簡易檢索 / 詳目顯示
| 研究生： |
薛鈞哲 Hsueh, Chun-Che |
|---|---|
| 論文名稱： |
光程對光學系統變數之梯度矩陣的建模 The Determination of Gradient Matrix of Optical Path Length With Respect to System Variables of An Optical System |
| 指導教授： |
林昌進
Lin, Psang-Dain |
| 學位類別： |
博士 Doctor |
| 系所名稱： |
工學院 - 機械工程學系 Department of Mechanical Engineering |
| 論文出版年： | 2011 |
| 畢業學年度： | 99 |
| 語文別： | 英文 |
| 論文頁數： | 111 |
| 中文關鍵詞： | 光程 、梯度矩陣 、公差分析 、公差分配 |
| 外文關鍵詞： | optical path length, gradient matrix, tolerance analysis, tolerance allocation |
| 相關次數： | 點閱：79 下載：2 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
光程差的重要性在於其可作為評估光學系統性能的評價標準。因此，本研究乃利用歪斜光線追蹤法，致力於發展光學系統全參數變化對光程影響的梯度矩陣。因為探討光學系統全參數變化對光程的影響時，目前的光學軟體多利用有限差分法，其計算概念是分別追蹤參數未變化前與參數有微變後的兩種光程，再使用有限差分法計算光程梯度。本研究的光程梯度矩陣法因使用微分概念避開有限差分法因分母微變量極小的問題，而且本研究在計算效率上僅需追蹤一次光線，優於目前有限差分法的多次光線追蹤。
在完成光學系統設計後進入加工製造之前，光學設計者必須考慮系統公差問題，並給予參數合理的公差範圍。因此公差分析與公差分配問題是光學設計者所關心的重要議題。本研究進一步將光程梯度矩陣法應用在公差分析與公差分配，前者可計算元件之製造誤差與組裝誤差對光學系統的光程影響，後者可對光學系統全參數設定公差允許範圍。模擬結果顯示，本理論因利用光程梯度法，在公差分析與公差分配的計算上，比有限差分法更具系統化與更有計算效率。
Determining the optical path length (OPL) difference is of fundamental importance because it provides a convenient means of estimating the performance of optical systems. Therefore, this study presents a novel mathematical method for determining the OPL gradient matrix relative to all the optical system variables such that the effects of variable changes can be evaluated in a single pass. In general, the effects of variable changes on the OPL of an optical system are evaluated by utilizing a raytracing approach to determine the OPL before and after the variable change, respectively, and then applying a FD approximation method to estimate the OPL gradient with respect to each individual variable. By contrast, the developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations.
An optical system design is not truly complete until the designer has defined a set of tolerances. Therefore the problems of tolerance analysis and tolerance allocation have been a matter of great concern to engineers. This study then utilizes the developed mathematical descriptions to both estimate the effects of manufacturing defects and alignment errors on the change of OPL and exit ray, respectively, and establish the permissible tolerance limits on each of the independent variables within the system based on the worst case method. Compared with existing methods, the major advantage of the proposed tolerance design method is that it is based on an optical geometry gradient matrix and therefore provides means of obtaining the allowable tolerance limits of all the independent variables in the optical system simultaneously. The results show that the developed approach is apparently more systematic, efficient, and accurate.
References
1. T. Suzuki and I. Uwoki, “Differential Method for Adjusting the Wave-Front Aberrations of a Lens System,” J. Opt. Soc. Am. 49, 402-404 (1959).
2. A. Sharma, “Computing Optical Path Length in Gradient-Index Media a Fast and Accurate Method,” Appl. Opt. 24, 4367-4370 (1985).
3. B. D. Stone and G. W. Forbes, "Differential ray tracing in inhomogeneos media," J. Opt. Soc. Am. A, Vol. 14, 2824-2836 (1997).
4. P. D. Lin and C. Y. Tsai, “General method for determining the first order gradients of skew rays of optical systems with non-coplanar optical axes,” Appl. Phys. B 91, 621-628 (2008).
