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University Microfilms International 300 N WAVEFRONT ERRORS PRODUCED BY MULTILAYER THIN-FILM OPTICAL COATINGS Item Type text; Dissertation-Reproduction (electronic) Authors Knowlden, Robert Edward Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 05/10/2021 11:15:02 Link to Item http://hdl.handle.net/10150/281959 INFORMATION TO USERS This was produced from a copy of a document sent to us for microfilming. While the most advanced technological means to photograph and reproduce this document have been used, the quality--is-heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help you understand markings or notations which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure you of complete continuity. 2. When an image on the film is obliterated with a round black mark it is an indication that the film inspector noticed either blurred copy because of movement during exposure, or duplicate copy. Unless we meant to delete copyrighted materials that should not have been filmed, you will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photo­ graphed the photographer has followed a definite method in "sectioning" the material. It is customary to begin filming at the upper left hand corner of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete. 4. For any illustrations that cannot be reproduced satisfactorily by xerography, photographic prints can be purchased at additional cost and tipped into your xerographic copy. Requests can be made to our Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases we have filmed the best available copy. University Microfilms International 300 N. ZEEB ROAD. ANN ARBOR, Ml 48106 18 BEDFORD ROW, LONDON WC1R 4EJ, ENGLAND 8116708 Knowlden, Robert Edward WAVEFRONT ERRORS PRODUCED BY MULTILAYER THIN-FILM OPTICAL COATINGS The University of Arizona PH.D. 1981 University Microfilms International 300 N. Zeeb Road, Ann Arbor, MI 48106 IVAVEFRONT ERRORS PRODUCED BY MULTILAYER THIN-FILM OPTICAL COATINGS by Robert Edward Knowlden A Dissertation Submitted to the Faculty of the COMMITTEE ON OPTICAL SCIENCES (GRADUATE) In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 198 1 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Final Examination Committee, we certify that we have read the dissertation prepared by Robert Edward Knowlden entitled Wavefront Errors Produced by Multilayer Thin-Film Optical Coatings and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy . il ft — // fhd ft Date IOM. <?. 4/li/ZI , t Date (~\ - . q, j /1? f $ Date Date Date Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College. X hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Dissertation Director Date STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to bor­ rowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or re­ production of this manuscript in whole or in part may be granted by the head of the major department or the' Dean of the Graduate College when in his judgment the proposed use of the material is in the in­ terests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED ACKNOWLEDGMENTS I wish to thank all of the people who have supported me through this work. Most especially I thank my parents, my advisor Bob Shannon, and Angus Macleod, who taught me most of the little I understand about optical thin films. I add that I will do my best to fail none of you. Thanks also are due Sherrie Cornett, who put this in its present form. iii TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS vi LIST OF TABLES x ABSTRACT xi 1. INTRODUCTION 1 Organization of the Dissertation 5 Use of the First Person 5 2. MULTILAYER THEORY AND ENHANCED REFLECTOR DESIGN 6 The Complex Plane Wave 6 The Matrix Formalism 7 The Optical Admittance 10 Reflection, Transmission and Optical Phase 11 Derivatives of the Phase 17 Basic Enhanced Reflectors 19 3. ANGLE OF INCIDENCE EFFECTS WITH ROTATIONALLY SYMMETRIC MIRRORS 24 Decomposition of Polarizations 24 Angles of Incidence for a Parabola 27 Computing Amplitudes and Phases 30 Extraction of the Focus Term 31 Examples 32 4. THE OPTICAL PHASE ON REFLECTION AS A FUNCTION OF STACK THICKNESS 46 An Infrared High-Reflectance Coating: Performance at IR and Visible Wavelengths 49 Measurements at Two Wavelengths 52 Inverting the Two-Wavelength Phase Difference Function . 