collisional properties. Four delays are selected for this investigat ion into collisionally coupled fluorescence with 455.403 nm excitaiton 1, 3, 5 is recorded along with the collisonally coupled state emitting at 389.178 nm. Some examples of the measur ed emission and fluorescence curves at 614.171 nm are shown in Figure 5 14 At 1 s the fluorescence appears to maintain for several tens of microseconds. While the emission and fluorescence traces were taken at significantly different dates, the
107 trend o f the emission shows that over the 100 ns window, the emission is flat. Therefore, the sustained intensity in the fluorescence curve could be a real fluorescence intensity. Such a long lifetime of fluorescence is likely due to the high electron number de nsity at that early delay. The frequent collisions could be transferring atoms into and out of long lived states near the upper energy level of the fluorescence emission. If any of the neighboring states have unfavorable spontaneous emission coefficients it is possible that the atoms in these levels will retain their energy long enough to repopulate the 614.171 nm upper energy level for some tens of nanoseconds. By 3 s in Figure 5 14 B the fluorescence intensity clearly reduces to the level of emission shortly after the probe laser ends. At this delay, there must be fewer collisions to sustain the excited state population paste the life of the probe pulse. A proper investigation into the behavior of the fluorescence at each delay requires an analysis with rate equations. Such an evaluation of the data is planned, but this discussion is not included here. These considerations also hold for the collisionally coupled state emitting at 389.178 nm. The waveforms for 389.178 nm share the same behavior at e arly delays. Again, the emission curves in these figures are intended to show the trend of the emission at these delays and not the absolute magnitude. Unlike the direct line fluorescence, the collisionally coupled level shows a lasting fluorescence inte nsity even at 3 s in Figure 5 15 B than the direct line fluorescence upper energy level. Such a conclusion is supported by the increase in the density of states near the ionization potenti al. By 5 s in Figure 5 15 C the 389.178 nm fluorescence reduces to the emission level after the probe pulse
108 ends. The long life of the fluorescence intensity for 389.178 nm is made very clear in the normalized waveforms of Figure 5 16 Since this sectio n does not care for the absolute magnitudes of the fluorescence and collisionally coupled emission, the normalized curves are more useful. Figure 5 1 6 shows the three traces at the four delays. These traces are plotted with the 455.403 nm scatter from th e probe laser to show their relative response time s. The signals for each trace are normalized to their peak value to show their relative behaviors. When looking at the normalized waveforms, it is important to understand how normalization affects a satur ated fluorescence signal. Taking an ideal sigmoid as the excitation step, Figure 5 1 7 A shows how a fluorescence signal is initially linear with the excitation. As the transition nears saturation, the fluorescence rolls off to some steady value. When the se two traces are normalized in Figure 5 1 7 B the fluorescence appears to be emitted before the excitation pulse. However, this is an artifact of the signal processing, but it is a good indicator of saturation. It is difficult to see the decay of the fluo rescence intensity to the background value of thermal emission. The ringing present is attributed to the triggering of the excimer laser used to pump the dye lasers. In theory, a simple dark subtraction could take care of this ringing, but a quick glance not a stationary artifact. Accordingly, the ringing must be endured. It is most significant at the low absolute intensity of the 389.178 nm emission. When looking at these four plots as a whole, one o bvious change is the shape of of fluorescence are at their closest values. This indicates that even the second pulse of
109 the 455.403 nm probe laser is nearing the sat uration mark. Since saturation is a rate process, early delays require higher probe laser powers to overcome the depopulation from frequent collisions. As time progresses and the electrons taking part in these collisions lose energy to them, achieving sa turation between two levels requires less probe laser power. If the fluorescence were linear with the excitation, the two waveforms would more closely track each other. waveform is nearing linearity, but saturation is checked as described in the previous chapter with the 0.3 optical density filter. The second feature that draws the eye is the response time of each trace. With increas ing delay, the gap between the rise of the direct line fluorescence and the collisionally coupled state grows. The