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Investigation of spatial filtering for planar range-resolved pulsed laser ablated plume imaging

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Title:
Investigation of spatial filtering for planar range-resolved pulsed laser ablated plume imaging
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Book
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English
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Winslow, James F
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University of South Florida
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Tampa, Fla.
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Subjects / Keywords:
confocal microscopy
PLD
pinhole
film
optics
profile
Dissertations, Academic -- Physics -- Masters -- USF   ( lcsh )
Dissertations, Academic -- Engineering Science -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: This thesis presents a study of the intensified charge-coupled device (ICCD) imaging of pulsed laser ablated plumes. Two-dimensional imaging of laser ablated plumes is a very important diagnostic for PLD. ICCD array photography is a useful tool for imaging PLD. The images obtained using the standard technique are characterized and compared with ICCD images of an altered plume, ICCD images intentionally violating standard imaging procedures, and film thickness. The depth resolving properties of a pinhole was investigated with the intention of applying it to PLD plume imaging. This results in a more thorough understanding of the depth resolving property of a pinhole. The investigation leads to a theoretical improvement for the resolution in confocal microscopy.
Thesis:
Thesis (M.S.)--University of South Florida, 2004.
Thesis:
Thesis (M.S.E.S.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by James F. Winslow.
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Title from PDF of title page.
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Document formatted into pages; contains 104 pages.

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aleph - 001474325
oclc - 56137820
notis - AJR7194
usfldc doi - E14-SFE0000370
usfldc handle - e14.370
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ABSTRACT: This thesis presents a study of the intensified charge-coupled device (ICCD) imaging of pulsed laser ablated plumes. Two-dimensional imaging of laser ablated plumes is a very important diagnostic for PLD. ICCD array photography is a useful tool for imaging PLD. The images obtained using the standard technique are characterized and compared with ICCD images of an altered plume, ICCD images intentionally violating standard imaging procedures, and film thickness. The depth resolving properties of a pinhole was investigated with the intention of applying it to PLD plume imaging. This results in a more thorough understanding of the depth resolving property of a pinhole. The investigation leads to a theoretical improvement for the resolution in confocal microscopy.
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Investigation of Spatial Filtering for Planar Range-Resolved Pulsed Laser Ablated Plume Imaging by James F. Winslow A thesis submitted in partial fulfillment of the requirements for the dual degrees of Master of Science Department of Physics College of Arts and Science and Master of Science in Engineering Science Department of Electrical Engineering College of Engineering University of South Florida Major Professor: Prit ish Mukherjee, Ph.D. Sarath Witanachchi, Ph.D. Robert Chang, Ph.D. Kenneth Buckle, Ph.D. Andrew Hoff, Ph.D. Date of Approval: May 27, 2004 Keywords: PLD, confocal microsco py, pinhole, film, optics, profile Copyright 2004, James F. Winslow

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ACKNOWLEDGEMENTS I would like to express my deepest gr atitude to Dr. Pritish Mukherjee for providing the guidance and freedom necessary to complete this thesis. I would also like to thank Dr. Sarath Witanachchi for his support and availability. I would like to thank Dr. Robert Chang, Dr. Kenneth Buckle, and Dr. Andrew Hoff for serving on my committee. Special thanks to Bobby Hyde, whose assistance was invaluable during this project. I would also like to thank the following people w ho have helped in many ways: Houssam Abou-Mourad, John Cuff, Sam Va lenti, Sue Wolfe, Evelynn KeetoneWilliams, Dr. Sam Sakmar, Dr. Myung Kim. I would especially like to thank my wi fe Celeste for her consideration, support, and assistance through my graduate study. Finally, I would like to thank God for all the blessings in my life.

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TABLE OF CONTENTS LIST OF FIGURES iii ABSTRACT vii CHAPTER 1. INTRODUCTION 1 1.1. Introduction 1 1.2. Pulsed Laser Deposition 1 1.3. Plume Imaging and Dynamics 3 1.4. Overview 5 CHAPTER 2. CHARACTERIZATION OF STANDARD ICCD IMAGES OF LASER ABLATED PLUMES 6 2.1. Standard ICCD Imaging Method 6 2.2. ICCD Imaging of Out-of-Object-Plane Objects 9 2.2.1. Experimental Setup 9 2.2.2. Results 11 2.3. ICCD Imaging of PLD Plumes Varying Plume Distance to Object Plane 21 2.3.1. Experimental Setup 21 2.3.2. Results 23 2.4. Comparing an Integrated ICCD Intensity Profile with a Planar Profile 25 2.4.1. Experimental Setup 25 2.4.2. Results 28 2.4.3. Thickness Profile vs. Image Intesity Profile 29 2.5. Comments 31 CHAPTER 3. DEPTH FILTERING PROPERTIES OF A PINHOLE 32 3.1. Introduction 32 3.2. Depth of Field for a Finite Pinhole 32 3.3. Application to PLD Imaging 36 3.4. Initial Expectations 36 CHAPTER 4. INVESTIGATION 38 4.1. Initial Experiments 38 4.1.1. Experimental Setup 38 4.1.2. Results 41 4.2. Effect of Focal Length, Object Size, and Pinhole Size on FWHM 42 4.2.1. Experimental Setup 42 i

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4.2.2. Results 44 4.3. Effect of Lens Diameter on FWHM 46 4.3.1. Experimental Setup 46 4.3.2. Results 48 4.4. Effect of Image Distance (Magnification) on FWHM 49 4.4.1. Experimental Setup 49 4.4.2. Results 51 4.5. Effect of Increasing Out-of-Plane Sensitivity to (De)Magnification 53 4.5.1. Experimental Setup 53 4.5.2. Results 56 4.6. Translating the Pinhole Detector Through the Image 57 4.6.1. Experimental Setup 57 4.6.2. Results 59 4.7. Discussion 60 CHAPTER 5. REVISED DESCRIPTION FOR LIGHT TERMINATION AT A PINHOLE 62 5.1. Chapter Overview 62 5.2. Geometric Description 62 5.3. Ray-Transfer Matrix Description 68 5.4. Analysis of the Results from Chapter 4 71 5.5. Consequence to Plume Imaging 74 CHAPTER 6. COMPARISON WITH CONFOCAL MICROSCOPY 75 6.1. Introduction 75 6.2. Derivation of Depth Response for Confocal Microscopy 77 6.3. Possible Improvement to Confocal Microscopy Depth Response 80 6.4. Depth of Field for a Finite Pinhole 83 CHAPTER 7. CONCLUSION 90 REFERENCES 94 ii

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LIST OF FIGURES Figure 1.1. Schematic of a Pulsed Laser Deposition System 2 Figure 1.2. Block Diagram of Experimental Apparatus Useful for Temporally and Spatially Resolved Optical Emission and Absorption Spectroscopy, Ion Probe Measurement, and ICCD Photography of Laser Plumes Used for PLD 4 Figure 2.1. Schematic for Typical PLD Imaging Using an ICCD System 6 Figure 2.2. ICCD Image of a Back-Lit Focusing Card Placed in a PLD Chamber 7 Figure 2.3. ICCD Image of a Back-Lit PLD Chamber After Focusing With a Focusing Card 8 Figure 2.4. Experimental Setup for ICCD Imaging of Out-of-Object-Plane Objects 10 Figure 2.5. Individually Normalized ICCD Images for 2.5 mm Object 12 Figure 2.6. Individually Normalized ICCD Images for 6.8 mm Object 13 Figure 2.7. Individually Normalized ICCD Images for 17 mm Object 14 Figure 2.8. Identically Normalized ICCD Images for 2.5 mm Object 16 Figure 2.9. Identically Normalized ICCD Images for 6.8 mm Object 17 Figure 2.10. Identically Normalized ICCD Images for 17 mm Object 18 Figure 2.11. Intensity Across the Image Diameters for the 2.5 mm Object at Varying Distances from the Lens 19 Figure 2.12. Intensity Across the Image Diameters for the 6.8 mm Object at Varying Distances from the Lens 19 Figure 2.13. Intensity Across the Image Diameters for the 17 mm Object at Varying Distances from the Lens 20 iii

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Figure 2.14. Schematic for ICCD Imaging of PLD Plumes Varying Plume Distance to Object Plane 22 Figure 2.15. ICCD Images of Ti Plumes at Varying Distances from the Object Plane Corresponding to a Fixed Image Plane of the Imaging System 24 Figure 2.16. Experimental Setup Used to Create a Planar Slice of a Ti Plume 27 Figure 2.17. Photograph of the PLD Chamber and the Aluminum Shield Used to Create a Planar Slice of a Ti Plume 27 Figure 2.18. Normalized Intensity Profiles at Substrate Holder for Full and Planar Plumes 28 Figure 2.19. Photograph of Si Wafer after Masked PLD of Titanium 29 Figure 2.20. Normalized Intensity Profiles at Substrate Holder for Full and Planar Plumes and Normalized Thickness from PLD of Titanium 31 Figure 3.1. Schematic of Depth Resolution Using a Pinhole 33 Figure 3.2. Diagram for Depth Resolution of a Finite Pinhole 34 Figure 3.3. Schematic for Pinhole Application to PLD 36 Figure 4.1. Initial Experimental Setup Testing Depth of Field 39 Figure 4.2. Normalized Intensity at Pinhole vs. Distance from Object to First Lens 41 Figure 4.3. Schematic and Parameters for Designed Experiment 42 Figure 4.4. Combinations of Parameters for Full-Factorial Designed Experiment 43 Figure 4.5. Trend-Line for Object Size and FWHM 44 Figure 4.6. Trend-Line for Focal Length and FWHM 45 Figure 4.7. Trend-Line for Pinhole Size and FWHM 45 Figure 4.8. Experimental Setup Testing Lens Diameter vs. FWHM 47 Figure 4.9. Normalized Intensity at Pinhole vs. Distance from Object to Lens 48 iv

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Figure 4.10. Trend-Line for Lens Diameter and FWHM 49 Figure 4.11. Experimental Setup Testing Image Distance from Lens vs. FWHM 50 Figure 4.12. Normalized Intensity at Pinhole vs. Distance from Object to Lens 52 Figure 4.13. Trend-Line for Image Distance and FWHM 52 Figure 4.14. Experimental Setup for a One-to-One Image of an Image 54 Figure 4.15. Experimental Setup for Five One-to-One Image of an Object 55 Figure 4.16. Normalized Intensity at Pinhole vs. Distance from Object to First Lens 57 Figure 4.17. Experimental Setup for Translating Pinhole into Image 58 Figure 4.18. Normalized Intensity at Pinhole vs. Distance from First Lens to First Pinhole 60 Figure 5.1. Light Paths Taken from Different Points of the Same Focal Plane 63 Figure 5.2. Light Paths Taken from a Point Outside the Focal Plane 64 Figure 5.3. Light Paths Taken from Multiple Points Outside the Focal Plane 65 Figure 5.4. Light Paths Taken from a Point Outside the Focal Plane 66 Figure 5.5. Geometric Construction for Finding Light Paths that Correspond to Paths Originating from the Point Conjugate to the Pinhole 67 Figure 5.6. Geometry for Obtaining the FWHM for Chapter 4 Experiments 72 Figure 5.7. Plot and Linear Fits of Measured FWHM vs. OD*s/LD 73 Figure 6.1. Schematic for a Confocal Microscope Employing Two Pinholes in the Optical System 75 Figure 6.2. The CSOM Configuration Used in the Derivation of the Depth Response 78 Figure 6.3. Application to a Second Pupil Function to a Pinhole Relay Lens to Improve Depth Response of CSOM 82 v

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Figure 6.4. Diagram for Depth Resolution of a Finite Pinhole Blocking the Center of the Lens 84 Figure 6.5. Diagram for the Shadow of a Center Blocked Lens 86 Figure 6.6. Proportion of Available Light from a Center Blocked Lens at Different Pinhole Distances 86 Figure 6.7. Diagram Used in Depth of Field Calculation 87 Figure 6.8. Normalized Intensity Values Through Pinhole vs. Object Distance Using Lenses Blocked at the Center 89 vi