55 Base Thickness Measurements 57 5. A MODIFIED COATING DESIGN TO ALLOW ACCURATE COATING THICKNESS PROFILE ESTIMATION 61 iv V TABLE OF CONTENTS--Continued Page An Error Function 61 An Optimization Technique: The Nonlinear Simplex Method 66 The Modified Design 70 Estimation of the Wavefront in the Infrared from Two Visible Measurements: Polynomials 73 Measurements Using Several Wavelengths 82 6. ROTATIONALLY SYMMETRIC COATING THICKNESS DISTRIBUTIONS .... 89 Vacuum Coating Geometries 89 The Use of Radial Polynomials 94 Determining a Radial Thickness Distribution from Measurements at Three Wavelengths 101 An Example 103 7. THE EFFECTS OF ERRORS ON THE ACCURACY OF ESTIMATION OF THE INFRARED WAVEFRONT FROM VISIBLE LIGHT INTERFEROGRAMS 109 Wavefront Measurements 114 The Need for a New Error Function 123 Choice of a Deposition Geometry 125 New Optimization Variables 130 An Example: Attainable Accuracy 131 The Initial Estimates 136 A Demonstration of the Effects of Wavefront Errors .... 138 The Effects of an Index Change 140 8. SUMMARY AND CONCLUSIONS 143 Additional Comments and Suggestions for Further Work . 147 APPENDIX A: A COATING DESIGN OF GUHA, SCOTT AND SOUTHWELL . 150 APPENDIX B: AN INFRARED ENHANCED REFLECTOR WITH REDUCED WAVEFRONT ERRORS DUE TO PROPORTIONAL THICKNESS CHANGES 160 LIST OF REFERENCES 170 LIST OF ILLUSTRATIONS Figure Page 1.1. Interferogram reproduced from Ramsay and Ciddor (1967) . 3 2.1. A single layer, with forward and backward travelling waves 9 2.2. Intensity change due to refraction at an interface .... 13 2.3. Two dielectric stacks indicating phase changes 16 3.1. Circular aperture: Cartesian and polar coordinates .... 25 3.2. Section of a parabola being tested at its center of curvature 29 3.3. Contours for Example 1, an f/1.5 parabola with a 6 layer coating 34 3.4. Contours for Example 2, an f/1.5 parabola with a 35 layer coating after Heavens and Liddell (1966) 37 3.5. Contours for Example 3, a parabola tested at its center of curvature 40 3.6. Contours for Example 4, a 90 degree cone with a 6 layer coating 43 4.1. Optical path in microns (p) at 0.4p as a function of relative thickness change (k) for a 35 layer design by Heavens and Liddell (1966) 48 4.2. Optical path (in p) for a 6 layer enhanced reflector as a function of k at the design wavelength, 3.8p 50 4.3. Optical path (in p) for the 6 layer 3.8p design at 0.6328p 51 4.4. Optical path (in p) for the 6 layer 3.8p design at 0.5145p 53 4.5. Two wavelength optical path difference for the 6 layer design at 0.5145p and 0.6328p 54 vi vii LIST OF ILLUSTRATIONS--Continued Figure Page 4.6. Representation of displaced Fizeau fringes for measuring the stack thickness 59 4.7. Optical path change (in y) for the 6 layer design at 0.6328p; the stack thickness goes from zero (k=-l) to the nominal (k=0) 60 5.1. Flow chart for the nonlinear simplex search algorithm (Nelder and Mead 1965) 69 5.2. Two wavelength optical path difference (in y) as a function of relative stack thickness change (k) for the 6 layer modified design 72 5.3. Optical path (in y) at 3.8y for the modified design as a function of k 74 5.4. Optical path (in y) at 0.6328y for the modified design as a function of k 75 5.5. Optical path at 0.5145y for the modified design 76 5.6. Optical path at 0.6328y for the modified design, from zero stack thickness (k=-l) to l.lx the nominal design thickness (k=0.1) 81 5.7. Optical path at 3.8y for the six layer quarter wave design over a 10% range in k 83 5.8. Two wavelength path difference functions (in y) for 0.4880m - 0.6328y (lower curve) and 0.5145y - 0.6328y (upper) 85 5.9.
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