gap is measured as the time difference between the half intensity of the two pulses. Since these traces are normalized, the delay in the re sponse time is simply the difference between each time value at 0.5 intensity. The relation is plotted in F igure 5 1 8 This indicates one of two phenomena. First, the energy distribution of the electrons active in the collisions is shifting to lower ene rgies. Second, the electron number density is falling which reduces the frequency of collisions. Reality being shades of grey, it is likely a combination of these two processes which contribute to the delay in the population of the collisionally coupled state. These same experiments and considerations are made for the 452.493 nm excitation scheme. Figure 5 1 9 Again, the transition to later delays shows the trend for the direct line fluorescence to peak sooner than the probe beam. Like the 455.403 nm excitation scheme, this is taken to represent the satu ration of the probed level. Additionally, at all delays shown
110 here, the pulse shape of the direct line fluorescence diverges greatly from the pulse shape of the probe beam. This is strong evidence for a much easier saturation of the 452.493 nm transition As mentioned before, good agreement between the probe and fluorescence traces indicates a linear response. A poor overlap between the normalized pulse shapes indicates that the transition is saturated even by the lower power peak 20 ns after the initia l pulse. The difference in response times for this excitation is all very short. The direct line fluorescence originates from a level that is only 0.45 eV below the collisionally coupled state with emission at 389.178 nm. Such a close energy spacing allo ws for much lower energy free electrons to populate between the two levels. By opening up the possible successful collisions to these lower energy electrons, the difference in response times between 489.997 nm and 389.178 nm is always less than 1 ns. Eve n at 10 s when the response time lags 2.5 ns for 455.403 nm excitation, the collisionally coupled level is populated within a nanosecond when probing with 452.493 nm. Conclusions A single line method for local temperature measurements is proposed. Two e xcitation schemes are evaluated with good agreement to a Boltzmann plot temperature, an accepted temperature calculation. The next step is to attempt the same evaluations on different analytes within different matrices at different concentrations It is possible that major elements may not be investigated by this method as a result of pre or post filtering by atoms. Also, some attention needs to be paid to noise sources for this calculation as t he propagated error strongly depends on the experimental co nditions. Perhaps the most important consideration for this temperature calculation is the elimination of the volume dependency. As was shown in
111 the results, inaccuracies within the volume ratio can cause the calculated temperature to be inaccurate by a factor of 2. However, the method still has good agreement on the order of magnitude. Two resolutions exist for this problem. First, as was described in the chapter, the temperature measurement could be executed on two transitions of varying energy diffe rence. An evaluation of this sort mathematically removes the volume elements. Another solution to this issue lies in the experimental implementation of the method. If a dye laser or OPO of adequate pulse energy could be procured, the measurement could b e done with a beam expanded probe. Assuming the probe beam had sufficient energy to saturate the entire plume, the volume of emission would equal the volume of fluorescence when the entire plume is probed. This method is also applied to the investigation of collisi on dynamics within the plasma with success. A clear relation is observed between the delay of response times and the energy separation of levels. The exact form of this relation cannot be define without a thorough rate equation investigation. Such an evaluation will be completed in future work. Saturation of the direct line fluorescence is confirmed by normalized waveforms of both excitation schemes.
112 Figure 5 1. Temperature dependence of the precision of the cal culated temperature from a 10 % error within the observed ratio. Figure 5 2. Separation of energy level dependence of the precision of the calculated temperature from a 10 % error within the observed ratio.
113 Figure 5 3. Lens geometry for spatially selecting regions of the plasma. Figure 5 4. Energy level diagram for Ba II. Both excitation and direct line fluorescence transitions are shown as well as the collisionally cou pled state.
114 Figure 5 5. Temporal profile of the excitation pulse at 455.403 nm. Figure 5 6. Repeatability of 4 temporal profiles of the 614.171 nm direct line fluorescence each averaged from 500 l aser shots.
