基于舍选抽样BRDF离散数值的散射光线追迹方法

Scattered Ray Tracing Based on Rejection Sampling Method with BRDF Discrete Numerical Value

提出了一种基于表面双向反射分布函数(BRDF)离散测量值直接追迹散射光线的方法,以各向同性表面为例,先对随散射角离散变化的表面BRDF离散测量数据组做空间坐标转换,由散射角半球空间转换到方向余弦空间;再通过等间距赋值插等值方式得到方向余弦空间内分布的BRDF数据;然后,利用舍选抽样法不受限于累积分布函数(CDF)求解过程的优点,设计新的散射概率模型,以方向余弦空间内BRDF数值比表示离散光线的概率分布,设定检验条件筛选出散射光线的空间坐标,实现散射光线追迹。为验证本文方法的准确性与适用性,设置相同的入射角、追迹光线数量等仿真参数,编制了本文光线追迹方法的仿真程序,对不同光机元器件建模仿真,对比商用LightTools软件的仿真结果,计算二者的通用质量指数UQI作为比对评价指标。结果表明,基于舍选抽样BRDF离散数值的散射光线追迹方法,运算结果数据准确,与商用LightTools软件的仿真结果相比,UQI值均在0.998以上,且波动范围小,本方法具有良好地适用性。

The effect of stray light on system signals in space platform optical machine systems cannot be ignored.The components of an optical machine system are essential sources of stray light,and their surface light scattering characteristics directly affect the distribution of stray light in the system.Ray tracing and stray light analysis based on the surface scattering characteristics of system components is an important research content in optical design and simulation.The Bidirectional Reflectance Distribution Function(BRDF)is commonly used to accurately characterize the scattering property of surface about optical machine structures in stray light analysis.The Monte Carlo method(MCM)is the primary method of scattered ray tracing in optical machine systems.It is commonly used in scientific research experiments and stray light analysis software.The core of Monte Carlo scattered ray tracing lies in the reasonable selection of the bidirectional scattering distribution function model and the correct construction of the probability model.In practical applications,due to the particularity of the micro-morphology and texture distribution of the surface of the system components,the surface scattering characteristics show complex and diversified features,which are accompanied by the innovation of machining technology and the appearance of new material surfaces.The number of BRDF models in the commercial software is small,and the application scenarios are limited,so the real-time measured discrete data of BRDF on the optical surface are needed.In some instances,the reconstruction of the BRDF function model and the numerical analysis process is complicated.Moreover,there are some problems,such as fitting errors and limitations of application conditions of the model.The inverse transformation method is often used to solve the probability model of ray tracing.Although the inverse transformation method can efficiently generate random samples that obey the specified distribution,the BRDF of most scattering models is modulated by ray coordinate variables.In the design process of complex probabilistic models based on the reconstructed BRDF model for complex PDF,there are problems such as Cumulative Distribution Functions(CDF)without analytical solutions.To simplify the modeling process of surface scattering and enhance the applicability of the scattered ray tracing method,this paper proposes a way to directly trace the scattered rays based on the surface discrete BRDF measurements.Under the condition that the surface is isotropic,the procedures are shown as follows:Firstly,the spatial coordinate transformation of the discrete measurement data of surface BRDF,which discontinuously varies versus the scattering angle,is converted from the scattering angle hemisphere space to the direction cosine space;Then,the BRDF data distributed in the direction cosine space is obtained by equal interval assignment interpolation equivalent method.Then,a new scattering probability model is designed using the advantage of the rejection sampling method unlimited to the CDF-solving process.The BRDF numerical ratio in the cosine space direction represents the probability distribution of discrete rays.The space coordinates of scattered rays are screened out by setting the test conditions to realize the scattering ray tracing.To verify the accuracy and applicability of the proposed method,the same incident angle,the number of tracing rays,and other parameters in the simulation were set.The simulation program is prepared in Matlab according to the proposed method,and the simulation results in Matlab are compared with those in LightTools.Wherein the BRDF model and parameters of Harvey,ABg,and multiple scattering surfaces characterizing the surface scattering characteristics of various optical and mechanical components were set in LightTools.Different visual and mechanical parts are modeled and simulated.BRDF data in the section where incident light and mirror-reflected light are located were obtained using the analytical formula of the BRDF model and its parameters.The above data were taken as the discrete measured data of BRDF in the simulation program of the proposed method in this paper.The general quality index UQI is the comparison evaluation index of the simulation results between commercial LightTools software and the proposed method.The results show that the scattering energy distribution obtained by the proposed ray tracing method is highly consistent with the LightTools simulation.The different optical and mechanical components are modeled and simulated,the UQI values are all above 0.998,and the fluctuation range is small.The calculation results of the ray tracing method in this paper are accurate and have good applicability.