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INVESTIGATION OF SPATIAL FILTERING FOR PLANAR RANGE-RESOLVED PULSED LASER ABLATED PLUME IMAGING James F. Winslow ABSTRACT This thesis presents a study of the intensified charge-coupled device (ICCD) imaging of pulsed laser ablated plumes. Two-dimensional imaging of laser ablated plumes is a very important diagnostic for PLD. ICCD array photography is a useful tool for imaging PLD. The images obtained using the standard technique are characterized and compared with ICCD images of an altered plume, ICCD images intentionally violating standard imaging procedures, and film thickness. The depth resolving properties of a pinhole was investigated with the intention of applying it to PLD plume imaging. This results in a more thorough understanding of the depth resolving property of a pinhole. The investigation leads to a theoretical improvement for the resolution in confocal microscopy. vii

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CHAPTER 1. INTRODUCTION 1.1. Introduction The advantages of using pulsed laser deposition (PLD) over other thin film deposition techniques such as chemical vapor deposition (CVD), molecular beam epitaxy (MBE), and sputtering make the characterization and optimization of PLD an important area in nanotechnology since there are many applications suited to PLD. The major advantage of PLD is that the deposited film is stoichiometrically identical to the target. Another advantage is that the evaporation power source is decoupled from the vacuum system. The evaporants are energetic and the film growths can be in reactive environments containing any gas, with or without plasma excitation. With the appropriate choice of laser, thin films of any material can be deposited. The two main disadvantages with PLD are micron-sized particulates within the films, and the narrow forward angular dispersion of the ablated material. Many creative techniques have been developed to limit the size and number of particulates in the films (Witanachchi et al., 1995; Cheung, 1994). 1.2. Pulsed Laser Deposition A pulsed laser deposition system consists of a target holder and a substrate holder within a vacuum chamber. An external high power laser with a wavelength that can be absorbed by the intended target material is focused onto the target, vaporizing a spot on 1

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the target. The vaporized material forms a rapidly expanding plume consisting of energetic species consisting of molecules, atoms, electrons, ions, micron-sized solid particulates, and molten globules (Cheung, 1994). A schematic of a PLD system can be seen in Figure 1.1. 4 8 2 3 5 6 7 1 Key 1-Excimer Laser 2-Focusing Lens 3-Heated Substrate Holder 4-Substrate 5-Pulsed Laser Ablated Plume 6-Target 7-Vacuum Chamber 8-Viewing Window Figure 1.1. Schematic of a Pulsed Laser Deposition System 2

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1.3. Plume Imaging and Dynamics A number of diagnostic techniques have been developed to assist in the characterization and modeling of the laser target interaction and plume dynamics. The following are some of the more widely used diagnostics. Time-of-flight mass spectrometry is used to characterize the kinetic energies of the ejected ions from the ablated surface. Ions are collected using electric fields and accelerated using a potential. The collected ions are then analyzed to find their mass to charge ratio. Mathematical simulation is used to derive the actual kinetic energy (Vertes et al., 1988). Ion probes are an invasive diagnostic that provides local information about plasma conditions within the plume. Ion probes are essentially biased wire tips placed in the path of the laser plume; the collected current is then displayed on an oscilloscope. The high plasma densities within the plume shield the charge within the plume from the voltage of the ion probe until it is very close to the probe (~10 m) and therefore accurate time of flight data can be recorded. A negative bias of V is usually enough to repel the arriving electrons in the plasma, allowing the flux of ions arriving at the probe to be recorded. Unfortunately, ion probes are invasive and cannot be used during deposition without affecting the deposited film (Segall and Koopman, 1973). Optical emission spectroscopy measures the light emitted by the laser ablated plume. Typical laser energy densities used for reasonable film deposition rates result in bright plumes extending multiple centimeters from the target. The diagnostic setup can be as simple as using a photodiode to measure the entire visible plume emission. The plume can also be imaged onto the entrance port of a spectrometer. By using known 3

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atomic spectroscopic lines and molecular bands, one can identify specific species within the plume. If measurements are spatially and temporally resolved, then time-of-flight and local populations of species can also be determined. Since most observed atomic transitions have lifetimes ~10 ns, but can be observed multiple s after the laser pulse, emission spectroscopy indicates the results of collisions within ~10 ns of the observed emission (Geohegan, 1994). Figure 1.2 illustrates the setup used for an ion probe, emission/absorption spectroscopy, and ICCD imaging. Figure 1.2. Block Diagram of Experimental Apparatus Useful for Temporally and Spatially Resolved Optical Emission and Absorption Spectroscopy, Ion Probe Measurement, and ICCD Photography of Laser Plumes Used for PLD (Geohegan, 1992) 4

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Two-dimensional imaging of laser ablated plumes is another very important diagnostic for PLD. Intensified-CCD (ICCD) array photography is a useful tool for imaging PLD. Because ICCD systems are electronically gated, they can be very accurately timed relative to the laser pulse (ns). This provides a very short shutter speed as well as very accurate post laser trigger timing method. These images are extremely useful in analyzing plume propagation and dynamics, especially plume propagation into background gases (Geohegan, 1994). 1.4. Overview The intention of this thesis was to develop a new in-situ PLD diagnostic that could provide local information about the laser ablated plume, as ion-probes do, but without interfering with the plume during deposition. A diagnostic of this sort would allow for real-time monitoring of a laser-ablated plume during deposition, which could then be compared directly to film characteristics. The structure of this thesis is as follows. The second chapter is a characterization of the images obtained using standard ICCD imaging. This characterization is important because when ICCD images are referred to in the literature, they are treated as highly representative of the plume and the non-focused light is never mentioned (Puretzky et al., 2000). Subsequent chapters explore the possibility and practicality of a novel imaging concept based on the principles of confocal microscopy. The thesis is concluded with a discussion of the findings in this thesis, as well as related future projects. 5

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CHAPTER 2. CHARACTERIZATION OF STANDARD ICCD IMAGES OF LASER ABLATED PLUMES 2.1. Standard ICCD Imaging Method Typical ICCD imaging of PLD plumes involves imaging a plume with a lens onto the ICCD array of the ICCD imaging system. There are two major considerations taken into account when setting up the system. First, the entire plume image must fit onto the ICCD array. Since a plume can be many centimeters long, and an ICCD array is likely to be on the order of a square centimeter (the ICCD array is roughly 0.8 cm tall by 1.25 cm wide), imaging usually involves demagnification. Object distance, image distance, and focal length must be PLD Deposition Chamber Plano-Convex Lens ICCD Camera Pulse Generato r Detector Controller Figure 2.1. Schematic for Typical PLD Imaging Using an ICCD System 6

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chosen to accommodate this requirement practically. Figure 2.1 is a schematic for typical PLD imaging using an ICCD system. Second, since the plume is a three-dimensional object without sharp boundaries, optical alignment of the system is implemented by focusing a two-dimensional object with sharp boundaries; backlit cutouts in sheets of rigid paper are used. Figure 2.2 shows the ICCD image of a focusing card 112 cm from the lens, resulting in a magnification of Figure 2.2. ICCD Image of a Back-Lit Focusing Card Placed in a PLD Chamber 7 approximately -0.2. The evenly spaced cutouts are 1 cm apart in order to visualize how much of the plume will be imaged onto the ICCD array. The two-dimensional object is placed along the plane where the center of the plume is expected. Once focused onto this plane, the ICCD system will then be focused onto the center of the plume. Figure 2.3 is

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an ICCD image of a back-lit PLD chamber after focusing with a focusing card. The card in this figure was 220 cm from the lens, resulting in a magnification of approximately -0.1. The target and substrate can be seen fairly clearly as would be expected since they are in the object plane. Substrate H o l der Target Figure 2.3. ICCD Image of a Back-Lit PLD Chamber After Focusing With a Focusing Card It is generally assumed that since the center of the plume is in the object plane corresponding to the image plane lying on the ICCD array, that the dominant part of the image will closely resemble the center of the plume. The PLD images resulting from this method of ICCD imaging are considered as integrated images that strongly favor the central plane of the plume and light from non-focal planes within the plume is generally 8

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ignored. Subsequent sections of this chapter test the validity of this assumption (Puretzky et al., 2002). 2.2. ICCD Imaging of Out-of-Object-Plane Objects Experiments were designed to test the assumption that focusing the light from the plane at the center of the plume onto an image plane located at the ICCD array would yield images that emphasized the light at the center plane of the plume. 2.2.1. Experimental Setup The imaging system for this experiment was a Princeton Instruments (Roper Scientific) ICCD Camera (384x576 pixels), PG-200 Pulse Generator, and ST-138 Detector Controller. The software used to run the system was WinView32. The controller temperature was set to 0C. The gate width for the ICCD was set to 10 ms, each image was 25 accumulations, and the camera gain was set to 0. For each image, a new background was saved, and each image includes both a flatfield and background subtraction. The imaging lens was an 18.5 cm focal length plano-convex lens with an 11.9 cm diameter. To create a two-dimensional object, a 12.7 cm diameter, 150 W light bulb was enclosed in a black box that had an opening facing the ICCD camera. This opening was covered with a thin sheet of nylon. This provided a uniformly illuminated, planar light source. The illuminated nylon was covered with black sheets of paper with circular cutouts of varying diameters to provide a way to vary object size. Attenuation was placed after the object using a neutral density filter of 2.1. Mounting this box on a 9

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translation stage allowed the distance of this planar object to the lens to be varied. The distance from the lens to the ICCD camera was held fixed. This fixed the image plane to an object plane independent of the location of the source of light. Figure 2.4 is a schematic of the experimental setup. 4 1 3 s 5 2 6 s Figure 2.4. Experimental Setup for ICCD Imaging of Out-of-Object-Plane Objects Key s-Variable Distance from Object to First Lens s-Fixed Distance from Lens to ICCD Camera 1-Light Source 2-Two-Dimensional Object with Attenuation 3-Plano-Convex Lens 4-ICCD Camera 5-Translation Stage 6-Optical Table 10

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For this experiment, the lens to ICCD camera distance was fixed at 26.2 cm, and the object to lens distance was varied from 51 cm to 73 cm in 2 cm increments. At each interval, a background was taken by covering the object. The object was then uncovered and an image was taken using the ICCD camera. The images presented are after both a background and flatfield subtraction. The object plane distance corresponding to a 26.2 cm image plane distance is 63 cm. Three object sizes were used. The objects were circles with diameters of 2.5 mm, 6.8 mm, and 17 mm. By holding the size and intensity of the object constant, this experiment tests the sensitivity of the ICCD camera to planes increasingly further from the object plane that corresponds to the image plane located at the ICCD array. The object plane that corresponds to the image plane at the ICCD array using the lens equation will henceforth be called simply the object plane. With respect to PLD, an ICCD image of a plume would be the sum of all two-dimensional layers both in and out of the object plane. 2.2.2. Results Figures 2.5, 2.6, and 2.7 show the sets of ICCD images taken at varying distances from the object plane for each object size. Each image is individually normalized using its maximum intensity. It is clear that the image resulting from the object at 63 cm from the lens (in the object plane) is the clearest image. This makes sense and was expected. As the object gets further from the object plane two observations are also apparent. The object begins to fade from the outside, and when the object gets closer to the lens, it is magnified and vice versa. So the resulting ICCD image is a combination of an increasing fading with increasing distance from the object plane, and increasing magnification of the 11

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12 73 cm from lens 71 c m from lens 69 cm from lens 67 cm from lens 65 cm from lens 63 cm from lens 61 cm from lens 59 cm from lens 57 cm from lens 53 cm from lens 51 cm from lens 55 cm from lens Figure 2.5. Individually Normalized ICCD Images for 2.5 mm Object

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13 73 cm from lens 71 cm from lens 69 cm from lens 67 cm from lens 65 cm from lens 63 cm from lens 61 cm from lens 59 cm from lens 57 cm from lens 53 cm from lens 51 cm from lens 55 cm from lens Figure 2.6. Individually Normalized ICCD Images for 6.8 mm Object

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14 73 cm from lens 71 cm from lens 69 cm from lens 67 cm from lens 65 cm from lens 63 cm from lens 61 cm from lens 59 cm from lens 57 cm from lens 51 cm from lens 53 cm from lens 55 cm from lens Figure 2.7. Individually Normalized ICCD Images for 17 mm Object

