本文為四百萬畫素超大廣角鏡頭設計由七片玻璃組成，鏡頭焦距為2.212 mm，鏡頭長度22.66 mm，F/#為2.2，最大半視角為80，在環境溫度-20C至60C對熱的分析與校正。
由於溫度變化不只會改變玻璃折射率，也會因鏡片與鏡片間熱脹冷縮，使鏡片曲率半徑、鏡片厚度、空氣間隙以及鏡面非球面係數及鏡筒也會有所改變。所以我們必須考量鏡片折射率的溫度係數(dn/dT)、鏡片膨脹係數(α)與鏡筒材質的膨脹係數(β)。
隨著環境溫度的變化，鏡片參數值也會改變，在設計消熱差的光學系統中，其有效焦距也改變，即系統總屈光度會有所變化。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，而達到消熱差設計，本文在消熱差設計過程中，是選用不同鏡筒材料的組合來達到消熱差的效果即利用此原理。
在環境溫度-20C至60C間的超大廣角鏡頭之MTF(180 lp/mm)可達到0.451以上；相對照度達78.06 %以上；短波長(F-line)至長波長(C-line) 橫向色差最大值為1.482 m，短波長(F-line)至參考波長(d-line) 橫向色差最大值為0.848 m；F-theta畸變最大值在0.78 %；而超大廣角鏡頭設計加公差之MTF(180 lp/mm)最小值為0.210。

The study is about the design of ultra-wide lens, which has 4 Mega pixel, and compose of seven glass, the focal length of the lens is 2.212 mm, the total length is 22.66 mm, F/# is 2.2, the maximum of half field-of-view is 80 degree. The purpose of the study is to discuss about thermal analysis and correction of the ultra-wide lens when the ambient temperature range from -20C to 60C.
The ambient temperature change not only making the refractive index of optical element change, but also making the radius, thickness of optical element, the space of air, the aspheric coefficient of surface and the mount are change. We must consider the temperature coefficient of the refractive index (dn/dT), the thermal expansion coefficient of the lens (α) and the thermal expansion coefficient of mount (β).
With the ambient temperature change, the optical parameter values of optical element are change. In addition, the optical construction change affects the location of the focus. So we design athermal optical system, we make the change in optical power which due to a temperature change (d/dT) is zero. The d/dT relate to the temperature coefficient (dn/dT) and the thermal expansion coefficient of the lens (α). If d/dT cannot be eliminate, using the thermal expansion coefficient of mount (β) compensate to achieve athermal design. In this study, we choose different mount material to athermalized.
In the ambient temperature range from -20C to 60C, the MTF (180 lp/mm) of the ultra-wide lens are larger than 0.451. The relative illumination can achieve 78.06 %. The maximum of lateral color from short wavelength (F-line) to long wavelength (C-line) is 1.482 m. The maximum of lateral color from short wavelength (F-line) to reference wavelength (d-line) is 0.848 m. The maximum of F-theta distortion is 0.78 %. And the minimum of MTF (180 lp/mm) of tolerance analysis is 0.210.

1. T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20, 156-160 (1981).
2. R. W. Wood, “Refraction of Light,” in Handbook of PhysicalOptics (Optical Society of America, Washington, DC, 1911).
3. R. Hill, “A Lens for Whole Sky Photography,” in Proceedings of the Optical Convention , (London, 1926) , pp.878-883.
4. 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.
5. W. Feng, B. Zhang, J. Röning, Z. Cao, X. Zong, “An Embedded Omnidirectional Vision Navigator for Automatic Guided Vehicles,” Proc. SPIE 7878 (2011).
6. Z. Huang, J. Bai and X. Hou, “A multi-spectrum fish-eye lens for rice canopy detecting,” Proc. SPIE 7849, 78491Z (2010).
7. 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).
8. D. S. Grey, “Athermalization of Optical Systems,” J. Opt. Soc. Am, 38, 542-546 (1948).
9. 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).
10. M. H. Horman, “Temperature analysis from multispectral infrared data,” Appl. Opt. 15(9), 2099–2104 (1976).
11. T. H. Jamieson, “Ultrawide waveband optics,” Opt. Eng. 23(2), 111–116 (1984).
12. M. Roberts and P. J. Rogers, “Wide waveband infrared optics,” Proc. SPIE 1013, 84–91 (1988).
13. Y. Tamagawa and T. Tajime, “Dual-band optical systems with a projective athermal chart: design,” Appl. Opt. 36(1), 297–301 (1997).