5. M. Avendano-Alejo and M. Rosete-Aguilar, “Optical path difference in a plane-parallel uniaxial plate,” J. Opt. Soc. Am. A 23, 926-932 (2006).
6. S. Purnet, B. Journet and G. Fortunato, “Exact calculation of the optical path difference and description of a new birefringent interferometer,” Opt. Eng., 38, 983-990 (1999).
7. J. Meiron, “The Use of Merit Functions on Wavefront Aberrations in Automatic Lens Design,” Appl. Opt. 7, 667-672 (1968).
8. N. Bokor and Z. Papp, “Optimization of kinoform lenses with the Monte Carlo method,” Appl. Opt. 37, 3685-3688 (1998).
9. G. Klemens and Y. Fainman, “Optimization-based calculation of optical nonlinear processes in a micro-resonator,” Opt. Exp. 14, 1494-1505 (1968).
10. S. J. Dobson and A. Cox, “Fast image-quality-based optimization of optical systems,” Appl. Opt. 37, 8008-8011 (1998).
11. C. J. Progler and D. M. Byrne, “Merit Functions for Lithographic Lens Design,” J. Vac. Sci. Technol. B 14, 3714-3718 (1996).
12. A. Yabe, “Optimal selection of aspherical surfaces in optical design,” Opt. Exp. 13, 7233-7242 (2005).
13. S. Barbero and S. Marcos, “Analytic tools for customized design of monofocal intraocular lenses,” Opt. Exp. 15, 8576-8591 (2007).
14. C. C. Hsueh and P. D. Lin, “Computationally-efficient gradient matrix of optical path length in axisymmetric optical systems,” Appl. Opt. 48, 893-902 (2009).
15. http://en.wikipedia.org/wiki/Single-lens_reflex_camera (June, 2011)
16. http://en.wikipedia.org/wiki/Binoculars (June, 2011)
17. http://en.wikipedia.org/wiki/Monocular (June, 2011)
18. E. J. Galvez and C. D. Holmes, “Geometric phase of optical rotators,” J. Opt. Soc. Am A 16, 1981-1985 (1999).
19. W. Mao, “Adjustment of reflecting prisms,” Opt. Eng. 34, 79-82 (1995).
20. I. Moreno, “Jones matrix for image-rotation prisms,” Appl. Opt. 43, 3373-3381 (2004).
21. L. Agrawal, A. Bhardwaj, S. Pal, and A. Kumar, “Jones matrix formulation of a Porro prism laser resonator with waveplates: theoretical and experimental analysis,” Appl. Phys. B 89, 349-357 (2007).
22. F. J. Duarte, “Beam transmission characteristics of a collinear polarization rotator,” Appl. Opt. 31, 3377-3378 (1992).
23. R. H. Ginsberg, “Image rotation,” Appl. Opt. 33, 8105-8108 (1994).
24. R. K. Appel and C. D. Dyer, “Low-loss ultrabroadband 90 degrees optical rotator with collinear input and output beams,” Appl. Opt. 41, 1888-1893 (2002).
25. L. Agrawal, A. Bhardwaj, S. Pal, A. Kumar, Appl. Phys. B 89, 349 (2007)
26. T. Hansel, J. , C. Falldorf, C. Von Kopylow, W. , R. Grunwald, G. Steinmeyer, U. Griebner, Appl. Phys. B 89, 513 (2007)
27. I. Moreno, G. Paez, and M. Strojnik, " Dove prism with increased throughput for implementation in a rotational-shearing interferometer," Appl. Opt. 42, 4515-4520 (2003)
28. E. Gutierrez-Herrera, M. Strojnik, " Interferometric tolerance determination for a Dove prism using exact ray trace," Opt. Commun. 281, 897-905 (2008)
29. D. A. Flickinger, R. N. Coffee, G. N. Gibson, and T. C. Weinacht, “Bichromatic, phase compensating interferometer based on prism pair compressors,” Appl. Opt. 45, 6187-6191 (2006).
30. G. Garcia-Torales, G. Paez, and M. Strojnik, “Simulations and experimental results with a vectorial shearing interferometer,” Opt. Eng. 40, 767-773 (2001).