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image with decreasing distance from the object to the lens. This was expected, but what was somewhat surprising was how far the object could be from the object plane while still providing an observable image. The smaller the object, the greater the effect of the fading sides relative to the entire image. Figures 2.5-2.7 showed the clarity of the ICCD images with varying distance. Figures 2.8-2.10 shows the ICCD sensitivity to objects at varying distances from the object plane. Figures 2.8, 2.9, and 2.10 show the ICCD images from Figures 2.5-2.7 with the unnormalized images all of which are at the same intensity scale. Figure 2.8 shows the center of the 2.5 mm object having increasing intensity up to 57 cm from the lens, and then steadily decreasing. Figures 2.9 and 2.10 show the center of the 6.8 mm and 17 mm objects having increasing intensity with decreasing object distance from the lens. These three sets of images indicate that image brightness increases as the object gets closer to the lens, but eventually decreases when the sides fade enough due to the object being out of focus. This behavior is a combination of the object going out of focus, and the fact that a lens will capture more light from closer objects. Figures 2.11, 2.12, and 2.13 show the intensity across the diameters of the images for each object size at varying distances from the object plane. These plots were obtained by choosing a single row of the ICCD image and converting it to ASCII, which could then be plotted in Excel by pixel. It is clear in each figure that the in-focus image (63 cm) has a less rounded top and sharper edges (indicating the clearer image), but is not the brightest image. 15

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16 73 cm from lens 71 cm from lens 69 cm from lens 67 cm from lens 65 cm from lens 63 cm from lens 61 cm from lens 59 cm from lens 57 cm from lens 53 cm from lens 51 cm from lens 55 cm from lens Figure 2.8. Identically Normalized ICCD Images for 2.5 mm Object

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17 73 cm from lens 71 cm from lens 69 cm from lens 67 cm from lens 65 cm from lens 63 cm from lens 61 cm from lens 59 cm from lens 57 cm from lens 53 cm from lens 51 cm from lens 55 cm from lens Figure 2.9. Identically Normalized ICCD Images for 6.8 mm Object

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18 73 cm from lens 71 cm from lens 69 cm from lens 67 cm from lens 65 cm from lens 63 cm from lens 61 cm from lens 59 cm from lens 57 cm from lens 53 cm from lens 51 cm from lens 55 cm from lens Figure 2.10. Identically Normalized ICCD Images for 17 mm Object

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020004000600080001000012000140001600050100150200250300PixelICCD Intensity 51cm 53cm 55cm 57cm 59cm 61cm 63cm 65cm 67cm 69cm 71cm 73cm Figure 2.11. Intensity Across the Image Diameters for the 2.5 mm Object at Varying Distances from the Lens. Note: All values are in arbitrary units. 0500010000150002000025000300003500050100150200250300350400450PixelICCD Intensity 51cm 53cm 55cm 57cm 59cm 61cm 63cm 65cm 67cm 69cm 71cm 73cm Figure 2.12. Intensity Across the Image Diameters for the 6.8 mm Object at Varying Distances from the Lens. Note: All values are in arbitrary units. 19

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050001000015000200002500030000350004000050100150200250300350400450PixelICCD Intensity 51cm 53cm 55cm 57cm 59cm 61cm 63cm 65cm 67cm 69cm 71cm 73cm Figure 2.13. Intensity Across the Image Diameters for the 17 mm Object at Varying Distances from the Lens. Note: All values are in arbitrary units. The important realization is that with ICCD imaging, image clarity does not coincide with image brightness when considering the objects distance from the lens. The clarity of the image depends on the thin lens equation, while the image brightness is a function of local image brightness, object distance to lens, feature size, and object distance from the object plane corresponding to the fixed image plane. This is very important with respect to ICCD imaging of PLD plumes. Instead of integrated images reflecting the center plane of the plume, the center of images will favor planes closer to the lens. This is due to the lens collecting more light from closer objects as well as magnifying closer planes. Also, the outer parts of the plume will be underrepresented in an ICCD plume image due to outer edges of images fading with increasing distance from the object plane. 20

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2.3. ICCD Imaging of PLD Plumes Varying Plume Distance to Object Plane The results from the previous experiment suggested that focusing on the plane at the center of a plume would not emphasize the intensity distribution of the plane at the center of the plume. In this experiment, typical ICCD imaging methodology for plume imaging was used, but the object plane was purposely set at different distances from the center plane of the plume, while holding both the object plane and image plane distances from the lens constant. 2.3.1. Experimental Setup As earlier, the imaging system for this experiment was a Princeton Instruments (Roper Scientific) ICCD Camera (384x576 pixels), PG-200 Pulse Generator, and ST-138 Detector Controller. The software used to run the system was WinView32. The controller temperature was set to 0C. The gate width for the ICCD was set to 50 s to capture the entire plume duration, each image was 25 accumulations, and the camera gain was set to 0. For each image, a new background was saved, and each image includes both a flatfield and background subtraction. The imaging lens was an 18.5 cm focal length plano-convex lens with an 11.9 cm diameter. For this experiment, the lens to ICCD camera distance was fixed at 20.2 cm. This corresponds to a 220.5 cm object plane distance. The images were taken with the center plane of the plume at 214.5, 216.5, 218.5, 220.5, 222.5, and 224.5 cm from the lens. At 220.5 cm, both the center plane of the plume and the object plane overlap. The images presented are after both a background and flatfield subtraction. Figure 2.14 is a schematic for the experimental setup. 21

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22 Figure 2.14. Schematic for ICCD Imaging of PLD Plumes Varying Plume Distance to Object Plane Plano-Convex Lens PLD Deposition Chamber Pulse Generato r Detector Controller ICCD Camera Flat Mirror Translation Stage Excimer Laser

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The laser used was a Lambda Physik COMPex KrF excimer laser. It was run at 1 Hz with an energy of 130-150 mJ per shot. The average fluence was 1180 mJ/cm 2 with a standard deviation of 37 mJ/cm 2 The pulse generator for the ICCD system was also used as the trigger for the excimer laser. The vacuum chamber was held at a pressure of 10 -3 torr of Argon. The target was titanium. 2.3.2. Results Figure 2.15 shows each image of the plume with varying the plume-to-object-plane distance. The plume images look very similar to each other despite having imaged a plane up to 4 cm behind and 6 cm in front of the plume center. This shows that the typical method of PLD imaging focusing on a plane inside the plume does not provide any better results than having not focused too accurately on the plume. Also, the plume images are not representative of the plume intensity at the object plane corresponding to the fixed image plane. Had this been the case, the out of focus plane images would have been very dark, as there is barely any plume 6 cm away from the center plane of the plume. Finally, it is clear from Figure 2.15 that the plumes located closer to the lens had brighter centers. So the intensity profile for ICCD images of PLD plumes can not be entirely attributed to the composition of or distribution of particles within the plume. Out of focus plume planes closer to the lens will tend to make bright and magnified contributions to the image. The intensity distribution within an image indicates the actual brightness within the plume as well as an increasingly non-representative contribution due to the out of focus parts of the plume. 23

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Middle of Plume 222.5cm from lens.220.5cm from lens is object planeMiddle of Plume 224.5cm from lens.220.5cm from lens is object planeMiddle of Plume 218.5cm from lens.220.5cm from lens is object planeMiddle of Plume 220.5cm from lens.220.5cm from lens is object planeMiddle of Plume 216.5cm from lens.220.5cm from lens is object planeMiddle of Plume 214.5cm from lens.220.5cm from lens is object plane Figure 2.15. ICCD Images of Ti Plumes at Varying Distances from the Object Plane Corresponding to a Fixed Image Plane of the Imaging System 24

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2.4. Comparing an Integrated ICCD Intensity Profile with a Planar Profile Since the intensity distribution of an ICCD image of a PLD plume is a combination of the actual intensity distribution within a plume and a non-representative contribution due to the out of focus plume light, an experiment was designed that would allow a comparison between a regularly imaged plume intensity profile at the substrate and a planar intensity profile at the substrate. 2.4.1. Experimental Setup The imaging system for this experiment was a Princeton Instruments (Roper Scientific) ICCD Camera (384x576 pixels), PG-200 Pulse Generator, and ST-138 Detector Controller. The software used to run the system was WinView32. The controller temperature was set to 0C. The gate width for the ICCD was set to 50 s to capture the entire plume duration, and each image was 100 accumulations. The imaging lens was an 18.5 cm focal length plano-convex lens with an 11.9 cm diameter. For this experiment, the lens to ICCD camera distance was fixed at 20.2 cm. The lens was set 220.5 cm from the center of the plume, which corresponds to the 220.5 cm object plane distance. Figure 2.14 is a schematic for the experimental setup. The laser used was a Lambda Physik COMPex KrF excimer laser. It was run at 2 Hz with an energy of 158-175 mJ. The average fluence was 1390 mJ/cm 2 with a standard deviation of 43 mJ/cm 2 The pulse generator for the ICCD system was also used as the trigger for the excimer laser. The vacuum chamber was held at a pressure of 5 x 10 -5 torr. A titanium target was used, and the target to substrate holder distance was 4 cm. 25

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The first image was a control image using standard ICCD imaging and PLD, with the ICCD camera gain set to 0. For the control image, both a flatfield and background subtraction was used. The second image was that of a planar slice of the plume by using an invasive shield. Figure 2.16 shows the experimental setup used to create a planar slice of the Ti plume. The shield was created from a sheet of aluminum and fixed to the vacuum chamber. A 1 mm by 80 mm vertical slit was cut in the aluminum sheet. The slit was positioned 1.2 cm from the substrate holder, 2.8 cm from the target, and located at the center of the plume. A hole was made in the shield to allow the laser to strike the target. To obtain a background image, the slit was covered during the laser ablation, and a 100-accumulation image was recorded at an ICCD camera gain setting of 7.5. Another 100-accumulation image was then taken at a 7.5 gain with the slit uncovered. The final planar image was the image obtained by subtracting the covered slit image from the uncovered slit image. A flatfield subtraction was used in all acquisitions. Because of the shield, only the 1.2 cm closest to the substrate holder was observable. Figure 2.17 shows a photograph of the chamber with the aluminum shield. 26

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27 1 2 3 5 LaserBeam 4 Figure 2.17. Photograph of the PLD Chamber and the Aluminum Shield Used to Create a Planar Slice of a Ti Plume 1 2 3 4 5 Key 1-Ti Target 2-Hole through shield for laser 3-Substrate holder 4-1mm x 80mm slit 5-Aluminum shield Figure 2.16. Experimental Setup Used to Create a Planar Slice of a Ti Plume Key 1-Ti Target 2-Hole through shield for laser 3-Substrate holder 4-1mm x 80mm slit 5-Aluminum shield

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2.4.2. Results To compare the integrated image with the image of the planar plume, a single column of each ICCD image was isolated. The column chosen was the one corresponding to immediately before the substrate holder. The information was converted to ASCII. After normalizing and plotting in Excel, the intensity profiles at the substrate holder for an entire plume and a planar slice of a plume imaged with the standard technique were compared. The results can be seen in Figure 2.18. 00.20.40.60.811.2050100150200250300350400450PixelsNormailized ICCD Intensity Planar Plume Full Plume Figure 2.18. Normalized Intensity Profiles at Substrate Holder for Full and Planar Plumes. Note: All values are in generic units. Figure 2.18 shows the intensity profile of the full plume decreasing at a slower rate than the planar plume. As suggested earlier, the intensity distribution across the full plume image does not accurately represent the intensity distribution at the center plane of the plume to which the object plane had been matched. 28

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2.4.3. Thickness Profile vs. Image Intensity Profile As a final comparison between the planar plume intensity profile and the full plume intensity profile, a thickness profile of a Ti film deposited under the same conditions mentioned in the experimental setup was considered. A 3 Si wafer was covered with of another 3 Si wafer to mask the wafer along its length and width from the center of the expected deposition. The deposition maximum was located by having cleaned the substrate holder, and depositing a Ti film on it. The masked Si wafer was placed on the substrate holder, centered over the deposition maximum. The laser used was a Lambda Physik COMPex KrF excimer laser. It was run at 4 Hz for 244 minutes with an energy of 158-175 mJ. The average fluence was 1390 mJ/cm 2 with a standard deviation of 43 mJ/cm 2 The vacuum chamber was held at a pressure of 5 x 10 -5 torr. A titanium target was used, and the target to substrate distance was 4 cm. Figure 2.19 is a photograph of a Si wafer after masked PLD of Ti. Figure 2.19. Photograph of Si Wafer after Masked PLD of Titanium 29

