Opt Lett. 2015 Aug 1;40(15):3472-5. doi: 10.1364/OL.40.003472.
The Fresnel transform is widely used in optics to calculate the free-space propagation of paraxial fields. Generally, there is no analytical solution for the Fresnel transform; therefore, the numerical methods are used often. In this Letter, we propose a new semi-analytical method to calculate the Fresnel transform, which is based on an extended Nijboer-Zernike theory. We calculate two examples to investigate how the sampling rate and maximal number of Zernike polynomials affect the accuracy of our results, and then use this method to calculate the reconstruction of two different kinds of holograms. At the end, we discuss the advantages and disadvantages of our method.
菲涅耳变换在光学中被广泛用于计算傍轴场的自由空间传播。通常，菲涅耳变换没有解析解，因此通常使用数值方法。在这封信中，我们提出了一种新的基于扩展的奈杰尔-泽尼克理论的计算菲涅耳变换的半解析方法。我们计算了两个例子来研究采样率和最大泽尼克多项式数如何影响我们结果的准确性，然后使用该方法计算两种不同类型的全息图的重建。最后，我们讨论了我们的方法的优缺点。
