Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination
Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination
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DOI：
10.1364/josaa.13.001670
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发表时间：
1996-08
影响因子：
1.9
通讯作者：
T. Gureyev;K. Nugent
中科院分区：
文献类型：
--
作者：
T. Gureyev;K. Nugent
文献综述[j]。点。A12, 1932(1995)]我们提出了一种利用级数展开的强度输运方程进行相位恢复的方法。在这里，我们开发了一种不同的方法来解决这个方程，它允许在不均匀照明的情况下恢复相位。虽然也是基于正交级数展开，但新方法不需要任何单独的边界条件，并且可以更容易地调整各种形状的孔径。讨论主要针对圆形孔径和泽尼克多项式的情况，但我们也概述了矩形孔径和傅里叶谐波的解决方案。考虑到快速傅里叶变换的可用性，后一个例子可能有一些实质性的优势。
In a previous paper [ J. Opt. Soc. Am. A12, 1932 ( 1995)] we presented a method for phase recovery with the transport-of-intensity equation by use of a series expansion. Here we develop a different method for the solution of this equation, which allows recovery of the phase in the case of nonuniform illumination. Though also based on the orthogonal series expansion, the new method does not require any separate boundary conditions and can be more easily adjusted for apertures of various shapes. The discussion is primarily for the case of a circular aperture and Zernike polynomials, but we also outline the solution for a rectangular aperture and Fourier harmonics. The latter example may have some substantial advantages, given the availability of the fast Fourier transform.