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To get the thickness profile, a Dektak 30 30ST Auto I surface texture profiler was used. Starting from the center of the wafer, multiple 1mm scan lengths were run passing from the masked area of the wafer to the area of the wafer where the film was deposited. These scans were taken in 1 mm increments along the Ti film edge from the center of the wafer to the edge of the wafer. This provided a vertical thickness profile that was in the same plane as the intensity profiles mentioned in section 2.4.2. The maximum film thickness measurement was 1077 yielding 0.07 /shot. This is consistent with previously found PLD deposition rates for Ti (Kools et al., 1992) and other metals (Kools, 1994). The measurements were normalized and plotted with the intensity profiles from before. In order to compare the thickness profile with the intensity profiles, pixels were converted to distance knowing that 4 pixels equaled 1 mm. This pixel to distance ratio was obtained using the ICCD images of the target and substrate holder. Figure 2.20 shows the normalized thickness profile and intensity profiles obtained earlier vs. the vertical distance along the substrate holder. The normalized thickness profile matched the normalized intensity profile at the substrate for the planar plume more closely than the profile for the full plume. The emission from a plume results from plasma excitation or recombination collisions (Geohegan, 1994). These events should be proportional to the amount of material present, and therefore the intensity profile at the substrate should be proportional to the film thickness profile. This is indicated by Figure 2.20. This comparison of film thickness and ICCD image intensity suggests a strong correlation between local plume intensity and film thickness. If plume intensity could be three-dimensionally mapped 30

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00.20.40.60.811.2024681012Distance (cm)Normalized ICCD Intensit y and Film Thickness Planar Plume Full Plume Ti Film Thickness Figure 2.20. Normalized Intensity Profiles at Substrate Holder for Full and Planar Plumes and Normalized Thickness from PLD of Titanium. Note: All values are in g eneric units. non-invasively, the intensity information could be compared with film properties, and eventually film properties could be monitored via imaging during deposition. 2.5. Comments Standard imaging for PLD is incapable of providing completely accurate spatial information for laser ablated plumes. There is no current non-invasive way to spatially map plumes. If such a method did exist, it would enable a great deal of insight into the dynamics of PLD as well as provide an in-situ diagnostic that could be directly correlated with deposited film characteristics. The remainder of this thesis is an investigation into such an in-situ method of PLD imaging. 31

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CHAPTER 3. DEPTH FILTERING PROPERTIES OF A PINHOLE 3.1. Introduction The combination of a lens and pinhole can be shown to preferentially image certain planes over others (Webb, 1999). Figure 3.1 shows how the image of a point in the focal plane (corresponding to the plane with the pinhole detector) will be focused to a point at the pinhole. Therefore, all the light that the lens captures originating from that particular point, will get to the detector through the pinhole. The image from points out of the focal plane will be imaged to planes before and after the pinhole detector plane. The pinhole will block a large and increasing portion of this light as the object point gets further from the focal plane. The portion of light captured by the pinhole is the ratio of the area of the pinhole and the area of the circle of light for the image at the pinhole detector plane. An infinitely small pinhole would capture only an infinitesimal portion of light from any point except the single point of light whose image terminates at the pinhole. 3.2. Depth of Field for a Finite Pinhole For a finite pinhole, there will be a range about the focal plane that will allow 100% of the light originating from a point through the pinhole. Figure 3.2 illustrates this situation and labels all the distances necessary for calculation. The pinhole diameter is 2r, the lens has a diameter of 2R, and a focal length f. The focal plane is located a 32

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Lens Pinhole Focal Plane Detector Sample Figure 3.1. Schematic of Depth Resolution Using a Pinhole distance s 2 from the lens, and the image (pinhole) plane is located a distance s 2 from the lens. Points located distances s 1 and s 3 from the lens will also allow 100% transmission through the pinhole, and they have corresponding images before and after the pinhole plane located at distances s 1 and s 3 from the lens respectively. The depth of field here 33

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will be s 1 to s 3 However, if the depth of field is defined to be the range that permits 50% or more of the light through the pinhole (assuming a uniformly intense spatial illumination of the object), then one can simply substitute into the following equations pinholerr22 (1) which yields twice the area of the pinhole. Focal Plane s1 s3 s2 Image Plane 2R, f s3' s1' s2' 2r Figure 3.2. Diagram for Depth Resolution of a Finite Pinhole The pinhole size determines s 3 -s 1 , which determines the depth of field s 1 -s 3 The lens equation 34

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'111ssf (2) gives )'('fsfss (3) and )('fssfs (4) These equations are valid using s 1 s 2 s 3 and their counterparts s 1 , s 2 , and s 3 . Similar triangles provides Rsrss')''(1212 (5) and Rsrss')''(1223 (6) So, )(''221rRRss (7) and )(''223rRRss (8) Using these equations, and knowing R, r 2 s 2 and f, one can find the depth of field that would allow 50% or more light through the pinole with radius from (1). pinholer 35

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3.3. Application to PLD Imaging Based on the previous section, depth-resolved point-by-point information about the PLD plume should be possible using a pinhole. If possible, one could use a delayed and gated detector and scan the plume by moving the lens and detector simultaneously in the x, y, and z directions. Doing so would allow for the construction of a three-dimensional spatial and temporal mapping of a plume. Figure 3.3 shows a schematic representation of this idea. Focal PlanePinholePlumeLens z y x Detector Figure 3.3. Schematic for Pinhole Application to PLD 3.4. Initial Expectations There are a number of practical constraints placed on the formulas in section 3.2 in applying them to PLD. First, s 1 > 35 cm because the lens must be outside the chamber, and the smallest chamber accessible is >30 cm from the plume to the window. Second, the radius of the pinhole readily available was .025 cm. Third, most available lenses had diameters of 4-5 cm, and the largest available was 11.9 cm. The initially desired depth of 36

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field was 1 cm or less. Finally, s 2 < 100 cm because of the intention of ultimately using a translation stage. Anything larger than 100 cm would be impractical. Using R=2.5 cm, s 2 =35 cm, and f=25 cm, an expected depth of field of 0.4 cm and s 2 value of 87.5 cm was calculated. Using R=6 cm, s 2 =35 cm, and f=25 cm, the depth of field calculated was 0.16 cm with s 2 =87.5 cm. Therefore the expected depth of field was on the order of a cm or less in an application to PLD. The following chapter investigates these expectations. 37

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CHAPTER 4. INVESTIGATION 4.1. Initial Experiments Based on the calculations from the previous section, experiments were designed to test and characterize the preceding expectations using a uniformly illuminated object. Once the depth resolving capabilities using a pinhole were determined, imaging and mapping of a plume was expected to follow. 4.1.1. Experimental Setup To test the depth of field, a pinhole-covered detector was set up at a fixed distance from a lens system. To isolate the depth dependence of the system, a uniform two-dimensional light source was necessary. By varying the distance of the two-dimensional light source from the fixed lens system, and recording the simultaneous outputs from the fixed pinhole detector, the depth dependence of the system could be recorded. To create a two-dimensional object, a 12.7 cm diameter, 150 W opaque light bulb was enclosed in a black box that had an opening facing the detector. The illuminated opening was covered with black sheets of paper with circular holes of varying diameters to provide a way to vary object size. This provided a uniformly illuminated, variable sized, planar light source. This box was mounted on a translation stage allowing variation in the distance of this planar object to the lens. The distance from the lens to 38

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the detector was held fixed. This fixed the image plane to an object plane independent of the location of the source of light. Figure 4.1 is a schematic of the experimental setup. s S D 5 2 3 1 4 8 7 Key s-Variable Distance from Object to First Lens D-Fixed Distance Between First and Second Lenses s'-Fixed Distance from Lens to Pinhole Detector 1-Light Source 2-Two-Dimensional Object 3-First Plano-Convex Lens 4-Second Plano-Convex Lens 5-Cardboard Tube 6-Photodiode with Pinhole Aperture 7-Translation Stage 8-Optical Table 6 Figure 4.1. Initial Experimental Setup Testing Depth of Field 39

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For the pinhole detector, a 9V reverse biased borosilicate silicon detector was used. The detector had an active area of 44 mm 2 a breakdown voltage of 30 V, capacitance of 130 pF, and a rise time of 24 ns. This detector was covered with a 0.05 cm diameter pinhole. The output of the photodiode was connected to a BNC output and attached to a Tektronix TDS 380 Oscilloscope. The recorded values from the oscilloscope were averaged over 256 measurements. The lens closest to the object was a plano-convex, 40 cm focal length (39.7 cm back focal length), 4 cm diameter lens. The lens closest to the detector was a plano-convex, 50 cm focal length (49.7 cm BFL), 5 cm diameter lens. The distance between the lenses (D in figure 4.1.) was set to 20 cm, and s was held at 50 cm. The object point corresponding to the pinhole on the detector would be 40 cm from the first lens. A 47.5 cm, 4.7 cm diameter cardboard tube was used between the second lens and the pinhole detector to reduce the amount of ambient light on the pinhole that did not originate from the second lens. Starting with the translation stage as far from the first lens as possible, the illuminated two-dimensional object was covered and a background voltage was recorded on the oscilloscope. The object was then uncovered and the voltage from the photodiode was recorded. This was done for increasingly smaller distances from the first lens. A 0.66 cm diameter circular object was used for the first run. The experiment was repeated with a 1.3 cm diameter circular object in a second run. 40

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4.1.2. Results The voltage readings were corrected with a background subtraction, normalized, and plotted vs. distance. Figure 4.2 shows the results. To characterize the results, full width at half maximum (FWHM) was used to describe the depth of field observed. To 00.20.40.60.811.281828384858Distance (cm)Normalized Intensity 1.3 cm Object 0.66 cm Object Left Line Right Line Half Max Figure 4.2. Normalized Intensity at Pinhole vs. Distance from Object to First Lens. N ote: All values are in g eneric units. measure the FWHM, the graphical method shown in Figure 4.2 was used. It was surprising that the FWHM for the 0.66 cm object was >19 cm, and the FWHM for the 1.3 cm object was > 40 cm. Obviously this was too large to be useful and the initial calculations from the previous chapter were not valid. The next set of experiments was geared towards finding out which parameters could be adjusted to decrease the FWHM. It was hoped that a practical combination could still be found that would provide a useful depth of field. 41

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4.2. Effect of Focal Length, Object Size, and Pinhole Size on FWHM The first three parameters investigated were focal length, object size, and pinhole size. Using a suitably designed experiment, the main effect for each variable with respect to FWHM could be obtained. 4.2.1. Experimental Setup To test the depth of field, a pinhole-covered detector was set up at a specific distance from a lens. The same translating, circular, planar light source and pinhole detector described in section 4.1.1 was used. Figure 4.3 shows the experimental setup used. 2FL Pinhole small=.05cm large=0.1cm Lens small=7.5 cm FL lar g e=18.5cm FL Object small=0.66cm diam. large=1.5cm diam. Translation sta g e s Photodet ect or Figure 4.3. Schematic and Parameters for Designed Experiment A two level full factorial designed experiment using the three variables was used. Since every combination of the three variables was performed, the main effect on FWHM of each variable could be identified. The main effect is defined as the average response of the experiments using the higher level of the particular variable minus the average 42

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response of the experiments using the lower level of the particular variable. This can be done with each variable, and therefore the main effects for each variable can be found. The pinhole levels were 0.05(-) and 0.1(+) cm, the focal length levels were 7.5(-) and 18.5(+) cm, and the object sizes were 0.66(-) and 1.5(+) cm. The combinations of parameters in each experiment can be seen in Figure 4.4 (Sall et al., 2001). ExperimentPinholeObjectFocal Length1+++2++-3+-+4+--5-++6-+-7--+8--Figure 4.4. Combinations of Parameters for Full-Factorial Designed Experiment It is clear that by comparing the average of experiments 1-4 with experiments 5-8, one can compare the effect that pinhole size had on the FWHM. The other parameters will be averaged out because there will be two high values and two low values for each set of averages. The main effect for object size can be found by averaging 1, 2, 5, and 6 vs. 3, 4, 7, and 8. Similarly for focal length, 1, 3, 5, and 7 vs. 2, 4, 6, and 8 get averaged. For each focal length, the experiment was set up for 1:1 imaging, so the distance from the lens to the detector was twice the focal length. As before, both a background and a full value reading were recorded on the oscilloscope at each distance from the object to the lens. Eventually normalizing and plotting the voltage reading, the FWHM for each run was found. 43

