针对不同粗糙度表面反射光泄漏问题, 对Torrance-Sparrow模型进行修正, 建立了双向反射分布函数数学模型,数值计算了影响双向反射分布函数的各个因素, 通过实验对建立的数学模型和数值计算结果进行了验证.结果表明：影响反射信息的主要因素有镜面反射, 漫反射和介质的吸收, 镜面反射包括反射面反射率、反射面上微面元倾斜角概率分布函数、入射光入射到反射面的微面元入射角和反射角引起的遮蔽因子, 其中, 主要影响因素是镜面反射; 若选定入射角和粗糙度, 随着反射角从0到π/2变化, 反射面双向反射分布函数是以镜面反射角为均值的高斯分布, 当反射角大于1.4 rad, 反射面双向反射分布函数值急剧增加, 高斯分布发生变形; 若选定镜面反射角方向接收反射信息, 随着反射面粗糙度的增加, 反射面双向反射分布函数值单调下降, 且变化较快; 当粗糙度大于0.3时, 双向反射分布函数接近0.

The light leak from different roughness surface reflected was studied. The bidirectional reflectance distribution function model is established by correcting Torrance - Sparrow model, and the influence factors on the bidirectional reflectance distribution function are numerical calculated. The mathematical model and numerical results are verified by experiments. The main factors affecting the reflected information are the mirror reflection, the diffuse reflection and the absorption of medium, which the mirror reflection includes the reflecting reflectivity of objects, the probability distribution function of micro-elements on reflection surface, the shading factors caused by incident ray incident angle and reflection angle. The main influencing factors is mirror reflection. When the incident angle and roughness are selected and reflection angle is varied from 0 to π/2, reflecting surface bidirectional reflectance distribution function is shown as Gaussian distribution based on the mirror reflection angle under the condition of small reflection angle. If the reflection angle is greater than 1.4 rad, reflective surface bidirectional reflectance distribution function value has increased dramatically and performed a deformation of Gaussian distribution. If the reflection angle of the mirror is selected to receive the reflection information, the bidirectional reflection distribution function of reflecting surface decreases monotonically and changes rapidly with the increase of the roughness of reflecting surface. When the roughness is greater than 0.3, the bidirectional reflection distribution function is close to 0.