本文為三鏡頭光學設計，作為下一世代自動駕駛系統影像識別使用，主要目的是讓自動駕駛系統在-30C至70C環境溫度下，影像皆可以清楚的辨識，增加自動駕駛系統的穩定與安全性。三鏡頭的特性如下：近距離鏡頭設計之物距範圍小於30m，焦距為3.6491 mm，F/#為2.2，最大半視角為75，中距離鏡頭設計之物距範圍30m - 70m，焦距為10.5081 mm，F/#為2.2，最大半視角為25，長距離鏡頭設計之物距範圍70-150m，焦距為18.287 mm，F/#為2.2，最大半視角為15。此三鏡頭設計都考慮環境溫度-30C至70C對熱校正。
隨著環境溫度的變化，鏡片的參數值會隨之改變，在消熱差的光學系統設計中，其有效焦距同步改變，即系統總屈光度會隨溫度變化而有所變化。在消熱差光學系統須使總屈光度與溫度之變化(d/dT)為零，如果d/dT無法消除則需使用鏡筒材質的膨脹係數(β)來補償，進而達到消熱差設計，本文在消熱差設計以優化不同鏡片與鏡筒材料的來達到消熱差的效果。
最終設計在環境溫度-30C至70C間的三焦段鏡頭之MTF(110 lp/mm)可達到0.6以上並並且切向與徑向的差異量小於0.1；相對照度達到86 %以上；短波長(F’-line)至長波長(C’-line) 橫向色差最大值為小於2.25um，畸變值小於2 %，材料優化後消熱差條件小於1.9110-6。

The thesis is about the design of three different focal lenses for next generation of autopilot. The purpose is that let the autopilot could be safe and stabilized to identify environment within temperature range from -30C to 70C. The three lens specifications are as follows: Lens with short focal length - Object distance is less than 30 meters, Focal length is 3.6491 mm, F/# is 2.2, and the maximum of half-FOV(field-of-view) is 75 degree; Lens with moderate focal length- Object distance is between 30 and 70 meters, Focal length is 10.5081 mm
,F/# is 2.2,and the maximum of half-FOV(field-of-view) is 25 degree; Lens with long focal length - Object distance is between 70 and 150 meters, Focal length is 18.287 mm, F/# is 2.2,and the maximum of half-FOV(field-of-view) is 15 degree.
The advantage of the three lenses is introducing thermal compensation to optical design at temperature between -30C and 70C. It means that little focal shifts at different temperature between -30C and 70C.
Temperature variation induces refractive index change of glass. Due to thermal expansion that lens radius, thickness of optical element, air gap, and the shape of mechanics are changed. Applying the thermal coefficient of the refractive index (dn/dT) of lens, thermal expansion coefficient of the lens (α) and the thermal expansion coefficient of mount (β) to optical simulation is necessary.
Lens parameters will vary with environmental temperature. Athermal design will let effective length change coherent with thermal variation. It means that diopter and thermal variation will change simultaneously. In Athermal system, the ration between diopter and thermal variation (d/dT) should be zero. If d/dT could not be eliminated, the thermal expansion coefficient (β) of the barrel will be used for athermal compensation. The thesis is focused on eliminating athermal effect by adjusting lens diopter and material of the barrel.
Conclusion that triple-focus lens between -30C and 70C has benefits as below: MTF @110lp/mm >0.6 and the gap between tangential and radial is small than 0.1, Relative illumination>86%, Later color between short wavelength (F’-line) and long one (C’-line)<2.25μm, Optical distortion<2%, athermalization is small than 1.9110-6.

1. T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20, 156-160 (1981).
2. https://www.nhtsa.gov/technology-innovation/automated-vehicles-safety
3. IHS, ADAS-Current and Future Perspectives. IHS Automotive Seminar , Frankurt, Germany. (2015,June).
4. SAE INTERNATIONAL, ADAS/CONNECTED CAR. Warrendale, PA, U.S.A. (2018,Dec).
5. Mobile vision technology Ltd, Forward-facing multi-image a vechicle . U.S.PATENT Pub. No. US2015/0103159 A1. (2015).
6. Google Inc, Cross-validating sensors of an autonomous vehcle, U.S. PATENT No. US9221396 B1. (2015).
7. Maria S. Greco, Automotive Radar. IEEE Radar Conference , Atlanta, U.S.A. (2012,May).
8. R. W. Wood, “Refraction of Light,” in Handbook of PhysicalOptics (Optical Society of America, Washington, DC, 1911).
9. R. Hill, “A Lens for Whole Sky Photography,” in Proceedings of the Optical Convention , (London, 1926) , pp.878-883.
10. J. Y. Zheng and S. G. Li, “Employing a fish-eye for scene tunnel Scanning,” in Asian Conference on Computer Vision,( Hyderabad, 2006), pp. 509.
11. W. S. Sun, C. L. Tien, Y. H. Chen, P. Y. Chu, “Ultra-wide angle lens design with relative illumination analysis,” J. Eur. Opt. Soc. –Rapid 11, 16001 (2016).
12. D. S. Grey, “Athermalization of Optical Systems,” J. Opt. Soc. Am, 38, 542-546 (1948).
13. M. J. Duggin, “Discrimination of targets from background of similar temperature, using two-channel data in the 3.5-4.1-m and 11–12-m regions,” Appl. Opt. 25(7), 1186–1195 (1986).
