基于三角形面光源频谱解析解的计算全息图快速生成算法

Fast Generation Algorithm of Computer-Generated Hologram Based on Triangular Surface Light Source Frequency Spectrum Analytic Solutions

在空间曲面光源的衍射场计算研究中,将曲面光源视为微小三角形面光源的集合是一种流行的算法。基于坐标仿射变换导出任意三角形面光源频谱完整的解析表达式,并给出了特殊频率点的解析表达式,解决了传统方法中部分三角形频谱丢失的问题,提高计算全息图重建像的质量。通过严格的理论分析及计算,准确求解并获得二维、三维任意三角形频谱的解析表达式,简化了求解三维基元三角形频谱的解析表达式,得到使用面元分割的三维物体计算全息图的快速计算方法。理论模拟及实验结果验证了算法的正确性。

In the study of diffraction field calculation of spatial curved surface light source, it is a popular algorithm that considering the curved surface light source as a set of small triangle surface light sources. The analytic expressions of arbitrary triangular surface light spectrum and special frequency point is derived based on coordinate affine transformation. The problem of partial triangular spectrum loss in the traditional method is solved and the quality of the reconstructed image of the hologram is improved. Through rigorous theoretical analysis and calculation, the analytical expressions of two-dimensional and three-dimensional arbitrary triangular spectrum is solved accurately. The analytical expression of three-dimensional primitive triangular spectrum is simplified. A fast calculation method of 3D objects computing holograms using surface element division is obtained. Theoretical simulation and experimental results verify the validity of this method.