115 Figure 5 7. Temperatures calculated from the direct line fluorescence at 614.171 nm about 1 mm from the surface. Figure 5 8. Temperatures calculated from the direct line fluorescence a t 614.171 nm grazing the surface.
116 Figure 5 9. Temperatures calculated using the conventional Boltzmann plot method on D33 aluminum alloy under the same conditions as the Ba II studies. Figure 5 10. Temperatures calculated w ith errors propagated from interpulse standard deviations.
117 Figure 5 11. Temperatures calculated from the direct line fluorescence at 489.997 nm after excitation by 452.493 nm. Figure 5 12. Tempera tures calculated from the collisionally coupled emission at 389.178 nm after excitation by 455.403 nm.
118 Figure 5 13. Temperature correction for volume ratio between emission and fluorescence. Data used here is typical for 4 s delay. Figure 5 14. 614.171 nm emission and fluorescence traces A) 1 s. B) 3 s.
119 Figure 5 15. 389.178 nm emission and fluorescence traces. A) 1 s. B) 3 s. C) 5 s. Figure 5 1 6 Fluorescence traces for 614.171 and 389.178 nm along with scatter from the excitation laser at 455.403 nm A) 1 s. B) 3 s. C) 5 s. D) 10 s.
120 Figure 5 1 7 Effect of normalization on a saturated fluorescence signal. A) Raw signal of probe laser and fluorescence. B) Normalized signals. Figure 5 1 8 Response time s calculated from difference between the half intensity of the direct line fluorescence at 614.171 nm an d collisionally coupled line at 389.178 nm.
121 Figure 5 1 9 Fluorescence traces for 489.997 and 389.178 nm along with scatter from the excitation laser at 452.493 nm. The traces correspond to four delays within the plasma. A) 3 s. B) 5 s. C) 10 s.
122 CHAPTER 6 CONCLUSIONS Completed Project Goals Presented herein is an experimental setup that combines the benefits of emission, fluorescence and imaging. Each of these techniques exhibits resolution for space and time. It is possible to easily switch between emission and fluorescence detection with no alteration to the system. The addition of the schlieren imaging require only two optical elements to be added to the emission collection optics. These two optical elements do not replace or remove any pre existing lenses or stops. Both pieces can be removed and replaced at no real detriment to either technique. The emission study shows a very fine spatial distribution but suffers from a lack of sensitivity The physical exten t of the plasma observed is smaller than the emissive volume observed during the spatially resolved fluorescence work. The highly selective optical collection requires a much more sensitive detector. With such a device, many more spatial points of collec tion could be added to the periphery of the map investigated here. Additionally, a more sensitive detector would be able to pull the weak lines out of the background or wings of neighboring lines. With more analytical lines for investigation, a more thor ough application of CF LIBS would be possible. Despite this limitation, very clear trends are observed for atomic emission and ionic emission. Atomic emission is strongest near the surface of the sample which agrees with the temperature distribution dete rmined by the CF LIBS program. While the distribution of electron number densities are more erratic, the magnitude of the densities agrees well with previous observed values. This is an encouraging fact that may indicate minor
123 adjustments to the techniqu e may resolve a structure to the electron number density distribution. Schlieren imaging studied with this setup agrees well with the theoretical expansion of a shockwave. Additionally, similar trends observed herein were reported by other LIP research gr oups. This useful imaging technique is applied while being minimally invasive to the existing emission and fluorescence setups. Spatially and time resolved LIF measurements show promise for quantitative mapping of the atoms and ions within the plasma plum e. While other work has been published featuring images of LIF within a plume, the technique executed within this work looks to give these values hard numbers by splicing the technique with the time of flight technique. By monitoring a window within spac e and changing the delay time, the change of atomic and ionic distributions within the plume is very clear. Finally, a thorough look into the dynamics of the plasma are conducted using barium ion. The application of a new, single line temperature measurem ent is executed and a simultaneous investigation into collisional coupling of states is possible. The time resolved data, while clearly indicating the time scale in which collisional rates among the various levels occur, can only be seen from a qualitativ e point of view. In addition, the fluorescence temperature measurement is not without its limitations. The evaluation of the technique made it clear that very specific energy level systems must be used to accurately implement the method. Observation vol ume considerations hinder the application of this new temperature technique. Future Project Goals Future work on the system will refine the methods already outlined by this document. Specifically, the space resolved emission measurements would benefit fro m