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4.2.2. Results Using JMP software, the trend-lines for each parameter were plotted. Figures 4.5-4.7 describe the behavior of the FWHM with each parameter. The main effect of object size is that FWHM increases as object size increases, which is consistent with section 4.1. The main effect of focal length in 1:1 imaging is that FWHM increases as focal length increases. These two effects are similar in magnitude. The main effect of pinhole size is an increasing FWHM with increasing pinhole size, but this effect is much weaker than the previous two. Notice, that the main effect for focal length depended on 1:1 imaging, so this effect could be confounded with lens to detector distance since the larger focal length experiments also had greater lens to photo-detector distances. FWHM (cm) 5 7.5 10 12.5 15 17.5 0.66 1.5Object Size (cm) Figure 4.5. Trend-Line for Object Size and FWHM 44

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FWHM (cm) 5 7.5 10 12.5 15 17.5 7.5 18.5Focal Length (cm) 2 Figure 4.6. Trend-Line for Focal Length and FWHM FWHM (cm) 5 7.5 10 12.5 15 17.5 0.05 0.1Pinhole2 (cm) Figure 4.7. Trend-Line for Pinhole Size and FWHM Pinhole ( cm ) 45

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The immediate goal here is not to determine the exact dependence of FWHM on each parameter, but to realize how strongly and in which direction each parameter will affect the FWHM. The long-term goal is to understand which properties, if possible, can be manipulated to provide a useful depth of field. 4.3. Effect of Lens Diameter on FWHM Since the pinhole depth of field calculations in chapter 3 appeared incorrect, each parameter was studied to obtain as much information as possible. Lens diameter was the next variable studied. 4.3.1. Experimental Setup In this experiment, the depth of field for different lens diameters was tested, holding everything else constant. An 18.5 cm focal length plano-convex lens with a diameter of 11.9 cm was used. The lens was placed 40 cm from the detector for each run. The object light source was a 12.7 cm diameter, 150 W opaque light bulb in a black box that had an opening facing the detector. The illuminated opening was covered with a black sheet of paper with a 1.5 cm diameter circular hole. This box was mounted on a translation stage allowing variation of the distance of this planar object to the lens. The pinhole detector was the same as that in section 4.1.1. For the first run, the lens was covered with a 4.75 cm diameter aperture. For the second run, a 9.06 cm aperture was used. For the last run, the full lens diameter of 11.9 cm was used. Everything else remained unchanged. Once again, a full value and a background value was taken from the oscilloscope for decreasing distances between the 46

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object and the lens. The background corrected values were normalized and plotted vs. object distance from the lens, and the FWHM was determined for each lens diameter. Figure 4.8 shows the experimental setup. 5 6 1 2 3 4 s S Figure 4.8. Experimental Setup Testing Lens Diameter vs. FWHM Key s-Variable Distance from Object to First Lens s'-Fixed Distance from Lens to Pinhole Detector 1-Light Source 2-Two-Dimensional Object 3-Plano-Convex Lens 4-Photodiode with Pinhole Aperture 5-Translation Stage 6-Optical Table 47

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4.3.2. Results The results can be seen in Figures 4.9 and 4.10. FWHM decreased as the lens diameter increased. The 9.06 cm diameter yields a lens area that is halfway between the areas for 4.75 cm and 11.9 cm diameter. FWHM was not linear with lens area, and was approximately twice as large for the 4.75 cm lens diameter than for the other two. 00.20.40.60.811.2010203040506070Distance (cm)Normalized Intensity 11.9 cm Diameter 9.06 cm Diameter 4.75 cm Diameter Figure 4.9. Normalized Intensity at Pinhole vs. Distance from Object to Lens. Note: All values are in g eneric units. 48

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FWHM (0.5) 12.5 15 17.5 20 22.5 25 27.5 4.75 9.06 11.9Lens 1 diam2 Figure 4.10. Trend-Line for Lens Diameter and FWHM L e n s Di a m Lens Diameter ( cm ) FWHM (cm) 4.4. Effect of Image Distance (Magnification) on FWHM Having studied the effects of pinhole size, object size, focal length, and lens diameter on the FWHM, the ratio of image distance to the calculated object distance (using the image distance and focal length) was the next parameter investigated. In other words, the pinhole detector was set at three different distances from the lens, and the lens was set a distance away from the translation stage so that the corresponding object plane (to the pinhole) would be near the center of the translation stage. 4.4.1. Experimental setup Figure 4.11 is a schematic for this experimental setup. In this section, a constant lens diameter, focal length, and object size was maintained. The three runs had differing distances from the lens to the photo-detector. The FWHM behavior, whether it increased or decreased with the fixed distance between the lens and the detector was investigated. 49

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3 2 1 6 5 Key s-Variable Distance from Object to First Lens s'-Fixed Distance from Lens to Pinhole Detector 1-Light Source 2-Two-Dimensional Object 3-Bi-Convex Lens 4-Photodiode with Pinhole Aperture 5-Translation Stage 6-Optical Table Figure 4.11. Experimental Setup Testing Image Distance from Lens vs. FWHM 4 s S 50

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In this experiment, the depth of field for varying image distances was tested, holding everything else constant. A 1.5 cm diameter illuminated circular object mounted on a translation stage was used. This planar object and the pinhole detector used are described in section 4.1.1. For the first run, the lens to detector distance was fixed at 100 cm. The second run had an image to lens distance of 50 cm. The detector to lens distance for the third run was 8.8 cm. A full value and a background value was taken from the oscilloscope for decreasing distances between the object and the lens. The background-corrected values were normalized and plotted vs. object distance from the lens, and the FWHM was determined for each image distance. 4.4.2. Results The results can be seen in Figures 4.12 and 4.13. FWHM decreased as the magnification increased. The shortest lens-detector distance had a FWHM > 40cm. The difference in FWHM between the very short image distance of 8.8 cm and the two larger distances was substantial. However, the difference in FWHM between the 50 cm and 100 cm image distances was not great. Although the depth of field values are still relatively large, it is worth noting that in the experiments so far, the normalized intensity curves generally peak at approximately the object distance that corresponds to the focal length and the image distance. 51

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00.20.40.60.811.2010203040506070Distance (cm)Normalized Intensity s' = 50 cm s' = 8.8 cm s' = 100 cm Figure 4.12. Normalized Intensity at Pinhole vs. Distance from Object to Lens. Note: All values are in generic units. FWHM (0.5) 7 7.5 8 8.5 5.4644809 12.658228M 2 Figure 4.13. Trend-Line for Image Distance and FWHM s / s 12.7 5.5 FWHM (cm) s/s (g enericunits ) 52

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4.5. Effect of Increasing Out-of-Plane Sensitivity to (De)Magnification In this experiment, the FWHM after taking a 1:1 image of a 1:1 image was measured. In a second experiment, the FWHM after five consecutive 1:1 images of an object was measured. The final in plane image would be the same size as the object, but with each additional 1:1 imaging, the out of plane image becomes more distorted. This results in a greater change in (de)magnification from out of object plane light. This experiment was a check to see if this idea was worth pursuing. 4.5.1. Experimental Setup There were two setups for this comparison, the first was two consecutive 1:1 images, and the second was five consecutive 1:1 images. The 0.66 cm diameter circular, illuminated, planar object and the pinhole detector used are described in section 4.1.1. The object was mounted on a translation stage allowing variation of the distance of this planar object to the lens. Figures 4.14 and 4.15 show the schematic for each experimental setup. The lenses in the first experiment (Figure 4.14) were, from left to right, an 18.5 cm focal length plano-convex lens and a 7.5 cm focal length bi-convex lens. The cardboard tube between the two lenses made the effective diameter of the first lens 4.7 cm. The second lens had a diameter of 4.8 cm. The dashed line in the figure represents the plane where a 1:1 image would lie. This image distance from each lens was 2 times the focal length of each lens, so s 1 =37 cm and s 2 =s 2 =15 cm. The pinhole detector was located at the image plane that would produce a 1:1 image of the first 1:1 image. 53

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54 1 8 7 2 4 S1 6 S2 S2 S1 3 5 Figure 4.14. Experimental Setup for a One-to-One Image of an Image Key s1-Variable Distance from Object to First Lens s1'-Fixed Distance to First 1:1 Image s2-Fixed Distance from First 1:1 Image s2'-Fixed Distance to Last 1:1 Image 1-Light Source 2-Two-Dimensional Object 3-First Plano-Convex Lens 4-Cardboard Tube 5-Second Bi-Convex Lens 6-Photodiode with Pinhole Aperture 7-Translation Stage 8-O p tical Table

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55 8 10 9 6 5 3 2 1 4 7 S5 S5 S4 S4 Key s1-Variable Distance from Object to First Lens s1'-Fixed Distance to First 1:1 Image s2-Fixed Distance from First 1:1 Image s2'-Fixed Distance to Second 1:1 Image s3-Fixed Distance from Second 1:1 Image s3'-Fixed Distance to Third 1:1 Image s4-Fixed Distance from Third 1:1 Image s4'-Fixed Distance to Fourth 1:1 Image s5-Fixed Distance from Fourth 1:1 Image s5'-Fixed Distance to Fifth 1:1 Image 1-Light Source 2-Two-Dimensional Object 3-First Plano-Convex Lens 4-Second Bi-Convex Lens 5-Third Bi-Convex Lens 6-Fourth Bi-Convex Lens 7-Fifth Bi-Convex Lens 8-Photodiode with Pinhole Aperture 9-Translation Stage 10-Optical Table S3 S3 Figure 4.15. Experimental Setup for Five One-to-One Image of an Object S2 S2 S1 S1

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The lenses for the second experiment (Figure 4.15) were, from left to right, an 18.5 cm focal length plano-convex lens, a 7.5 cm focal length bi-convex lens, a 7.5 cm focal length bi-convex lens, a 3 cm focal length bi-convex lens, and a 3 cm focal length bi-convex lens. The first lens had an 11.9 cm diameter and the rest of the lenses had 4.9 cm diameters. The dashed lines in the figure represent the plane at which a 1:1 image would lie. The lenses were spaced so that each lens was twice the focal length from the image preceding it. These images of images were located at a distance twice the focal length behind each lens. The final image plane is where the pinhole detector was placed. For each setup, as the object was brought forward toward the first lens in 2 cm increments, a background and full value of the detector was measured using the oscilloscope. The values were background corrected, normalized, and plotted vs. distance from the lens. The FWHM for each was measured. 4.5.2. Results Both sets of experiments ended with approximately the same FWHM. The first experiment had a FWHM of 12.8 cm, and the experiment that took 5 consecutive 1:1 images of an object had a FWHM of 11.6 cm. This indicated that this idea for decreasing the FWHM was not worth pursuing. Also, the difference in size could have resulted from the fact that the effective diameter of the first lens in the first experiment was smaller than the diameter of the first lens used in the second experiment. The results for this experiment can be seen in Figure 4.16. 56

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00.20.40.60.811.20102030405060Distance (cm)Normalized Intensity Two 1 to 1 Images Five 1 to 1 Images Figure 4.16. Normalized Intensity at Pinhole vs. Distance from Object to First Lens. N ote: All values are in g eneric units. 4.6. Translating the Pinhole Detector Through the Image So far, the experimental setups used have translated the object so that its image (through differing systems) would move past the pinhole. An experiment was designed to show if there would be any advantage to translating the pinhole through the image of an object. If this is to make a useable difference, then a noticeably smaller FWHM for the depth of field should be measured. Otherwise, translating the pinhole instead of the object will not be useful, and the investigation into using a pinhole for depth resolving a three-dimensionally illuminated object could be ended. 4.6.1. Experimental Setup The experiments in 4.1. 4.5. translated the object toward the lens; in this experiment, the pinhole detector was translated toward the image of the object. The 57

