Phase retrieval using the logarithmic Hilbert transform and the Fourier-series expansion
Phase retrieval using the logarithmic Hilbert transform and the Fourier-series expansion
复制标题
使用对数希尔伯特变换和傅立叶级数展开进行相位检索
DOI：
10.1364/josaa.5.000257
复制
发表时间：
1988
影响因子：
1.9
通讯作者：
N. Nakajima
中科院分区：
文献类型：
--
作者：
N. Nakajima
以往的研究表明，利用傅里叶级数展开可以从一维物体的傅里叶变换平面上观察到的两个强度恢复相位。本文提出了一种利用对数希尔伯特变换和傅里叶级数展开的改进方法。从零点在复平面上的分布证明，厄米特物函的傅里叶变换位相不能用以前的方法求取，但可以用本文的方法求取。用本方法重建的结果也显示在计算机模拟中。
Previously it was shown that one can solve the phase-retrieval problem from two intensities observed at the Fourier-transform plane of an object in one dimension by using the Fourier-series expansion. In this paper, an improved method using the logarithmic Hilbert transform and the Fourier series expansion is proposed. It is proved from the distribution of zeros in the complex plane that the Fourier-transform phase of Hermitian object functions cannot be retrieved by using the previous method but can be retrieved by using the method in this paper. The results reconstructed by the present method are also shown in computer simulations.