A two-step phase-retrieval method in Fourier-transform ghost imaging

2008 ◽  
Vol 281 (20) ◽  
pp. 5130-5132 ◽  
Author(s):  
Guanrong Ying ◽  
Qing Wei ◽  
Xia Shen ◽  
Shensheng Han
Keyword(s):  
Fourier Transform ◽  
Phase Retrieval ◽  
Ghost Imaging ◽  
Retrieval Method

New phase retrieval method for single-shot x-ray Talbot imaging using windowed Fourier transform

2011 ◽  
Author(s):  
Kentaro Nagai ◽  
Hidenosuke Itoh ◽  
Genta Sato ◽  
Takashi Nakamura ◽  
Kimiaki Yamaguchi ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Phase Retrieval ◽  
Single Shot ◽  
Retrieval Method ◽  
X Ray ◽  
Windowed Fourier Transform ◽  
New Phase

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Correspondence Fourier-transform ghost imaging

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Chenyu Hu ◽  
Ruiguo Zhu ◽  
Hong Yu ◽  
Shensheng Han
Keyword(s):  
Fourier Transform ◽  
Ghost Imaging

scholarly journals Measurement of Small-Slope Free-Form Optical Surfaces with the Modified Phase Retrieval

Micromachines ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 82
Author(s):  
Xinxue Ma ◽  
Jianli Wang ◽  
Bin Wang ◽  
Xinyue Liu
Keyword(s):  
Wave Front ◽  
Phase Retrieval ◽  
Computation Time ◽  
Experimental Arrangement ◽  
Free Form ◽  
Retrieval Algorithm ◽  
Retrieval Method ◽  
Optical Surfaces ◽  
Image Capturing ◽  
Phase Retrieval Algorithm

In this paper, we demonstrate the use of the modified phase retrieval as a method for application in the measurement of small-slope free-form optical surfaces. This technique is a solution for the measurement of small-slope free-form optical surfaces, based on the modified phase retrieval algorithm, whose essence is that only two defocused images are needed to estimate the wave front with an accuracy similar to that of the traditional phase retrieval but with less image capturing and computation time. An experimental arrangement used to measure the small-slope free-form optical surfaces using the modified phase retrieval is described. The results of these experiments demonstrate that the modified phase retrieval method can achieve measurements comparable to those of the standard interferometer.

scholarly journals Two-Step Phase Retrieval Algorithm Using Single-Intensity Measurement

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Cheng Zhang ◽  
Meiqin Wang ◽  
Qianwen Chen ◽  
Dong Wang ◽  
Sui Wei
Keyword(s):  
Phase Retrieval ◽  
Fourier Spectrum ◽  
Retrieval Algorithm ◽  
Improved Method ◽  
Retrieval Method ◽  
Intensity Measurements ◽  
Successful Recovery ◽  
Reconstruction Quality ◽  
Low Probability ◽  
Phase Retrieval Algorithm

Aiming at the problem that the single-intensity phase retrieval method has poor reconstruction quality and low probability of successful recovery, an improved method is proposed in this paper. Our method divides the phase retrieval into two steps: firstly, the GS algorithm is used to recover the amplitude in the spatial domain from the single-spread Fourier spectrum, and then the classical GS algorithm using two intensity measurements (one is recorded and the other is estimated from the first step) measurements is used to recover the phase. Finally, the effectiveness of the proposed method is verified by numerical experiments.

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