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object and pinhole detector are described in section 4.1.1. The 1.5 cm diameter circular object was mounted on a translation stage allowing variation of the distance of this planar object to the lens. Figure 4.17 shows the experimental setup. 1 3 4 6 5 7 8 2 S2 S2 Figure 4.17. Experimental Setup for Translating Pinhole into Image S1 Key s1-Fixed Distance from Object to First Lens s1'-Variable Distance to First Pinhole to Lens s2-Fixed Distance from First Pinhole to Second Lens s2'-Fixed Distance from Second Lens to Second Pinhole 1-Light Source 2-Two-Dimensional Object 3-First Plano-Convex Lens 4-First Pinhole 5-Second Bi-Convex Lens 6-Photodiode with Pinhole Aperture 7-Translation Stage 8 Opt i ca l T ab l e S1 58

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The lens nearest the object was an 18.5 cm focal length plano-convex lens with an 11.9 cm diameter. The first pinhole is a sheet of aluminum with a pinhole aperture 0.075 cm. The second lens is a 7.5 cm focal length bi-convex lens with a 4.9 cm diameter. The second pinhole is the 0.05 cm pinhole detector described above. The object to first lens distance is 37 cm (twice the focal length for 1:1 imaging). The distance from the first pinhole to the second lens equals the distance from the second lens to the second pinhole. This distance is twice the focal length of the second lens, 15 cm. The image for the first pinhole is at the second pinhole. The pinhole-lens-pinhole section was translated into the image of the object. As the pinhole-lens-pinhole section was brought forward toward the first lens in 2 cm increments, a background and full value of the detector was measured using the oscilloscope. The values were background corrected, normalized, and plotted vs. distance from the lens. 4.6.2. Results The measured FWHM for this setup was 19.7 cm. Obviously, moving the pinhole into the image was no better than moving the object toward the lens. Figure 4.18 shows the results. 59

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00.20.40.60.811.2102030405060Distance (cm)Normalized Intensity Translated Pinhole Figure 4.18. Normalized Intensity at Pinhole vs. Distance from First Lens to First Pinhole. Note: All values are in g eneric units. 4.7. Discussion From ray diagrams, it is known that using a pinhole detector should emphasize the light coming from the object point that corresponds to the pinhole via the thin lens equation. The other light should be dramatically reduced. However, the experiments in Chapter 4 showed that the initial expectations for using a pinhole to filter out out-of-focal plane light were incorrect. This also means that the model for the behavior of light using a pinhole-lens combination was flawed. A better understanding of how the out-of-focal plane light behaves was needed to create an imaging system to resolve the light in a PLD plume planarly. The main effects of a number of parameters were studied in the hopes of manipulating them to provide decent depth resolution that could be applied to a plume. The following are the findings of this chapter. 60

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In the preceding experiments, it was shown that increasing the two-dimensional object size led to an increase in the FWHM of the depth resolution curve. A weak dependence of FWHM on pinhole size was found; decreasing the pinhole size decreased the FWHM. Increasing the focal length increased the FWHM when 1:1 imaging was used. The FWHM decreased as the diameter of the nearest lens to the object was increased. Placing the pinhole detector at a plane where the image was magnified resulted in a smaller FWHM than placing the detector closer in a plane where the image was less magnified. Taking more consecutive 1:1 images, thereby increasing an images magnification sensitivity to the object being out of the focal plane, did not result in a practically smaller FWHM. Finally, translating the pinhole through the image resulted in the same order of magnitude FWHM of the depth resolution curve, as did translating the object toward the first lens. The initial description of how the light from an object is observed through a pinhole was incorrect. Using the results from this chapter, a different description that will agree with the data will be presented. With this new description, it is hoped that the attempt to get depth dependant information from a plume will be more likely. 61

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CHAPTER 5. REVISED DESCRIPTION FOR LIGHT TERMINATION AT A PINHOLE 5.1. Chapter Overview Based on the results from Chapter 4, the initial pinhole concept from Chapter 3 was revised. These revisions are based on a geometric interpretation of the object light pathways and they account for the behavior of the FWHM for the depth of field measured in the previous chapter. The geometric description is then justified analytically. Finally, this new description is used to consider the practicality of using a pinhole on a PLD system for depth resolution of a plume. 5.2. Geometric Description 62 As was shown in Chapter 3, an infinitely small pinhole will capture only an infinitesimal portion of light from any point in the object except from the single point of light within the object whose light entirely terminates at the pinhole. This single preferred point of light will be emphasized on a detector located behind the pinhole. Using a finite sized pinhole should still emphasize the location near the point whose image terminates at the pinhole. Figure 5.1 illustrates the paths of light rays originating from different points on an object plane corresponding to the image plane through a thin lens. The blue arrows represent light that will terminate at the pinhole. The red arrows represent light that will be blocked by a pinhole. It is clear that light originating from within this plane will be entirely blocked by the pinhole except for a single point. This

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Figure 5.1. Light Paths Taken from Different Points of the Same Focal Plane point on the object plane whose light will terminate at the pinhole via every pathway through the lens will be known as the conjugate point to the pinhole. All points in the object plane except for the conjugate point to the pinhole are entirely blocked by the pinhole and can not account for the large depth of fields measured in Chapter 4. Next the light originating from a plane other than the focal plane in considered. For an infinitely small pinhole, only an infinitesimal amount of light should terminate at the pinhole. Figure 5.2 illustrates the paths of light rays originating from a point outside the object plane corresponding to the image plane through a thin lens. The blue arrow represents the path from that point that will terminate at the pinhole. The red arrows represent the paths that will be blocked by the pinhole. Only a tiny portion of the light from this point that gets to the lens makes it through the pinhole. For an infinitely small pinhole, this portion of light arriving at the pinhole would be negligible. A sufficiently 63

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Figure 5.2. Light Paths Taken from a Point Outside the Focal Plane small pinhole should make the out of focal plane light negligible relative to the light from the focal point. This is the assumption that the ideas in section 3.3. were based upon. The problem with the reasoning in section 3.3. arises when you consider a continuum of light at a plane other than the focal plane. The planar objects used in Chapter 4 as well as a plume in pulsed laser deposition are both continuous sources of light. Figure 5.3 illustrates this situation. As before, the blue arrows represent the light paths that terminate at the pinhole. The red arrows represent the light paths that will be blocked by the pinhole. Figure 5.3 shows that although the majority of light from each point is blocked by the pinhole, each point does contribute a tiny portion of its light through the pinhole. With a continuum of points, there will be a continuum of contributions through the pinhole. Even for an infinitely small pinhole, a continuum of light will provide an infinite number of infinitesimal contributions that will sum to a 64

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Figure 5.3. Light Paths Taken from Multiple Points Outside the Focal Plane finite amount. It is intuitive that a plane of light outside the focal plane will contribute the same amount of light through the pinhole as does the conjugate point to the pinhole. This observation will only be true when the plane and the conjugate point to the pinhole are at the same intensity and the plane entirely fills the solid angle between the conjugate point to the pinhole and the lens. Figure 5.4 illustrates the situation when the object out of the focal plane does not fill the solid angle between the point conjugate to the pinhole and the lens. Again, the blue arrows show the light paths that will terminate on the pinhole and the red arrows show the light paths that will be blocked by the pinhole. In this situation, the outer part of the lens does not direct any light from the plane toward the pinhole. This results in less light from the plane terminating at the pinhole than there would be from the conjugate point to the pinhole. If the plane were reduced to a point, then the calculations 65

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Unused Lens area Unused Lens area Figure 5.4. Light Paths Taken from a Point Outside the Focal Plane in Chapter 3 would be correct. This implies that the light reaching the pinhole from an illuminating planar object as it is translated from beyond the focal plane, through the focal plane, and closer than the focal plane to the lens would plateau until the object no longer filled the solid angle between the conjugate point to the pinhole and the lens. These plateaus are evident in Figure 4.2, and support this claim. Every light ray that leaves the conjugate point to the pinhole toward the lens will terminate at the pinhole. It follows that any light ray that follows the path of one of the rays from the conjugate point to the pinhole to the lens will also terminate at the pinhole. Figure 5.5 is a geometric construction of this situation. The distance to the conjugate point to the pinhole is given in terms of the pinhole distance from the lens, s, and the focal length, f, of the lens using the thin lens equation, 66

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y1 s' s'*f/(s'-f) s Figure 5.5. Geometric Construction for Finding Light Paths that Correspond to Paths Originating from the Point Conjugate to the Pinhole '111ssfconjugate (9) Solving for the distance from the conjugate point to the pinhole to the lens, yields conjugates )'('fsfssconjugate (10) In Figure 5.5, light traveling from the out of focal plane point y 1 above the optical axis and at an angle of with respect to the optical axis will follow the path of the light ray leaving the conjugate point to the pinhole at an angle of For every angle leaving the conjugate point to the pinhole, there will be a corresponding value of y 1 at a distance s 67

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from the lens, that will travel along the same path terminating at the pinhole. From Figure 5.5, it is clear that tan)'('1sfsfsy (11) Rearranging and solving for y 1 tan)'()''(1fssfssfsy (12) This is the solution of rays that will terminate at the pinhole in terms of angle, and distance, y 1 from the optical axis. If (10) is substituted in place of s into (12), as is the situation for the conjugate point to the pinhole, y conjugatesconjugate 1 =0 results. This means that at the point on the optical axis a distance from the lens, the light rays terminating at the pinhole are independent of This is exactly what is expected. s 5.3. Ray-Transfer Matrix Description Section 5.2. relied on a geometric interpretation of the behavior of the light that terminates at a pinhole based on intuition and the experiments from Chapter 4. Checking these results against a more fundamentally accepted view for the behavior of light was desirable. Since the experiments in Chapter 4 and the setup in section 5.2. were circularly symmetric optical systems formed by a succession of refracting surfaces all centered about the same optical axis, the ray-transfer matrix can be used to describe them. In systems such as that described, the system can be completely characterized by its effect on an incoming ray of arbitrary position, y 1 and direction, 1 at an input plane. 68

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The system will alter the ray until it has a new position, y 2 and direction, 2 at an output plane. Assuming paraxial rays, the relationship between y 1 1 y 2 and 2 is linear and one can write the relationship in the form 112 BAyy (13) and 112 DCy (14) or 111122yMyDCBAy (15) where A, B, C, and D are real numbers. Matrix M is known as the ray-transfer matrix. Consecutive optical components whose ray transfer matrices are M 1 M 2 ,,, M N are equivalent to a single matrix M= M N M 2 M 1 (16) (Saleh, Teich, 1991). The matrix for free-space propagation for a distance d along the optical axis is 101dMfp (17) and the matrix for transmission through a thin lens is 1101fMtl (18) (Pedrotti, 1993). To compare results from the ray-transfer matrix with the results from section 5.2., the same optical system will be used. The system is comprised of a free-space 69

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propagation through a distance s, transmission through a thin lens, and another free space propagation through a distance s. The resulting matrix using (16), (17), and (18) is 101110110'1'sfsMMMMsfs (19) After matrix multiplication, 11''1'1fsfssfsfsM (20) Using (15) and (20), 112''1'1ssfsyfsy (21) and 11211fsyf (22) In the case of a pinhole, 2 is not important because the direction the light is entering the pinhole is unimportant; the detector will measure it independent of the direction. However, y 2 =0 can be chosen to represent the pinhole. This is the case for an infinitely small pinhole. Setting y 2 =0 gives 11''1'10ssfsyfs (23) Solving for y 1 11)'()''(fssfssfsy (24) 70

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This is identical to the result found in section 5.2 once it is remembered that the ray-transfer matrix assumes paraxial rays, where tan Therefore the behavior for the termination of light at a pinhole through a lens described in section 5.2. is probably correct. 5.4. Analysis of the Results from Chapter 4 The results from Chapter 4 can be analyzed using the explanation provided in the prceding sections. The expected FWHM for depth resolution using the explanation in section 5.2 can be calculated and compared with the results from Chapter 4 to see how well they agree. Figure 5.6. shows the geometry for obtaining the FWHM in the experiments using a uniformly illuminated two-dimensional planar cicular object. In Figure 5.6, the lens diameter of the first lens in each system is labeled LD, the object diameter for each experiment is labeled OD, and the aperture diameter is labeled AD. Aperture diameter in Figure 5.6 is defined as the diameter of the cone reaching from the point conjugate to the pinhole to the lens, at the plane where the object lies. The distance s in the figure is the distance from the lens to the conjugate point to the pinhole. FWHM/2 is the object distance from the conjugate point to the pinhole that would correspond to a decrease in intensity through the pinhole by half. 71