124 a more sensitive detector behind the spectrograph. This increase in sensitivity could decrease the time window of the measurement and allow for investigating the weaker emissivity of the plume edges. A more detailed investigation into the time dependen ce of such measurements would require the use of an echelle spectrograph. Repeating the analysis with a conventional grating spectrograph is unrealistic for bo th time and data management. The requirement of repeated measurements over the span of days int roduces too many sources for noise or drift. The future of the schlieren studies should seek to mimic the contrast and magnification observed by Vogel  Such a refinement to the system may require more alteration to the emission collection optics. Specifically, a larger focal length lens may be required to collimate the refracted light from the pla sma. By extending that working arm, the displacement from center will also increase. This increased displacement results in an easier segregation between refracted and undisturbed light. A real improvement to the system could be realized with the use of a proper imaging camera. Scientific cameras, while sensitive, lack the spatial resolution for detailed work. The fluorescence techniques can be applied to many other analytes in other matrices. The spatially resolved measurements have a dimension of inf ormation ignored here. By marrying the time of flight and imaging techniques, the spatially resolved information retains the spectral width of each line observed. In this work, only the fluorescence intensities were evaluated, but an investigation into t he spectral line widths is possible with this instrumentation. Temperatures calculated with this setup need to be confirmed using the two wavelength method described in the discussion. Meanwhile, the collisional dynamics of the system could be investigat ed as a function of
125 pressure or ablation laser power. These simple variables could shed light on the connection between plasma formation and electron number densities well into the life of the plasma. The qualitative interpretation of the collisional dyn amics needs to be examined by a detailed rate equation approach. This future work will focus on the rates of population and depopulation for selected atomic and ionic levels. Finally, the absorption abilities of the system need to be evaluated completely. This work builds upon the dissertation of Dr. Benoit Lauly  While much of his work was done with transmission imaging of Cs within a plasma plume, the design of the instrument in this work focuses on the interrogation of an Ar line at 852.144 nm. With this con allow for interrogation of the plasma structure. Some preliminary results in this vein are shown in Figure 6 1. No data manipulation is done on this data save for an arbitrary off set introduced to give all traces the same initial intensity. As the signal moves up to less negative values, the laser intensity is being attenuated by the plasma. The legend to the right shows the frequency difference from the Ar line center. A plasma is formed on an aluminum sample, D33, under an argon atmosphere. At earlier delay times, the argon transition is wider, showing absorption of the laser diode out to 10 GHz from the line center. This width is much reduced by 3.5 s where little attenuati on is seen even 3.3 GHz off peak. The shared attenuation earlier than 1 s is attributed to the phenomenon described in Chapter 3. Plasma and shockwave formation can change the refractive index near the sample surface which can deflect the diode laser be am. This investigation is in its infancy and can use some refining. For now, the method is
126 setup for monochromator detection which ignores spatial information. Future work should aim to integrate imaging techniques similar to the work of Dr. Lauly.
127 Figure 6 1. Absorption of a diode laser as it is tuned away from the center of an argon metastable absorption profile. The legend indicates the spectral distance from the center.
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142 BIOGRAPHICAL SKETCH Daniel Shelby was born in Evansville, Indiana. After attending high school at F. J. Reitz High School, he moved to Bloomington, Indiana to earn a degree in c hemistry from Indiana University. In May of 2006, he gr aduated from IU with a Bachelor of Science in c hemistry and m athematics and research experience with Dr. Gary Hieftje. Dani el began his graduate school studies with Dr. Nicol Omenetto at the University of Florida in the fall of 2006 He graduated in the summer of 2011 with a Doctor of Philosophy in chemistry from the University of Florida.