14. M. H. Horman, “Temperature analysis from multispectral infrared data,” Appl. Opt. 15(9), 2099–2104 (1976).
15. T. H. Jamieson, “Ultrawide waveband optics,” Opt. Eng. 23(2), 111–116 (1984).
16. M. Roberts and P. J. Rogers, “Wide waveband infrared optics,” Proc. SPIE 1013, 84–91 (1988).
17. Y. Tamagawa and T. Tajime, “Dual-band optical systems with a projective athermal chart: design,” Appl. Opt. 36(1), 297–301 (1997).
18. J. L. Rayces, L. Lebich, “Thermal compensation of infrared achromatic objectives with three optical materials,” Proc. SPIE 1354, 752-759 (1990).
19. I. Friedman, “Thermo-optical analysis of two long-focal length aerial reconnaissance lenses,” Opt. Eng. 20, 161-165 (1981).
20. W. Shi, M. E. Couture, “Long wave infrared zoom projector thermal analysis and compensation,” Opt. Eng. 39, 2705-2714 (2000).
21. M. Bayar, Ő. F. Farsakoğlu, “Mechanically active athermalization of a forward looking infrared system,” Infrared Physics & Technology 43, 91-99 (2002).
22. C. W. Kuo, C. L. Lin, and C. Y. Han, “Dual field-of-view midwave infrared optical design and athermalization analysis,” Appl. Opt. 49(19), 3691–3700 (2010).
23. Y. Tamagawa, S. Wakabayashi, T. Tajime, and T. Hashimoto, “Multilens system design with an athermal chart,” Appl. Opt. 33, 8009-8013 (1994).
24. Y. Tamagawa, T. Tajime, “Expansion of an athermal chart into a multilens system with thick lenses spaced apart,” Opt. Eng. 35, 3001-3006 (1996).
25. Y. J. Kim, Y. S. Kim, and S. C. Park, “Simple graphical selection of optical materials for an athermal and achromatic design using equivalent Abbe number and thermal glass constant,” Journal of the optical society of Korea 19, 182-187 (2015).
26. R. C. Simmons and P. A. Blaine, ‘‘Stability of aberrations with temperature in fast thermal imaging zoom telescopes,’’ Proc. SPIE 916, 19–26 (1988).
27. C. W. Kuo, J. M. Miao, and C. H. Tai, “Midwave infrared optical zooming design and kinoform degrading evaluation methods,” Appl. Opt. 50(18), 3043–3049 (2011).
28. G. P. Behrmann and John P. Bowen, “Influence of temperature on diffractive lens performance,” Appl. Opt. 32, 2483-2489 (1993).
29. C. Londoňo, W. T. Plummer, P. P. Clark, “Athermalization of a single-component lens with diffractive optics,” Appl. Opt. 32(13), 2295-2302 (1993).
30. R. M. Hudyma, “Athermal MWIR Objectives,” Proc. SPIE 2540, 229-235 (1995).
31. V. Povey, “Athermalisation technique in infrared systems,” Proc. SPIE, 655, 142–153 (1986).
32. R. Q. Wu, K. Huang, H. Yang, J. Wang, Y. Liu, “Analysis of athermalizing performance of thermal infrared optical system with Cassegrain antenna,” Optik 121, 1904-1907 (2010).
33. H. S. Yang et al., “Three-shell-based lens barrel for the effective athermalization of an IR optical system,” Appl. Opt. 50(33), 6206-6213 (2011).
34. A. H. Wang, Q. H. Wang, X. F. Li and D. H. Li, “Combined lenticular lens for autostereoscopic three dimensional display,” Optik 123, 827-830 (2012).
35. O. V. Ponin and A. A. Sharov, “Apochromatic thermally nonmisadjustable objectives for wide-range multispectral space imaging,” J. Opt. Technol. 80, 230-232 (2013).
36. B. N. Walker, R. H. James, D. Calogero, and I. K. Iiev, “Impact of environmental temperature on optical power properties of intraocular lenses,” Appl. Opt. 53, 453-457 (2014).
37. Schott, Optical Glass Catalogue Excel (Schott Inc., Germany, June, 2012).
38. P. J. Rogers, “Athermalized FLIR optics,” Proc. SPIE 1354, 742-751 (1990).
39. Schott, “TIE-29: Refractive index and dispersion,” in Proc. Schott Technical information (Schott Inc., Germany, 2015).
40. Schott, “TIE-19: Temperature coefficient of the refractive index,” in Proc. Schott Technical information (Schott Inc., Germany, July 2008).
41. J.M. Palmer, B.G. Grant.The Art of Radiometry (SPIE press Bellingham WA, USA, 2010).
42. Grant R. Fowles, Introduction to Modern optics. Second ed, New York.Holt Rinehart and Winston Inc.
43. Schott, “TIE-35: Transmittance of optical glass ,” in Proc. Schott Technical information (Schott Inc., Germany, Oct 2005).
44. Automotive Image Sensor
https://www.sony-semicon.co.jp/products_en/IS/sensor4/index.html
45. SUMITOMO E6007LHF
https://www.sumitomo-chem.co.jp/sep/english/products/lcp/
46. 高鳳遙，「超大廣角鏡頭在溫度-20C至60C對熱的分析與校正之鏡頭設計」，國立中央大學，碩士論文，民國105年。
47. 徐英舜，「汽車超大廣角於溫度-30C至70C消熱差與高相對照度之鏡頭設計」，國立中央大學，碩士論文，民國106年。