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sLens Diameter (LD)Aperture Diameter (AD)FWHM/2Object Diameter (OD) Figure 5.6. Geometry for Obtaining the FWHM for Chapter 4 Ex p eriments According to section 5.2., the intensity at the pinhole detector should drop to one half its maximum value when the object area is equal to half the area due to the aperture diameter. The object area is 22_ODareaObject (25) The area due to the aperture diameter is 22_ADareaAperture (26) 72

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The object area is half the aperture area, so ODAD2 (27) Using similar triangles in Figure 5.6, LDsADFWHM2 (28) Rearranging these two equations together yields LDsODLDsODLDsADFWHM8.2222 (29) This is a simple result. It claims that the measured FWHM from Chapter 4 depend only on the lens diameter, the distance of the point conjugate to the pinhole from the lens, and the object diameter. The rest of the parameters are insignificant. To test this result, OD*s/LD was calculated for every experiment in Chapter 4 and plotted vs. the measured FWHM values. Figure 5.7 shows the results. 0.005.0010.0015.0020.0025.0030.0035.0040.0045.000.002.004.006.008.0010.0012.0014.0016.00OD*s/LDFWHM Figure 5.7. Plot and Linear Fits of Measured FWHM vs. OD*s/LD. N ote: All values arein cm. 73

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There are two linear fits in Figure 5.7. The red line is the least squares line fitting the data. The equation of this line is 9912.1444.2LDsODFWHM (30) with a coefficient of determination of The blue line is the least squares line with a forced intercept of zero fitting the data. The equation of this line is 9027.02R LDsODFWHM742.2 (31) with a coefficient of determination of Both coefficients of determination are very high, suggesting a strong linear dependence between the variables plotted. Also, the slope of each linear fit (2.444 and 2.742) is very close to the theoretical value of 8841.02R 8.222 It is important to realize that the theoretical solution, (29), is for a perfect pinhole. Further calculations are necessary for a finite pinhole, but as Figure 5.7 shows, this result is very close even for finite pinholes. 5.5. Consequence to Plume Imaging Simply plugging reasonable numbers for LD (12 cm), s (3 cm), and OD (3 cm) into the equation found in section 5.4, a FWHM value of approximately 25 cm is obtained. This is the depth resolution for each two-dimensional plane within the three-dimensional plume. Since the plume is much smaller than 25 cm, depth resolution from the light of a PLD plume using a pinhole is unobtainable. 74

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CHAPTER 6. COMPARISON WITH CONFOCAL MICROSCOPY 6.1. Introduction Confocal microscopy is a widely used technique that provides three-dimensional images of samples. The explanation for the depth resolution involves the use of pinholes. A main argument for the resolution in depth in confocal microscopy is optical sectioning. Figure 3.1 is typical of the drawings used to describe optical sectioning. Because the techniques for depth resolution in confocal microscopy are similar to the ones attempted in this project, it is important to identify the differences that allow confocal microscopy to be used successfully. Figure 6.1 is a schematic for a typical confocal microscope. A point light source Figure 6.1. Schematic for a Confocal Microscope Employing Two Pinholes in the O p tical S y stem ( Corle Kino 1996 ) 75

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is used to form a diffraction-limited spot in the sample. A beamsplitter is then used to deflect the reflected beam to a separate detector pinhole. The objective lens is used twice in this process. Only a single point is illuminated at a time, and the image is formed by scanning the point over the sample. Depth resolution occurs because when the sample is moved out of the focal plane of the lens, the reflected light reaching the pinhole is defocused and does not pass through it. Therefore, a detector behind the pinhole will measure rapidly decreasing intensity with the defocus distance, and the image disappears (Corle, Kino, 1996). The explanation given for this decrease in measured intensity is that light originating from points away from the focal plane will be defocused at the confocal aperture, and will be detected weakly (Sheppard, 1994). Obviously the main difference between confocal microscopy and this project is a single illuminated point. Chapters 3 and 5 explained that if the object were reduced to a point source, then the expected depth resolution in Chapter 3 would apply. However, the spot of light in confocal microscopy comes from the objective lens, and will still illuminate out of plane parts of the sample. As was shown earlier, a continuum of light encompassing the solid angle from the focal plane to the lens will produce the same amount of light as the point in the focal plane whose image terminates at the pinhole. However, the main difference in confocal microscopy is that the intensity drops as a function of distance from the focal plane. So the most important feature for depth resolution is not the second conjugate pinhole, it is the fact that the sample is illuminated by the first pinhole through the objective lens. The sensitivity of the detector behind the second pinhole to the defocused planes in their entirety is the same as to the single point in the focal plane. The reason the defocused 76

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planes disappear is that the intensity at those planes decreases very rapidly with the distance from the focal plane, not because the image of a point out of the focal plane is out of focus at the detector. However, the second pinhole does reject light from points adjacent to the one illuminated, and helps refine the image when considering diffraction and the point spread function of the spot. When looking closely at the spot of light, there is a complicated structure to the intensity distribution. This pattern is the point spread function (PSF). The point spread function can be thought of as the probability of a photon reaching a particular point. A photon is 10 5 times more likely to reach the focal point than to reach a point far from it, still within the light cone. Each pinhole in a confocal microscope will have a point spread function associated with it. Therefore, the point spread function within the whole microscope will be the product of the point spread functions of the two pinholes. By multiplying the PSF of each pinhole together, the probability for photons reaching any point far from the focal point decreases dramatically. For example, peaks in the PSF for individual pinholes that were 0.01 times the main peak intensity now become 0.0001 (Webb, 1999). 6.2. Derivation of Depth Response for Confocal Microscopy The following derivation for the depth response of a confocal scanning optical microscope (CSOM), taken from Confocal Scanning Optical Microscopy and Related Imaging Systems by Corle and Kino, uses nonparaxial scalar theory with an infinitesimally small pinhole and a plane reflector. The formulas refer to Figure 6.2. They considered a CSOM using a collimated beam illuminating the objective. The beam 77

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Figure 6.2. The CSOM Configuration Used in the Derivation of the Depth Res p onse ( Corle Kino 1996 ) reflected from the sample will pass back through the objective and is reflected by a beamsplitter to a pinhole relay lens. The relay lens focuses the reflected beam onto an infinitesimally small pinhole detector. The objective can be characterized by a pupil function P(). The amplitude and phase of the pupil function may vary with the angle between a ray from the pupil plane to the focal point and the lens axis. It is assumed that the dimensions of the lens pupil are large compared to the wavelength of light. Also assumed is that the sine condition for a perfect lens is obeyed, 'sinsin Mn (32) M is the magnification of the optical system, n is the index of refraction of the material between the sample and objective, is the angle between a ray to the objective pupil and the optical axis, and is the angle formed by the corresponding ray at the pinhole. This 78

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condition is applicable to large angle systems, but requires that a perfect image at the image plane is obtained for points in the object plane that are a small distance apart. They also assumed that the amplitude of the input beam at the pupil plane is uniform with a value of 0),,(rI (33) When a perfect plane mirror is placed at the focal plane of the objective lens, the amplitude of the reflected signal from the ray passing through the pupil plane at ,,r is 022),,(),,(PrPrIR (34) by symmetry. P() is squared because the ray travels through the objective twice. After reflecting off the mirror, the rays terminate at the pinhole forming an angle with the optical axis. The signal V(0) received at the on-axis pinhole in front of the detector is proportional to the integral of over the angle ),,(rR This yields ''sin)0(0'020dPVplane (35) 0' is the maximum angle subtended by the focused beam at the pinhole. When the planar mirror is moved a distance z from the focal plane, the image of the focused spot in the mirror will move by 2z from the focal plane. The fields along a reflected ray in the pupil plane of the lens passing through ,,r pick up an additional phase shift of cos2knz where 2k (36) The amplitude of the reflected field on the ray at the pupil of the objective is proportional to the incident field times the phase factor cos2expjknz So, 79

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cos202cos22),,(),,(jknzIjknzRePrePr (37) The normalized electric field amplitude V(z) is calculated by integrating the reflected field over the angles in the focused beam. If it is assumed as before in (33), then V(z) normalized to its value for the mirror located at the focal plane is ''sin''sin)(0002cos202dPdePzVjknzplane (38) Here, 0 is the half-angle subtended by the focused beam at the objective lens. Corle and Kino continue their derivation, but these results for V(0) and V(z) are sufficient for the next section. These equations are for a perfect lens absent spherical and chromatic abberation with a uniformly illuminated lens pupil. The depth response will worsen with the introduction of these irregularities. A photodiode detects the intensity, which is proportional to the absolute value of V(z) (Corle, Kino, 1996). 6.3. Possible Improvement to Confocal Microscopy Depth Response The equations describing the depth response for CSOM, derived by Corle and Kino, shown in the previous section are ''sin)0(0'020dPVplane for the electric field amplitude at the pinhole detector for the reflected light from the focal plane, and ''sin''sin)(0002cos202dPdePzVjknzplane 80

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for the normalized electric field amplitude at the pinhole detector for the reflected light from a plane a distance z from the focal plane. These equations refer to Figure 6.2. It is important to realize that V(0) is an integration from 0 to 0' or the entire angle accepted by the pinhole detector. This agrees with the earlier claim in Chapter 5 that the light arriving at the pinhole from the conjugate point to the pinhole via the lens equation is independent of the angle of the ray leaving that point, as long at the light gets to the lens. In the derivation above, they use a plane mirror, and so 0' will correspond to 0 However, an illuminated point in many samples will not reflect only as a plane mirror, but in every direction. This would lift the restriction that 0' must correspond to 0 The equation for V(z) is an integration from 0 to 0 or the half-angle subtended by the focused beam at the objective lens. The light from the focal plane depends on the angle of light accepted by the pinhole detector, while the out of focal plane light arriving at the detector pinhole depends on the angle that the illuminating beam makes with the optical axis. One can imagine placing an additional pupil function at the pinhole relay lens that would only allow light from larger angles of It could be something as simple as covering the pinhole relay lens at its center. This sort of pupil function would change the limits of integration from some value pupil determined by the second pupil function, to 0' The collimated beam illuminating the objective could be held to a smaller diameter than the diameter that could be accepted by the objective. By using this second pupil function at the relay lens, the limits of integration for both V(0) and V(z) would be changed from 0 to 0' and 0 to 0 to pupil to 0' By choosing pupil to correspond to 81

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0 the limits of integration for V(z) would be effectively 0 to 0 making V(z) equal to zero. The corresponding rays for 0 at the pinhole were chosen to be smaller than 0' therefore pupil will be smaller than 0' and V(0) would not be zero. Physically, the second pupil would block the out of plane light from entering the pinhole, while still allowing light from the point at the focal plane to pass through the pinhole. This configuration takes advantage of the fact that light entering the pinhole detector from out of the focal plane has an angular dependence, while light from the point at the focal plane does not. Beamsplitter 2 n d Pupil Function Pinhole Relay Lens Objective Focal Plane Pinhole Figure 6.3. Application to a Second Pupil Function to a Pinhole Rela y Lens to Im p rove De p th Res p onse of CSOM 82

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Figure 6.3 illustrates how this could work. Based on the above derivation, it is plausible that the use of a second pupil function at the relay lens would eliminate macroscopic effects of out of plane light from confocal microscopy and improve depth resolution, but diffraction and the PSF would continue to contribute to the depth response. It should be noted that the lateral resolution of a confocal microscope is inversely proportional to the numerical aperture, so by choosing to only use the objective partially by the collimated beam as in Figure 6.3, one would gain improved depth resolution at the expense of diminished lateral resolution (Webb, 1999). However, an approximation for the depth of field can be made for a finite pinhole, as was done in Chapter 3. 6.4. Depth of Field for a Finite Pinhole This additional pupil function would exclude all out of focal plane light for an infinitely small pinhole light source and detector, but a finite pinhole would behave differently. In the following section, the depth of field for a finite pinhole for a point source of light is recalculated when a pupil function similar to that described above is used. This result can be compared to the depth calculated in Chapter 3. Figure 6.4 is similar to the diagram from Chapter 3, but the light striking the center of the lens is blocked. 83