31. Donald L. Sullivan, "Alignment of Rotational Prisms," Appl. Opt. 11, 2028-2032 (1972).
32. A. N. de Oliveira, S. P. Walborn and C H Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B: Quantum Semiclass. Opt. 7, 288–292 (2005).
33. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett. 88, 257901 (2002).
34. R. Zambrini and S. M. Barnett, “Quasi-Intrinsic Angular Momentum and the Measurement of Its Spectrum,”Phys. Rev. Lett. 96, 113901 (2006).
35. N. Gonzalez, G. Molina-Terriza, and J. P. Torres, “How a Dove prism transforms the orbital angular momentum of a light beam,” Opt. Exp. 14, 9093-9102 (2006).
36. S. K. Gupta and R. Hradaynath, “Angular tolerance on Dove prisms,” Appl. Opt. 22, 3146-3147 (1983).
37. Nur S. F. Ozkan, W. Lee Hendrick, Philippe J. Marchand, and Sadik C. Esener, “Misalignment tolerance analysis of free-space optical interconnects via statistical methods”, Appl. Opt. 41, 2686-2694 (2002).
38. M. Rimmer, “Analysis of Perturbed Lens Systems, ” Appl. Opt. 9, 533-537 (1970)
39. A. M. Ghodgaonkar and R.D. Tewari, “Measurement of apex angle of the prism using total internal reflection,” Opt. & Laser Tech. 36, 617-624 (2004).
40. J. F. Lee and C. Y. Leung, “Method of calculating the alignment tolerance of a Porro prism resonator,” Appl. Opt. 28, 3691-3697 (1989).
41. J. F. Lee and C. Y. Leung, “Beam pointing direction changes in a misaligned Porro prism resonator,” Appl. Opt. 27, 2701-2707 (1988).
42. J. F. Lee and C. Y. Leung, “Lateral displacement of the mode axis in a misaligned Porro prism resonator,” Appl. Opt. 28, 5278-5284 (1989).
43. E. Gutierrez, M. Strojnik, and G. Paez, “Tolerance determination for a Dove prism using exact ray trace,” Proc. SPIE 6307, pp. 63070K (2006).
44. P. D. Lin and C. Y. Tsai, “First-order gradients of skew rays of axis- symmetrical optical systems,” J. Opt. Soc. Am. A 24, 776-784 (2007).
45. C. C. Hsueh and P. D. Lin, “Gradient matrix of optical path length for evaluating the effects of variable changes in a prism,” Appl. Phys B 98, 471-479, 2010.
46. D. F. Feder, “Differentiation of ray-tracing equations with respect to construction parameters of rotationally symmetric optics, ” J. Opt. Soc. Am. 58, 1494-1505 (1968).
47. Lin Psang Dain and Te-Tan Liao, “Skew-Ray Tracing and Sensitivity Analysis of Geometrical Optics, ” Transactions of the ASME Journal of Manufacturing Science and Engineering 122, 338-349 (2000).
48. W. J. Smith, Modern Optical Engineering (3rd ed., Edmund Industrial Optics, Barrington, N.J., 2001).
49. E. Hecht, Optics (3rd edition, Addison Wesley Longman, Inc., New York, 1998).
50. M. LAIKIN, LENS DESIGN (Marcel Dekker, 1995), Chapter 5, page72.
51. F. A. Jenkins, H. E. White, Fundamentals of Optics (4rd ed., WcGraw-Hill, 1981).
52. M. Atsushi and S. Nobuo, “Design of a Four-element, Hollow-cube Corner Retroreflector for Satellities by Use of a Genetic Algorithm,” Appl. Opt. 37, 438-442 (1998).
53. N. Shojiro and K. Jun, “Retroreflector Using Gradient-index Rods,” Appl. Opt. 30, 815-822 (1991).
54. L. Z. James, “Cube Corner Retroreflector Test and Analysis,” Appl. Opt., 15, 445-452 (1976).
55. J. Y. Yen, C. S. Jeng and K. C. Fan, “Servo Design for 3D Laser Tracking Measurement System,” Transactions of the ASME Journal of Dynamic System, Measurement and Control 118, 476-481 (1996).
