Modification of geometrical attenuation factor of bidirectional reflection distribution function based on random surface microfacet theory

Liu Hong; Zhu Jing-Ping; Wang Kai

doi:10.7498/aps.64.184213

Abstract

The reflection attenuation factor given by Blinn has been widely used as an important factor in the bidirectional reflectance distribution function (BRDF) model based on geometrical optics theory for nearly half a century. However, Blinn's attenuation factor is based on microfacet theory and geometry of equicrural V-grooves caused sharp turning points and obvious error in its function curves. In this paper, a modified geometry attenuation factor based on random surface microfacet theory is presented. We assume that the surface is composed of a large number of microfacets, and the slope of each microfacet is independent of each other and follows Gaussian distribution. The attenuation effect is caused by the masking and shadowing factors in adjacent microfacets. Depending on the slope angles of microfacets, reflection falls in three submodels, i.e., passing model, semi-passing model, and masking/shadowing model when discussing masking/shadowing factor. The modified attenuation factor is given in an integral expression. The modified geometry attenuation factor is simulated and compared with Blinn's geometry attenuation factor. The sharp turning point in Blinn's attenuation factor curve is eliminated and the error of the BRDF curve is reduced. The result shows that the modified geometry attenuation factor reaches better physical rationality and significantly improves the accuracy of BRDF model. Compared with Blinn's geometry attenuation factor, the modification reduces the standard error between BRDF model and existing data from 0.0636 to 0.0084. The cause of the error in Blinn's geometry attenuation factor is analyzed, the equicrural V-grooves assumption of Blinn's geometry attenuation model considers too much reflection attenuation in the condition of small incident angle and large reflect angle. The modification in this paper is based on random surface microfacet theory, in which the angular dependence of adjacent microfacet is eliminated, for this reason the accuracies of geometry attenuation model and BRDF model are improved.

Keywords:

bidirectional reflectance distribution function model /
geometry attenuation factor /
microfacet theory

PACS:

42.15.-I
42.25.Fx	(Diffraction and scattering)
42.68.Mj	(Scattering, polarization)

Authors and contacts

1.
Shanxi Key Laboratory of Information Photonic Technique, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China;
2.
The State Key Laboratory of Astronautic Dynamics, Xi'an Satellite Control Center, Xi'an 710043, China

Corresponding author: Zhu Jing-Ping, jpzhu@mail.xjtu.edu.cn

References

[1]	Renhorn I G E, Boreman G D 2008 Opt. Express 16 12892
[2]	Yuan Y, Sun C M, Zhang X B 2010 Acta Phys. Sin. 59 2097(in Chinese) [袁艳, 孙成明, 张修宝 2010 物理学报 59 2097]
[3]	Sun L J, Tian Z S, Ren X Y, Zhang Y C, Fu S Y 2014 Acta Phys. Sin. 63 134211(in Chinese) [孙兰君, 田兆硕, 任秀云, 张延超, 付石友 2014 物理学报 63 134211]
[4]	Torrance K E, Sparrow E M 1967 J. Opt. Soc. Am. 57 1105
[5]	Wellems D, Ortega S, Bowers D, Boger J, Fetrow M 2006 Opt. A: Pure Appl. Opt. 8 914
[6]	Priest R G, Meier S R 2002 Opt. Eng. 41 988
[7]	Blinn, James F 1977 Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques San Jose, California, July 20-22, 1977 pp192-198
[8]	Cook R L, Torrance K E 1982 ACM Trans. Graph. 1 7
[9]	Hyde M W, Schmidt J D, Havrilla M J 2009 Opt. Express 17 22138
[10]	Xiao D H, Torrance K E, Francois X S, Donald P G 1991 Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques Las Vegas, July 28-August 2, 1991 p175

