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With the advantages of simple structure, low-cost, large field of view, and high image quality, the transmission optical system is widely used in detection system, microscope, telescope, etc. However, the research on the illumination distribution law in the focal plane of transmission optical system is rarely reported. In this paper, this issue is studied. During the study on the first-order scattered light distribution law in the focal plane of the transmission optical system, the limitations of the two-parameter Harvey bi-directional scatter distribution function (BSDF) scattering theory are found, namely in the condition of small scattering angle, the two-parameter Harvey BSDF theory cannot accurately describe the scattering properties of the optical surface material. So the scattering model of the transmission optical system under small scattering angle is established by introducing parameter l, and the accuracy of the new theoretical model is verified experimentally. This model complements the two-parameter Harvey BSDF scattering model and broadens the application scope of the Harvey BSDF scattering model so that it can better explain the imaging law of scattered light spot in the focal plane of transmission optical system. At a small scattering angle, the conclusions can be drawn from the new theoretical model as follows. 1) The irradiance of the final image plane increases linearly with the increase of the incident optical power. 2) In the transmission optical system, the contribution of each optical surface with the same scattering properties to scattered spot irradiance in the final image plane can be expressed by a Gaussian function. 3) The irradiance of scattered spot in the final image plane can be expressed as the superposition of n Gaussian functions, where n is the number of optical surfaces with different scattering properties in the transmission optical system.
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Keywords:
- Harvey BSDF scattering theory /
- transmission optical system /
- focal plane spot first-order surface scattering /
- Gaussian distribution
[1] Jiang Y S, Nie M Y, Zhang C H, Xin C W, Hua H Q 2015 Acta Phys. Sin. 64 024101 (in Chinese)[江月松, 聂梦瑶, 张崇辉, 辛灿伟, 华厚强 2015 64 024101]
[2] Nicodemus F E, Richmond J C, Hsia J J, Ginsberg I W, Limperis T 1977 Geometrical Considerations and Nomenclature for Reflectance (Washinton, D.C.:National Bureau of Standards) pp7-8
[3] Dereniak E L, Brod L G, Hubbs J E 1982 Appl. Opt. 21 4421
[4] Hu D J, Zhang Z Y, Du J L 2015 Chin. Phys. B 24 104202
[5] He Y, Wu J 1997 Acta Opt. Sin. 17 1202 (in Chinese)[何毅, 吴健 1997 光学学报 17 1202]
[6] Liu M, Cheng C F, Ren X R 2015 Chin. Phys. B 24 094202
[7] Fan D 2013 Acta Opt. Sin. 33 267 (in Chinese)[范镝 2013 光学学报 33 267]
[8] Zhang J B, Ding L, Wang Y P, Zhang L, Wu J L, Zheng H Y, Fang L 2016 Chin. Phys. B 25 034201
[9] Huang H L, Chen Z Y, Sun C Z, Liu J L, Pu J X 2015 Chin. Phys. Lett. 32 104202
[10] Harvey J E 1976 Ph. D. Dissertation (Arizona:University of Arizona)
[11] Stover J C 1990 Optical Scattering:Measurement and Analysis (New York:McGraw-Hill) pp23-44
[12] 12 Bennett H E, Porteus J O 1961 JOSA 51 123
[13] 13 Harvey J E, Vernold C L, Krywonos A, Thompson P L 1999 Appl. Opt. 38 6469
[14] 14 Harvey J E, Goshy J J, Pfisterer R N 2014 Proc. SPIE 9205 01
[15] 15 Peterson G L 2004 Proc. SPIE 5178 184
[16] 16 Sun K, Jiang H M, Cheng X A 2011 Opt. Precision Engineer. 19 493 (in Chinese)[孙可, 江厚满, 程湘爱 2011 光学精密工程 19 493]
[17] Veach E 1997 Ph. D. Dissertation (California:Stanford University)
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[1] Jiang Y S, Nie M Y, Zhang C H, Xin C W, Hua H Q 2015 Acta Phys. Sin. 64 024101 (in Chinese)[江月松, 聂梦瑶, 张崇辉, 辛灿伟, 华厚强 2015 64 024101]
[2] Nicodemus F E, Richmond J C, Hsia J J, Ginsberg I W, Limperis T 1977 Geometrical Considerations and Nomenclature for Reflectance (Washinton, D.C.:National Bureau of Standards) pp7-8
[3] Dereniak E L, Brod L G, Hubbs J E 1982 Appl. Opt. 21 4421
[4] Hu D J, Zhang Z Y, Du J L 2015 Chin. Phys. B 24 104202
[5] He Y, Wu J 1997 Acta Opt. Sin. 17 1202 (in Chinese)[何毅, 吴健 1997 光学学报 17 1202]
[6] Liu M, Cheng C F, Ren X R 2015 Chin. Phys. B 24 094202
[7] Fan D 2013 Acta Opt. Sin. 33 267 (in Chinese)[范镝 2013 光学学报 33 267]
[8] Zhang J B, Ding L, Wang Y P, Zhang L, Wu J L, Zheng H Y, Fang L 2016 Chin. Phys. B 25 034201
[9] Huang H L, Chen Z Y, Sun C Z, Liu J L, Pu J X 2015 Chin. Phys. Lett. 32 104202
[10] Harvey J E 1976 Ph. D. Dissertation (Arizona:University of Arizona)
[11] Stover J C 1990 Optical Scattering:Measurement and Analysis (New York:McGraw-Hill) pp23-44
[12] 12 Bennett H E, Porteus J O 1961 JOSA 51 123
[13] 13 Harvey J E, Vernold C L, Krywonos A, Thompson P L 1999 Appl. Opt. 38 6469
[14] 14 Harvey J E, Goshy J J, Pfisterer R N 2014 Proc. SPIE 9205 01
[15] 15 Peterson G L 2004 Proc. SPIE 5178 184
[16] 16 Sun K, Jiang H M, Cheng X A 2011 Opt. Precision Engineer. 19 493 (in Chinese)[孙可, 江厚满, 程湘爱 2011 光学精密工程 19 493]
[17] Veach E 1997 Ph. D. Dissertation (California:Stanford University)
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