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An absolute measuring principle and method of bidirectional reflection distribution function （BRDF） is presented. A spectral radiation meter with 3 nm spectral resolution and a three-dimensional rotating system with 001° accuracy are utilized to establish the automatic measuring platform. The spectral BRDF of typical space target’s surface materials （yellow and silver tinfoil） is measured in the range of 400—2500 nm. Measured results show that the scattering angle，which corresponds to the maximum value of BRDF curve，is generally in the specular reflection direction；the other BRDF values change slowly as scattering angle varies，declining from middle to both sides and approximately following the cosine distribution. A BRDF error analysis method is introduced by using the RMS error calculation，which provides a new way for the BRDF measurement system evaluation. The measurement error is 495%. With five-parameter model of BRDF and the simulated annealing （SA） algorithm，the optimum parameters of the model at each wavelength in the measured spectrum are retrieved at intervals of 1 nm. A comparison of the data calculated by the parametric model with the data measured originally verifies the feasibility and reliability of the modeling. The measuring and modeling results can provide reference data for space target detection and identification.
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Keywords:
- bidirectional reflection distribution function （BRDF） /
- absolute measurement /
- error analysis /
- parametric model
[1] ［1］Wu Z S，Dou Y H 2003 Acta Optica Sinica 23 1250 （in Chinese）［吴振森、窦玉红 2003 光学学报 23 1250］
[2] ［2］Zhang S Q，Shi Y L，Lu Y L 2009 Acta Phys. Sin. 58 2768 （in Chinese）［张拴勤、石云龙、卢言利 2009 58 2768］
[3] ［3］Wang A X，Zhang X J，Zhang H L，Feng J 2008 Laser & Infrared 38 519 （in Chinese）［王安祥、张晓军、张涵璐、冯健 2008 激光与红外 38 519］
[4] ［4］Li C，Wang Y M，Zhang Z M 2008 Spectroscopy and Spectral Analysis 28 865 （in Chinese）［李聪、王咏梅、张仲谋 2008 光谱学与光谱分析 28 865］
[5] ［5］Cheng J L，Shi Z，Li H Y 2008 Spectroscopy and Spectral Analysis 28 1007 （in Chinese）［程街亮、史舟、李洪义 2008 光谱学与光谱分析 28 1007］
[6] ［6］Peng Y J，Zhang S P，Wang Y H，Yang Y Q 2008 Chin. Phys. B 17 3505
[7] ［7］Qiao Y B，Da N，Chen D P，Qiu J R 2007 Acta Phys. Sin. 56 7023 （in Chinese）［乔延波、达宁、陈丹平、邱建荣 2007 56 7023］
[8] ［8］Ding J，Yang Q H，Tang Z F，Xu J，Su L B 2007 Acta Phys. Sin. 56 2207 （in Chinese）［丁君、杨秋红、唐在峰、徐军、苏良碧 2007 56 2207］
[9] ［9］Zhang B S，Liu W Q，Wei Q N，Wu Z S，Zhao J F 2006 Chin. J. Quant. Electron 23 533 （in Chinese）［张百顺、刘文清、魏庆农、吴振森、赵剑锋 2006 量子电子学报 23 533］
[10] ］Jia H，Li F T 2004 Acta Optica Sinica 24 230 （in Chinese）［贾辉、李福田 2004 光学学报 24 230］
[11] ］Wolff L B 1994 J. Opt. Soc. Am. A 11 2956
[12] ］Zhan Y L，Wang L 1990 Acta Phys. Sin. 39 4 （in Chinese）［战元龄、王立 1990 39 4］
[13] ］Cook R L，Torrance K E 1982 ACM Transactions on Graphics 1 7
[14] ］Nicodemus F E 1970 Applied Optics 9 1474
[15] ］Wei Q N，Liu J G，Jiang R X 1996 Acta Optica Sinica 16 1425 （in Chinese）［魏庆农、刘建国、江荣熙 1996 光学学报 16 1425］