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2.	刘承麟，战俊彤，张肃，王超，付强，李英超，段锦，姜会林. 基于改进型Blinn遮蔽函数的目标材料表面可见光偏振反射研究. 中国光学(中英文). 2024(05): 1162-1174 . 百度学术
3.	GU Xiansong，FU Qiang，WANG Liya，LIU Xuanwei，FAN Xinyu，DUAN Jin，LI Yingchao. Analysis and inversion of target polarization characteristics based on pBRDF. Journal of Systems Engineering and Electronics. 2024(05): 1073-1083 . 必应学术
4.	林海. 智能仿真虚拟实验室中的产品展示技术及实现. 科技与创新. 2023(07): 53-55+58 . 百度学术
5.	于洁，巩蕾，王海斌，王利国，杨利红，李瑶，阳志强. 伪装涂层红外偏振模型优化及辐射特性研究. 中国激光. 2023(13): 111-118 . 百度学术
6.	杨志勇，张志伟，蔡伟，陆高翔. 积分型二向反射分布函数几何衰减因子分析改进. 光学学报. 2022(10): 246-254 . 百度学术
7.	朱达荣，胡子粮，汪方斌，金蓄，何峰. 基于遮蔽函数修正的金属表面自发辐射偏振模型. 激光与光电子学进展. 2022(13): 382-387 . 百度学术
8.	王金海，李华，魏力. 基于C-T模型的光学元件加工表面的光学特性研究. 光学技术. 2021(02): 172-177 . 百度学术
9.	张弛，吴鑫，谢建. 基于双向反射分布函数的海面红外偏振特性表征模型. 光学精密工程. 2020(06): 1303-1313 . 百度学术
10.	段存丽，刘王云，赵鹏程，陈玉娇，张苏娟. 基于不同粗糙度表面反射的液晶屏显示信息泄漏研究. 光子学报. 2019(03): 218-226 . 百度学术
11.	王耀东，陈桂波，张烨，韩颖，谭勇，蔡红星. 基于Davies理论的粗糙面光散射特性研究. 长春理工大学学报(自然科学版). 2016(05): 45-50 . 百度学术
12.	赵青，赵建科，徐亮，刘峰，李朝辉. 航天消光黑漆双向反射分布函数的测量与应用. 光学精密工程. 2016(11): 2627-2635 . 百度学术

其他类型引用(8)

[1]	Renhorn I G E, Boreman G D 2008 Opt. Express 16 12892
[2]	Yuan Y, Sun C M, Zhang X B 2010 Acta Phys. Sin. 59 2097(in Chinese) [袁艳, 孙成明, 张修宝 2010 物理学报 59 2097]
[3]	Sun L J, Tian Z S, Ren X Y, Zhang Y C, Fu S Y 2014 Acta Phys. Sin. 63 134211(in Chinese) [孙兰君, 田兆硕, 任秀云, 张延超, 付石友 2014 物理学报 63 134211]
[4]	Torrance K E, Sparrow E M 1967 J. Opt. Soc. Am. 57 1105
[5]	Wellems D, Ortega S, Bowers D, Boger J, Fetrow M 2006 Opt. A: Pure Appl. Opt. 8 914
[6]	Priest R G, Meier S R 2002 Opt. Eng. 41 988
[7]	Blinn, James F 1977 Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques San Jose, California, July 20-22, 1977 pp192-198
[8]	Cook R L, Torrance K E 1982 ACM Trans. Graph. 1 7
[9]	Hyde M W, Schmidt J D, Havrilla M J 2009 Opt. Express 17 22138
[10]	Xiao D H, Torrance K E, Francois X S, Donald P G 1991 Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques Las Vegas, July 28-August 2, 1991 p175

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期刊类型引用(12)

1.	余越，王利国，王彪，阳志强，张格，靳皓然，吴振森，赵保银，巩蕾. 六参数光谱双向反射分布函数模型几何衰减因子优化. 光子学报. 2025(01): 100-110 . 百度学术
2.	刘承麟，战俊彤，张肃，王超，付强，李英超，段锦，姜会林. 基于改进型Blinn遮蔽函数的目标材料表面可见光偏振反射研究. 中国光学(中英文). 2024(05): 1162-1174 . 百度学术
3.	GU Xiansong，FU Qiang，WANG Liya，LIU Xuanwei，FAN Xinyu，DUAN Jin，LI Yingchao. Analysis and inversion of target polarization characteristics based on pBRDF. Journal of Systems Engineering and Electronics. 2024(05): 1073-1083 . 必应学术
4.	林海. 智能仿真虚拟实验室中的产品展示技术及实现. 科技与创新. 2023(07): 53-55+58 . 百度学术
5.	于洁，巩蕾，王海斌，王利国，杨利红，李瑶，阳志强. 伪装涂层红外偏振模型优化及辐射特性研究. 中国激光. 2023(13): 111-118 . 百度学术
6.	杨志勇，张志伟，蔡伟，陆高翔. 积分型二向反射分布函数几何衰减因子分析改进. 光学学报. 2022(10): 246-254 . 百度学术
7.	朱达荣，胡子粮，汪方斌，金蓄，何峰. 基于遮蔽函数修正的金属表面自发辐射偏振模型. 激光与光电子学进展. 2022(13): 382-387 . 百度学术
8.	王金海，李华，魏力. 基于C-T模型的光学元件加工表面的光学特性研究. 光学技术. 2021(02): 172-177 . 百度学术
9.	张弛，吴鑫，谢建. 基于双向反射分布函数的海面红外偏振特性表征模型. 光学精密工程. 2020(06): 1303-1313 . 百度学术
10.	段存丽，刘王云，赵鹏程，陈玉娇，张苏娟. 基于不同粗糙度表面反射的液晶屏显示信息泄漏研究. 光子学报. 2019(03): 218-226 . 百度学术
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