切削加工表面由于微观不平度及镜面效应的存在，使得照射其上的光线具有多次散射及后向散射的特性，从而影响了以工件表面图像3维重建形貌的精度。提出了一种基于二向反射分布函数的表面重建算法，构造了以Hapke模型表达的金属切削表面重建方程。该算法以重建方程离散化为手段，计算出光源和物体的倾角和偏角，得到光源和物体的梯度值，最后采用全微分方程对物体表面高度进行恢复。通过对实际切削加工表面图像3维形貌重建结果与触针式测量结果的对比表明，重建形貌粗糙度轮廓贴近实测粗糙度轮廓，证明了本文算法的准确、有效性，为加工表面3维形貌的重建提供了新的思路和方法。

Multiple scattering and backward scattering on rough surface is caused by surface roughness and mirror effect， and this affects the precision of shape from shading arithmetic accordingly. This paper reconstructs the reflection map equation by using a bidirectional reflectance distribution function and the Hapke model. After the equation discretization， we calculated tilt and slant of the lighting and the surface， then get the height gradient of the lighting and the surface， recover the height data with a total differentiation method. The comparison of reconstruction of real cutting surface and the measured stylus profile result shows this algorithm is accurate and effective， and it inspires new thinking ways for the shape from shading of metal cutting surface for cutting surfaces.