Generalized Phase-Shifting Phase Retrieval Approach Based on Time-Domain Fourier Transform

2015 ◽  
Vol 42 (9) ◽  
pp. 0908004
Author(s):  
张望平 Zhang Wangping ◽  
吕晓旭 Lü Xiaoxu ◽  
刘胜德 Liu Shengde ◽  
赵晖 Zhao Hui ◽  
钟丽云 Zhong Liyun
2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen

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.


2009 ◽  
Vol 17 (4) ◽  
Author(s):  
R. Sitnik

AbstractThis paper presents a fast and reliable approach for phase modulo 2π-calculation from a single fringe pattern. It calculates correct phase values even for very complex and variable shape gradients based on a locally variable fringe period determined for the entire image. In the paper, a new two-step method for wrapped phase calculation is proposed. It is performed through the use of a method based on a multiple local fast Fourier transform for estimation of a local fringes period map and a 5-point spatial carrier phase shifting (SCPS) formula for phase modulo 2π-calculation. The described approach is verified by a correct demodulation of a real fringe pattern taken by a 3D-shape measurement system.


2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.


Author(s):  
Roghayeh Yazdani ◽  
Hamidreza Fallah

In digital holography, errors of the reference field degrade the quality of the reconstructed object field. In this paper, we propose an effective method in phase-shifting digital holography in which the reference field does not need to be known and perfect. The unknown complex amplitudes of both reference and object fields are derived simultaneously. The method employs only five digital holograms and a single execution of a phase retrieval algorithm. So, the required measurements and algorithm executions in this method are fewer than those in other methods; it suggests a simpler and faster method. The effectiveness of the suggested method is indicated by simulation, under noise-free and noisy conditions. Moreover, the capability of the method to extract full information about the phase singularities in both fields is demonstrated.


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