[16] ］Zhang S Q，Shi Y L，Huang C G，Lian C C 2007 Acta Phys. Sin. 56 5508 （in Chinese）［张拴勤、石云龙、黄长庚、连长春 2007 56 5508］
[17] ］Qi C，Yang M H，Sun X G，Dai J M 2003 Chinese Journal of Lasers 30 146 （in Chinese）［齐超、杨茂华、孙晓刚、戴景民 2003 中国激光 30 146］
[18] ］Zhao Z Y，Dai J M，Li Y 2007 Infrared Technology 29 579 （in Chinese）［赵忠义、戴景民、李颖 2007 红外技术 29 579］
[19] ］Wu Z S，Xie D H，Xie P H，Wei Q N 2002 Acta Optica Sinica 22 897 （in Chinese）［吴振森、谢东辉、谢品华、魏庆农 2002 光学学报 22 897］
[20] ］Cao Y H，Wu Z S，Zhang H L，Wei Q N，Wang S M 2008 Acta Optica Sinica 28 792 （in Chinese）［曹运华、吴振森、张涵璐、魏庆农、汪世美 2008 光学学报 28 792］
[21] ］Vicente J D，Lanchares J，Hermida R 2003 Physics Letters A 317 415
[22] ］Li S Y，Du Z H，Wu M Y，Zhu J，Li S L 2001 Acta Phys. Sin. 50 1260 （in Chinese）［李树有、都志辉、吴梦月、朱静、李三立 2001 50 1260］
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[1] ［1］Wu Z S，Dou Y H 2003 Acta Optica Sinica 23 1250 （in Chinese）［吴振森、窦玉红 2003 光学学报 23 1250］
[2] ［2］Zhang S Q，Shi Y L，Lu Y L 2009 Acta Phys. Sin. 58 2768 （in Chinese）［张拴勤、石云龙、卢言利 2009 58 2768］
[3] ［3］Wang A X，Zhang X J，Zhang H L，Feng J 2008 Laser & Infrared 38 519 （in Chinese）［王安祥、张晓军、张涵璐、冯健 2008 激光与红外 38 519］
[4] ［4］Li C，Wang Y M，Zhang Z M 2008 Spectroscopy and Spectral Analysis 28 865 （in Chinese）［李聪、王咏梅、张仲谋 2008 光谱学与光谱分析 28 865］
[5] ［5］Cheng J L，Shi Z，Li H Y 2008 Spectroscopy and Spectral Analysis 28 1007 （in Chinese）［程街亮、史舟、李洪义 2008 光谱学与光谱分析 28 1007］
[6] ［6］Peng Y J，Zhang S P，Wang Y H，Yang Y Q 2008 Chin. Phys. B 17 3505
[7] ［7］Qiao Y B，Da N，Chen D P，Qiu J R 2007 Acta Phys. Sin. 56 7023 （in Chinese）［乔延波、达宁、陈丹平、邱建荣 2007 56 7023］
[8] ［8］Ding J，Yang Q H，Tang Z F，Xu J，Su L B 2007 Acta Phys. Sin. 56 2207 （in Chinese）［丁君、杨秋红、唐在峰、徐军、苏良碧 2007 56 2207］
[9] ［9］Zhang B S，Liu W Q，Wei Q N，Wu Z S，Zhao J F 2006 Chin. J. Quant. Electron 23 533 （in Chinese）［张百顺、刘文清、魏庆农、吴振森、赵剑锋 2006 量子电子学报 23 533］
[10] ］Jia H，Li F T 2004 Acta Optica Sinica 24 230 （in Chinese）［贾辉、李福田 2004 光学学报 24 230］
[11] ］Wolff L B 1994 J. Opt. Soc. Am. A 11 2956
[12] ］Zhan Y L，Wang L 1990 Acta Phys. Sin. 39 4 （in Chinese）［战元龄、王立 1990 39 4］
[13] ］Cook R L，Torrance K E 1982 ACM Transactions on Graphics 1 7
[14] ］Nicodemus F E 1970 Applied Optics 9 1474
[15] ］Wei Q N，Liu J G，Jiang R X 1996 Acta Optica Sinica 16 1425 （in Chinese）［魏庆农、刘建国、江荣熙 1996 光学学报 16 1425］
[16] ］Zhang S Q，Shi Y L，Huang C G，Lian C C 2007 Acta Phys. Sin. 56 5508 （in Chinese）［张拴勤、石云龙、黄长庚、连长春 2007 56 5508］
[17] ］Qi C，Yang M H，Sun X G，Dai J M 2003 Chinese Journal of Lasers 30 146 （in Chinese）［齐超、杨茂华、孙晓刚、戴景民 2003 中国激光 30 146］
[18] ］Zhao Z Y，Dai J M，Li Y 2007 Infrared Technology 29 579 （in Chinese）［赵忠义、戴景民、李颖 2007 红外技术 29 579］
[19] ］Wu Z S，Xie D H，Xie P H，Wei Q N 2002 Acta Optica Sinica 22 897 （in Chinese）［吴振森、谢东辉、谢品华、魏庆农 2002 光学学报 22 897］
[20] ］Cao Y H，Wu Z S，Zhang H L，Wei Q N，Wang S M 2008 Acta Optica Sinica 28 792 （in Chinese）［曹运华、吴振森、张涵璐、魏庆农、汪世美 2008 光学学报 28 792］
[21] ］Vicente J D，Lanchares J，Hermida R 2003 Physics Letters A 317 415
[22] ］Li S Y，Du Z H，Wu M Y，Zhu J，Li S L 2001 Acta Phys. Sin. 50 1260 （in Chinese）［李树有、都志辉、吴梦月、朱静、李三立 2001 50 1260］
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