An Improved Geometric Test for Optical Surfaces A Thesis Submitted for the Degree of Doctor of Philosophy of the University of London by Young-Soo Kim Department of Physics and Astronomy University College University of London 1998 ProQuest Number: U642131 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest. ProQuest U642131 Published by ProQuest LLC(2015). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. Microform Edition © ProQuest LLC. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 An Improved Geometric Test for Optical Surfaces Abstract As the quality of large optics are required to be more accurate, even to the diffraction limit, more accurate testing methods are needed. For example, large telescope optics consist of aspheric concave and convex mirrors with significant aspheric departures. Testing these optics using classical methods usually requires the use of a null lens or mirror. However, the null corrector itself can be wrong and thus lead to incorrect test results. One example is the primary mirror of Hubble Space Telescope. In order to avoid such a mistake, at least two independent test methods should be applied. A new test method - a quantitative knife-edge test (AQuaKET) - has been developed by revolutionizing one of the oldest testing method, the Foucault test. One of the advantages of the Foucault test is that it does not need any additional optical components which can introduce errors, whereas a disadvantage is that it does not give a quantitative result. Whilst maintaining the merits of the Foucault test, AQuaKET embodies novel ideas for acquiring quantitative results. The thesis describes the application of opto-electronic, data acquisition, and data processing techniques including refined simplex method to the Foucault test. Test results of three mirrors are presented which validate the reliability of the method for testing optics with high accuracy, including aspheric mirrors. Several potential improvements are discussed and future work is suggested. Finally, the overall methodology developed is compared with other approaches currently available. Glossary and symbols A AT Anglo-Australian Telescope ADASS Astronomical Data Analysis Software and Systems AQuaKET A Quantitative Knife-Edge Test ASP Astronomical Society of the Pacific °C temperature in Celsius CC conic constant CCD Charge-Coupled Device CFHT Canada-France-Hawaii Telescope CGH Computer-Generated Hologram CoC Centre of Curvature CORI COaxial Reference Interferometer, HST COSTAR Corrective Optics Space Telescope Axial Replacement, HST DOS Disk Operating System ESO European Southern Observatory exp exponential F Focal ratio FWHM Full Width Half Maximum HET Hobby-Eberly telescope HST Hubble Space Telescope INT Isaac Newton Telescope IR Infrared LET Large Binocular Telescope MAI Multiple Annular Interferograms MMT Multiple Mirror Telescope MPIA Max-Planck-Institut für Astronomie Nt Refractive index at a temperature t OPD Optical Path Difference OS Operating System PC Personal Computer P-V Peak-to-Valley RC Ritchey-Chrétien RMS Root Mean Square RNC Reflective Null Corrector ROC Radius Of Curvature SNI Sub-Nyquist Interferometry SPI Scatter-plate interferometry STD Standard deviation UCL University College London, London, U.K. U.K. United Kingdom UKIRT United Kingdom Infrared Telescope U.S.A. United States of America UV Ultraviolet VLT Very Large Telescope, ESO WHT William Herschel Telescope Zi Coefficient of Zemike polynomials Ô standard deviation X wavelength variance V frequency Z angle between two lines Contents Abstract 2 Glossary and symbols ................................................................................. 3 Contents 5 List of Tables 10 List of Figures 13 1. Introduction 17 1.1 Optical telescopes .................................................................... 18 1.1.1 History of optical telescopes 18 1.1.2 Large telescopes and their optics ..................... 20 1.1.3 A problem in Hubble Space Telescope: primary mirror .. 25 1.1.4 Accuracy requirements: the Gemini telescopes as an example 26 1.1.5 Probable height error estimation from slope error ....... 29 1.2 Optical testing ................................................................................. 32 1.2.1 General categorization of test methods 32 1.2.2 Test methods for large aspheric optics 33 1.2.3 Test methods for large convex mirror 37 1.3 Foucault test .................................................................................... 39 1.3.1 Principle of the Foucault test 40 1.3.2 Advantages and disadvantages of the Foucault test ..... 42 1.3.3 Accuracy of the Foucault test: survey of papers ..... 43 1.4 A Quantitative Knife-Edge Test (AQuaKET) 44 1.4.1 Previous works 44 1.4.2 Goals of AQuaKET 45 1.4.3 Principle of AQuaKET 46 1.5 Description of following chapters ................................................. 49 2. Equipment .................................................................................................... 51 2.1 Light source and accessories 54 2.1.1 Accuracy estimation on intensity variation .................. 54 2.1.2 Halogen lamp 57 2.1.3 He-Ne laser 58 2.2 Two knife-edges and supports ..................................................... 63 2.2.1 Set-up errors of the stages ................................................ 63 2.2.2 Micropositioner ............................................................... 68 2.3 CCD camera and frame grabber 69 2.4 Parallax .................................................................... 71 3. Data Acquisition ........................................................................................... 76 3.1 Mirror image size 78 3.2 Alignment 80 3.2.1 Multi-axes measurement ........................................... 81 3.2.2 Multi-areas measurement ........................................... 91 3.2.3 Accuracy and diffraction effect ............................... 97 3.3 Mirror image capture 99 3.3.1 Knife movements 99 3.3.2 Binning and data size 100 3.3.3 Step size 103 3.3.4 Saving data and measuring time ............................... 104 4. Data Processing ............................................................................................ 107 4.1 Finding knife position 109 4.1.1 Intensity subtraction method .......................................... 110 4.1.2 Finding peak step ........................................................ 115 4.1.3 Intensity difference area .................................................. 118 4.1.4 Blade angle correction 119 4.2 Direct slope calculation method .................................................... 121 4.3 Local focus sensing method .......................................................... 125 4.3.1 Local focus calculation 125 4.3.2 Slope calculation 127 4.3.3 Accuracy estimation 131 4.4 Height calculation .............................................................................. 132 4.4.1 Height calculation method 133 4.4.2 Numerical integration methods 134 4.4.3 Height error calculation 137 4.5 Zemike polynomials .......................................................................... 139 4.5.1 Zemike polynomials in Cartesian coordinates ................. 139 4.5.2 Zemike polynomials fitting ............................................... 140 4.5.3 Derivation of Seidel coefficients ...................................... 143 5. Refined Simplex Method ............................................................................... 145 5.1 General features of the simplex method 146 5.1.1 History 146 5.1.2 Basic idea of minimization 147 5.1.3 Principle of the simplex method .................................. 147 5.1.4 Advantages and disadvantages 153 5.1.5 Test mn of the simplex method .................................. 154 5.2 Initial condition 155 5.2.1 Basic idea 156 5.2.2 Test results 157 5.3 Shrinkage 162 6. Results and Discussion .................................................................................. 164 6.1 The big mirror test ............................................................................. 165 6.1.1 AQuaKET result 165 6.1.2 Scatter-plate interferometry 175 6.1.3 Test result by scatter-plate interferometer ..................... 177 6.1.4 Discussions on the test results 179 6.2 The small mirror test ......................................................................... 180 6.2.1 AQuaKET result 181 6.2.2 Aspherics test 188 6.3 The metal mirror test ..................................................................... 197 6.3.1 AQuaKET result 198 6.3.2 Test result of scatter-plate interferometry .................. 201 6.4 Discussion ...................................................................................... 202 6.4.1 Test limit on asphericity .................................................. 202 6.4.2 Environmental effects ..................................................... 204 6.4.3 User-friendly software .................................................... 207 6.4.3 Testing time .................................................................... 209 7. Conclusions ................................................................................................