光衍射数值模拟中不同抽样方法的适用性分析

Suitability of Different Sampling Methods for Digital Simulations of the Optical Diffraction

基于标量衍射理论和快速傅里叶变换,分析了光衍射的数值模拟时可以采用的不同抽样方法及其适用性。理论分析表明,按照抽样对象的不同,存在三种适用范围不同的算法:传递函数抽样法、点扩展函数抽样法和加权函数抽样法。其适用范围分别为衍射距离小于、大于和等于特征距离的情况。在Matlab软件环境下给出了三种算法的模拟计算实例,并与相应的实验结果进行了比较,证明了理论分析的正确性。最后还给出了一种无需改变抽样点数和抽样间隔就可计算任意距离衍射过程的自适应抽样算法及其在数字全息再现中的应用实例。

Sampling methods for digital simulations of the optical diffraction based on scalar diffraction theory and fast Fourier transform are analyzed. There exist three sampling methods according to the sampling objects： the transfer function sampling, the point-spread function sampling and the weighting function sampling. Theoretical analysis reveals that these sampling methods hold true in different ranges of diffractive distances, which can be distinguished by a feature diffraction distance. Under definite sampling space and sampling number, the sampling methods hold true only when the diffraction distance is smaller than, larger than and equal to the feature distance, respectively. For demonstration of the correctness of the theoretical analysis, a digital simulation based on Matlab solfware and an experimental result are given and discussed. Finally, an adaptive sampling algorithm is proposed for reconstruction of a digital hologram, which could he suitable for anv diffraction distances.