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2RB, f Focal Plane s1 s3 s2 Image Plane 2R, f s3' s1' s2' 2r Figure 6.4. Diagram for Depth Resolution of a Finite Pinhole Blocking the Center of the Lens The pinhole diameter is 2r, the lens has a diameter of 2R, and a focal length f. The focal plane is located a distance s 2 from the lens, and the image (pinhole) plane is located a distance s 2 from the lens. Points located distances s 1 and s 3 from the lens will also allow 100% transmission through the pinhole, and they have corresponding images before and after the pinhole plane located at distances s 1 and s 3 from the lens respectively. The depth of field here will be s 1 -s 3 for 100% transmission. The pinhole 84

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size determines s 3 -s 1 , which determines the depth of field s 1 -s 3 Equations (2)-(8) from section 3.2. still apply. Blocking the center of the lens will not change the depth of field for 100% transmission through the pinhole, but it will be shown that it does quickly reduce the depth of field for transmissions less than 100%. Figure 6.5 illustrates the effect of blocking the center of the focusing lens. Because the object distances, image distances and focal lengths are the same, the shadow from the blocked center of the lens will behave as the light cone through the lens, but with a different lens radius. With an unblocked lens, the light intensity through the pinhole decreases because the proportion of light for the image approaches zero. With a center blocked lens, this is also true, but the intensity becomes zero once the cone for the shadow completely covers the pinhole. Instead of approaching zero, the intensity becomes zero at a specific image distance. Figure 6.6 illustrates this point. In Figure 6.6, the pinhole at 1 is engulfed by the shadow of the blocked part of the lens, and so no intensity gets through. The pinhole at location 2 allows the full amount of available light through. The pinhole at location 3 allows about half of the available light through. This is unlike an unblocked lens, in which large portions of the total available light would pass through the pinhole at locations 1,2, and 3. 85

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86 Figure 6.6. Proportion of Available Light from a Center Blocked Lens at Different Pinhole Distances Figure 6.5. Diagram for the Shadow of a Center Blocked Lens 1 2 3

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The portion of available light through the pinhole is equivalent to the total light that would arrive from a larger diameter unblocked lens through the pinhole, minus the portion of light that would have arrived from a smaller unblocked lens through the pinhole. The larger lens diameter would be that of the entire lens, and the smaller lens diameter is the same diameter that blocks the center light. Figure 6.7 shows the diagram S 2r 2 2 2R2 2R1 C Figure 6.7. Diagram Used in Depth of Field Calculation used to calculate the depth of field for a finite pinhole when the center of the lens is blocked. R 1 is the radius of the lens, R 2 is the radius of the blocked part of the lens, r is the pinhole radius, C is a constant distance from the lens to the pinhole, s is the image distance for a specified object distance, 1 is radius of the cone of light for the lens at the 87

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pinhole, and 2 is the radius of the shadow cast by the blocked part of the lens at the pinhole. From similar triangles, 11''CsRs and 22''CsRs This allows one to solve for 1 and 1 The amount of light that passes through the pinhole will be proportional to 212222122212rr but when r1 the maximum value for intensity is reached, and when r2 the value will be zero. Arbitrarily using f = 3, C = 6, r = 0.003, R 1 = 10, and R 2 = varying fractions of R 1 and plotting the results, one can see the change in depth sensitivity between a lens, and lenses with varying degrees of blocked centers. Figure 6.8 shows the normalized intensity through the pinhole as a function of object distance, for a lens with varying degrees of blocking. It is clear that the lesser blocked lens will have a larger depth of field than the increasingly blocked lenses. Comparing the FWHM of the unblocked lens with the FWHM of the lens whose center blocker has a radius half the lens radius, an improvement of roughly 20% is graphically estimated. This improvement depends solely on the ratio of the blocker radius to lens radius, and not on the arbitrary constants chosen initially. 88

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-0.200.20.40.60.811.255.566.577.5Object DistanceNormalized Intensity No Block 3/10 R Block 5/10 R Block 7/10 R Block 9/10 R Block Figure 6.8. Normalized Intensity Values Through Pinhole vs. Object Distance Using Lenses Blocked at the Center. Note: All values are in g eneric units. Mathematically, it appears that using a second pupil function that would block the center of the lens before the detector pinhole should improve the depth resolution in confocal microscopy. However, this may end up being impractical because of the point spread function, diffraction, too great a loss in lateral resolution, spherical and chromatic aberration, or cost/benefit considerations. Further investigation into the practical application of this idea is warranted. 89

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CHAPTER 7. CONCLUSION The initial purpose of this thesis was to create a PLD diagnostic that could provide depth-resolved information about the intensity within the plume, without interfering with the plume. Standard PLD imaging techniques using ICCD imaging were characterized. This characterization showed that ICCD images of laser ablated plumes are not representative of the plane at which the imaging system is focused to. Instead, the intensity distributions within ICCD images of plumes are a complicated function of the actual plume intensity distribution, plume distance from the imaging lens, and the distance from the focal plane. This is an important result, as the literature never comments on the strength that the unfocused light has on the final image. Also shown was the relevance that a planar intensity distribution within a plume has with respect to film characteristics, namely film thickness. Chapter 2 illustrated the problems with standard ICCD imaging; it also demonstrated potential benefits in having planar resolution in imaging for PLD. An experimental design was formulated to obtain depth-resolved information about the light intensity within a PLD plume utilizing the depth filtering properties of a pinhole. Chapter 3 justified the idea and calculated the expected resolution. Chapter 4 went about testing this design and its expectations. It was then realized that the assumptions made during the calculations in Chapter 3 were not entirely correct. 90

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Different parameters were studied in the hopes of combining them in a way that would still be able to planarly resolve a plume. After examining the dependence of depth of field on each parameter studied in Chapter 4, a more complete description of the behavior expected when imaging using a pinhole-covered detector was presented in Chapter 5. The data from Chapter 4 fit this revised description very well. Surprisingly, the wide variety of FWHM in Chapter 4 were all successfully explained by a simple model using an infinitely small pinhole, despite the many variables changed throughout Chapter 4. Chapter 5 corrects a commonly held misconception about the depth resolving behavior associated with the use of a pinhole. A pinhole-covered detector will only discriminate against a single out of focal plane point of light. Distributions of out of focal plane light will have the same amount of light terminate at the pinhole detector as an illuminating point in the focal plane conjugate to the pinhole, providing that the distribution covers the entire solid angle between the conjugate point to the pinhole and the lens. In coming to understand this, the depth resolving success of confocal microscopy was examined. Chapter 6 clears up a commonly held misconception about depth resolution in confocal microscopy. The depth resolution is largely the result of being illuminated at a single point. Being illuminated at a single point causes the intensity at planes outside the focal plane to decrease quickly. The pinhole covering the detector assists in the depth (and lateral) response, but the pinhole light source is the most important feature in a confocal microscope. In Chapter 6, a known mathematical derivation of the depth response was used to suggest an idea that could improve the depth 91

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resolution in confocal microscopes. This improvement is suggested mathematically and may be implemented in the future. Although the initial intentions of this thesis were not achieved, this thesis was successful in that it did bring clarity and better understanding to interpreting ICCD images of laser ablated plumes, the concept of pinhole depth selectivity, and confocal microscopy fundamentals. Most importantly, a possible technique to improve the depth response in confocal microscopy was suggested and supported mathematically. Nevertheless, a PLD diagnostic that could non-invasively extract information about the intensity distribution of PLD plumes would still be extremely useful. Such a diagnostic would allow spatial and temporal analysis of plumes, and comparisons with film properties could be analyzed. This would allow direct in-situ analysis of film properties during deposition. Such a diagnostic would also allow for three-dimensional mapping of plumes, which would lead to better modeling of the processes occurring in the laser-ablated plasma plumes. Future projects could include formulating a mathematical deconvolution using present plume models that could extract the information about the intensity distribution at the focal plane. Also, taking ICCD images using a pinhole camera setup rather than a lens would provide an integrated image of every plane of the plume, but every plane would be in focus, unlike conventional imaging in which only the single plane is in focus. Another project could involve laser-induced fluorescence (LIF), which is already in use as a PLD diagnostic. In LIF, a tunable dye laser is used to optically pump ground state species to a selected exited state. The spontaneous emission that follows is then recorded using an interference filter or spectrometer. LIF provides spatial and temporal 92

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information about plumes, and has been used to spatially map different species angular velocity distributions (Geohegan, 1994-chrisey book). Although LIF is slightly invasive, the idea of inducing fluorescence could be used to spatially map a plume. This in conjunction with filtering and ICCD imaging could provide planar two-dimensional maps for plumes. A two-dimensional spatially and spectrally resolved fiber-optical filter developed in our laboratory could be used in conjunction with ICCD imaging for such applications (Mukherjee et al., 2001). 93

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REFERENCES J. T. Cheung, in: D. B. Chrisey and G.K. Hubler (Eds), Pulsed Laser Deposition of Thin Films, New York: Wiley, 1994, pp. 1-18. T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems, California: Academic Press, 1996, pp. 31-44, and 147-183. D. B. Geohegan, in: D. B. Chrisey and G.K. Hubler (Eds), Pulsed Laser Deposition of Thin Films, New York: Wiley, 1994, pp. 115-161. D. B. Geohegan, Laser Ablation of Electronic Materials: Basic Mechanisms and Applications, E. Fogarassy and S. Lazare, (Eds), North Holland, pp. 73, 1992a. J. C. S. Kools, in: D. B. Chrisey and G.K. Hubler (Eds), Pulsed Laser Deposition of Thin Films, New York: Wiley, 1994, pp. 455-469. J. C. S. Kools, C.J.C Nillesen, S.H. Brongersma, E. van de Riet, and J. Dieleman, J. Vac. Sci. Technol., Vol. A10, pp. 1809, 1992. P. Mukherjee, S. Chen, S. Witanachchi, A Novel Continuously Tunable, High Spectral Resolution Optical Filter for Two-Dimensional Imaging, Review of Scientific Instruments, Vol. 72, pp. 2624-2386, 2001. F. L. Pedrotti, S.J., and L. S. Pedrotti, Introduction to Optics, Second Edition, New Jersey: Prentice Hall, 1993, pp. 30-72. A. A. Puretzky, D. B. Geohegan, X. Fan, and S. J. Pennycook, Dynamics of Single-Wall Carbon Nanotube Synthesis by Laser Vaporization, Applied Physics A, Vol. 70, pp. 153-160, 2000. A. A. Puretzky, D. B. Geohegan, X. Fan, and S. J. Pennycook, In Situ Imaging and Spectroscopy of Single-Wall Carbon Nanotube Synthesis by Laser Vaporization, Appl. Phys. Lett., Vol. 76, no. 2, pp. 182-184, 2000. 94

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A. A. Puretzky, H. Schittenhelm, X. Fan, M. L. Lance, L. F. Allard Jr., and D. B. Geohegan, Investigations of Single-Wall Carbon Nanotube Growth by Time-Restricted Laser Vaporization, Physical Review B, Vol. 65, 245425 (1-9), 2002. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, New York: John Wiley & Sons, Inc., 1991, pp. 26-34. J. Sall, A. Lehman, and L. Creighton, JMP Start Statistics, Second Edition, California: Duxbury, 2001, pp. 365-412. S. B. Segall and D. W. Koopman, Physics Fluids, Vol. 16, pp. 1149, 1973. C. J. R. Sheppard, in P. C. Cheng, T. H. Lin, W. L. Wu, and J. L. Wu (Eds) Multidimensional Microscopy, New York: Springer-Verlog, 1994, pp. 1-29. A. Vertes, P. Juhasz, P. Jani, and A. Czitrovszky, Int. J. Mass Spectrom. Ion Process, Vol. 83, pp. 45, 1998. R. H. Webb, in P. M. Conn (Eds), Methods in Enzymology, California: Academic Press, 1999, pp. 3-26. S. Witanachchi, K. Ahmed, P. Sakthivel, and P. Mukherjee, Dual-Laser Ablation for Particulate-Free Film Growth, Appl. Phys. Lett., Vol.66, no. 12, pp. 1469-71, 1995. 95