14. J. L. Rayces, L. Lebich, “Thermal compensation of infrared achromatic objectives with three optical materials,” Proc. SPIE 1354, 752-759 (1990).
15. I. Friedman, “Thermo-optical analysis of two long-focal length aerial reconnaissance lenses,” Opt. Eng. 20, 161-165 (1981).
16. W. Shi, M. E. Couture, “Long wave infrared zoom projector thermal analysis and compensation,” Opt. Eng. 39, 2705-2714 (2000).
17. M. Bayar, Ő. F. Farsakoğlu, “Mechanically active athermalization of a forward looking infrared system,” Infrared Physics & Technology 43, 91-99 (2002).
18. 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).
19. D. W. Anderson, “M1A2 tank commander’s independent thermal viewer optics: optics design perspective,” Proc. SPIE 1970, 128–138 (1993).
20. M. Norland, A. Rodland, A. Ingulstad and K. Kråkenes, “Design of high performance IR sensor,” Proc. SPIE 2269, 462–471 (1994).
21. A. Goldberg, T. Fischer, and S. Kennerly, “Dual band QWIP MWIR/LWIR focal plane array test results,” Proc. SPIE 4028, 276–287 (2000).
22. R. Simmons, P. A. Manning, and T. Chamberlain, “The design of passively athermalised narrow and wide field of view infrared objectives for OBSERVER unmanned air vehicle,” Proc. SPIE 5612, 236–248 (2004).
23. Gao Ming, Chen Yang, Liu Jun, Lv Hong, “Design of dual-band shared-aperture Co-zoom optical system,” Infrared Physics & Technology 64, 40-46 (2014).
24. C. W. Kuo, “Achromatic triplet and athermalized lens assembly for both midwave and longwave infrared spectra,” Opt. Eng. 53, 021102 (2014).
25. Y. Tamagawa, S. Wakabayashi, T. Tajime, and T. Hashimoto, “Multilens system design with an athermal chart,” Appl. Opt. 33, 8009-8013 (1994).
26. Y. Tamagawa, T. Tajime, “Expansion of an athermal chart into a multilens system with thick lenses spaced apart,” Opt. Eng. 35, 3001-3006 (1996).
27. 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).
28. R. C. Simmons and P. A. Blaine, ‘‘Stability of aberrations with temperature in fast thermal imaging zoom telescopes,’’ Proc. SPIE 916, 19–26 (1988).
29. 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).
30. G. P. Behrmann and John P. Bowen, “Influence of temperature on diffractive lens performance,” Appl. Opt. 32, 2483-2489 (1993).
31. C. Londoňo, W. T. Plummer, P. P. Clark, “Athermalization of a single-component lens with diffractive optics,” Appl. Opt. 32(13), 2295-2302 (1993).
32. R. M. Hudyma, “Athermal MWIR Objectives,” Proc. SPIE 2540, 229-235 (1995).
33. V. Povey, “Athermalisation technique in infrared systems,” Proc. SPIE, 655, 142–153 (1986).
34. 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).
35. 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).
36. 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).
37. O. V. Ponin and A. A. Sharov, “Apochromatic thermally nonmisadjustable objectives for wide-range multispectral space imaging,” J. Opt. Technol. 80, 230-232 (2013).
38. 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).
39. Schott, Optical Glass Catalogue Excel (Schott Inc., Germany, June, 2012).
40. P. J. Rogers, “Athermalized FLIR optics,” Proc. SPIE 1354, 742-751 (1990).
41. Schott, “TIE-29: Refractive index and dispersion,” in Proc. Schott Technical information (Schott Inc., Germany, 2015).
42. Schott, “TIE-19: Temperature coefficient of the refractive index,” in Proc. Schott Technical information (Schott Inc., Germany, July 2008).
43. Y. Bai, T. W. Xing, W. M. Lin and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1),181-185 (2012).
44. S. Thibault, J. Gauvin, M. Doucet and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962, 596211 (2005).
45. 陳筠涵，「行車紀錄器超廣角鏡頭設計」，國立中央大學，碩士論文，民國103年。