56. Pamphlet, on-Target Tracking, “Chesapeake Laser System Inc.,” Three and Five Axis Laser Tracking System, US-Patent 4, 714, 339, Dec. 22, 1987.
57. P. Haschberger, O. Mayer, V. Tank and H. Dietl, “Ray Tracing Through an Eccentrically Rotating Reflector Used for Path-length Alteration in a New Michelson Interferometer,” J. Opt. Soc. Am. 8, 1991-2000 (1991).
58. P. D. Lin and C. H. Lu, “Analysis and Design of Optical System by Use of Sensitivity Aanlysis of Skew Ray Tracing,” Appl. Opt. 43, 796-807 (2004).
59. Kim, Hoo-shik, “Image intensifier camera,” United States Patent 7164135 (2007).
60. http://lib.store.yahoo.net/lib/opticsplanet/trijicon-advanced-combat-optical-gunsights-catalog.pdf
61. C. C. Hsueh , P. D. Lin and Jose Sasian, “A worst case based methodology for the tolerance analysis and tolerance allocation of optical systems,” Appl. Opt. 98, 6179-6188 (2010).
62. E. T. Fortini, "Dimensioning for Interchangeable Manufacturing," Industrial Press, pp.48 (1967).
63. M. F. Spotts, " Dimensioning Stacked Assemblies," Machine Design, pp.60 (1978).
64. P. D. Lin and K. F. Ehmann, "Inverse Error Analysis for Multi-axis Machines," ASME Journal of Engineering for Industry 118, pp.88-94 (1996).
65. B. Benhabib, R. G. Fenton, and A. A. Goldenberg, " Computer-Aided Joint Error Analysis of Robots," IEEE Journal of Robotics and Automation RA-3, 317-322 (1987).
66. M. F. Spotts, "Allocation of Tolerances to Minimize Cost of Assembly," ASME J. Engng Ind, 95, 762-764 (1973).
67. K. W. Chase, and W. H. Greenwood, "Computer-Aided Tolerance Selection," CATS User guide. ADCATS Report No.86-2, Brigham Young University (1986).
68. F. H. Speckhart, "Calculation of Tolerance Based on a Minimum Cost Approach," ASME J. Enging. Ind , Vol.94, No.2,pp. 447-453 (1972).
69. M. P. Kothiyal and C. Delisle, “Shearing interferometer for phase shifting interferometry with polarization phase shifter,” Appl. Opt. 24, 4439-4442 (1985).
70. H. Kadono, N. Takai, and T. Asakura, “New common-path phase shifting interferometer using a polarization technique,” Appl. Opt. 26, 898-904 (1987).
71. H. Schreiber and J. Schwider, “Lateral shearing interferometer based on two Ronchi phase gratings in series,” Appl. Opt. 36, 5321-5324 (1997).
72. G. W. R. Leibbrandt, G. Harbers, and P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 35, 6151-6161 (1996).
73. D. W. Griffin, “Phase-shifting shearing interferometer,” Opt. Lett. 26, 140-141 (2001).
74. H. H. Lee, J. H. You, and S. H. Park, “Phase-shifting lateral shearing interferometer with two pairs of wedge plates,” Opt. Lett. 28, 2243-2245 (2003).
75. J. B. Song, Y. W. Lee, I. W. Lee, and Y. H. Lee, “Simple phase-shifting method in a wedge plate lateral-shearing interferometer,” Appl. Opt. 43, 3989-3992 (2004).
76. S. Chatterjee, “Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter,” Opt. Laser Technol. 37, 43-49 (2005).
77. R. Xu, H. Liu, Z. Luan and L. Liu , “A phase-shifting vectorial-shearing interferometer with wedge plate phase-shifter,” J. Opt. A: Pure Appl. Opt., 7, 617-623 (2005).
78. P. D. Lin and C. K. Sung, “Camera calibration based on Snell's law,” J. Dyn. Syst. Meas. Control-Trans. ASME 128, 548-557 (2006).
校內：2016-07-06公開校外：2016-07-06公開