Hillenbrand Matthias, Hoffmann Armin, Kelly Damien P, Sinzinger Stefan
J Opt Soc Am A Opt Image Sci Vis. 2014 Jun 1;31(6):1206-14. doi: 10.1364/JOSAA.31.001206.
An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first Rayleigh-Sommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately 800× in comparison to the normal angular spectrum method, while the memory requirements are reduced by more than 99%.
讨论了一种用于计算透镜焦区内非傍轴标量场分布的高效算法。该算法基于瑞利 - 索末菲第一衍射积分的快速傅里叶变换实现，并假设光瞳平面上的输入场比焦区内的场范围更大。在输出平面的有限区域上定义一个采样网格，称为瓦片。将输入场划分为多个大小与输出瓦片相同的单独空间区域。最后，将输入瓦片相干相加形成一个求和瓦片，并传播到输出平面。由于仅传播单个瓦片，因此显著降低了计算负载和内存需求。该方法与子像素采样技术或线性调频Z变换相结合，以在输出平面中实现比输入平面更小的采样间隔。对于给定示例，与常规角谱方法相比，所得方法可实现约800倍的加速，同时内存需求减少超过99%。
