Noise-robust Phase Gradient Retrieval Formulation for Phase-shifting Interferometry

Dae-Seo Park,오범환,박세근,이일항,Jaehyun Park,이승걸 한국광학회 2010 Current Optics and Photonics Vol.14 No.2

Modification of the phase gradient formulation is proposed in order to make phase retrieval less susceptible to noise. The modified formulation is derived from separation of the phase terms and the intensity modulation terms of interferograms, and subsequent differentiation to reduce the noise-induced error of the phase gradient vector. Its performance is evaluated and compared to that of the conventional formulation, and noise-robust nature is confirmed.

Color-coded LED microscopy for quantitative phase imaging: Implementation and application to sperm motility analysis

Lee, Wonchan,Choi, Jun-Ho,Ryu, Suho,Jung, Daeseong,Song, Jaewoo,Lee, Jong-Seok,Joo, Chulmin Elsevier 2018 Methods Vol.136 No.-

<P><B>Abstract</B></P> <P>Color-coded light-emitting diode (LED) microscopy (cLEDscope) is a novel computational microscopy technique capable of multi-contrast and quantitative phase imaging of biological specimens using color-multiplexed illumination. Using specially designed LED patterns, it is capable of recording multiple differential phase contrast (DPC) images in a single exposure and employs a computational algorithm to retrieve the phase distribution of the specimens. Herein, we describe the detailed procedures in the cLEDscope implementation for quantitative phase imaging. Several notable features and caveats in the cLEDscope setup and image processing are also outlined. The imaging model is derived for our specific configuration, and the associated phase-retrieval algorithms are presented on the basis of a weak-object transfer function. As an illustrative application of the quantitative cLEDscope, we demonstrate its utility as a sperm-motility analyzer by exploiting its real-time quantitative imaging capability.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Describes quantitative phase imaging in color-coded LED microscopy (q-cLEDscope). </LI> <LI> Detailed procedures and notes for q-cLEDscope implementation are provided. </LI> <LI> Demonstrates motility analysis of human sperm cells via q-cLEDscope. </LI> </UL> </P>

Resolution of Closely-Positioned Optical Vortices by Phase-Shifting Interferometry

강전웅,홍정기 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.53 No.6

Optical vortices have been usually identified by using the characteristic fork-like structure in the interference pattern formed between a reference beam and the optical vortex field. It might, however, lead to misinterpretation of the property of vortices when the reference beam’s phase difference between vortices is less than π. We confirmed this experimentally and propose that closely positioned optical vortices can be resolved better by analyzing the phase map obtained through phase-shifting interferometry. Optical vortices have been usually identified by using the characteristic fork-like structure in the interference pattern formed between a reference beam and the optical vortex field. It might, however, lead to misinterpretation of the property of vortices when the reference beam’s phase difference between vortices is less than π. We confirmed this experimentally and propose that closely positioned optical vortices can be resolved better by analyzing the phase map obtained through phase-shifting interferometry.

Improving the Capture-range Problem in Phase-diversity Phase Retrieval for Laser-wavefront Measurement Using Geometrical-optics Initial Estimates

Li Jie Li,Wen Bo Jing,Wen Shen,Yue Weng,Bing Kun Huang,Xuan Feng 한국광학회 2022 Current Optics and Photonics Vol.6 No.5

To overcome the capture-range problem in phase-diversity phase retrieval (PDPR), a geometricaloptics initial-estimate method is proposed to avoid a local minimum and to improve the accuracy of laser-wavefront measurement. We calculate the low-order aberrations through the geometrical-optics model, which is based on the two spot images in the propagation path of the laser, and provide it as a starting guess for the PDPR algorithm. Simulations show that this improves the accuracy of wavefront recovery by 62.17% compared to other initial values, and the iteration time with our method is reduced by 28.96%. That is, this approach can solve the capture-range problem.

Retrieving Phase from Single Interferogram with Spatial Carrier Frequency by Using Morlet Wavelet

Hongxin Zhang,Mengyuan Cui 한국광학회 2023 Current Optics and Photonics Vol.7 No.5

The Morlet wavelet transform method is proposed to analyze a single interferogram with spatial carrier frequency that is captured by an optical interferometer. The method can retain low frequency components that contain the phase information of a measured optical surface, and remove high frequency disturbances by wavelet decomposition and reconstruction. The key to retrieving the phases from the low-frequency wavelet components is to extract wavelet ridges by calculating the maximum value of the wavelet transform amplitude. Afterwards, the wrapped phases can be accurately solved by multiple iterative calculations on wavelet ridges. Finally, we can reconstruct the wavefront of the measured optical element by applying two-dimensional discrete cosine transform to those wrapped phases. Morlet wavelet transform does not need to remove the spatial carrier frequency components manually in the processing of interferogram analysis, but the step is necessary in the Fourier transform algorithm. So, the Morlet wavelet simplifies the process of the analysis of interference fringe patterns compared to Fourier transform. Consequently, wavelet transform is more suitable for automated programming analysis of interference fringes and avoiding the introduction of additional errors compared with Fourier transform.

A Study of the Extraneous Self-Imaging Phenomenon under a Multimode Interference Configuration

이상선,홍종균 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.53 No.3

This study analyzes the phase-mismatching values of guided modes in a multimode waveguide with a weak-guiding conguration. In addition, a previously undefined self-imaging phenomenon, refered to herein as the extraneous self-imaging (Ex SI) phenomenon, was found to result from the modal phase-mismatching effect. The evolution principle of the Ex SI phenomenon is theoreticaly veried while the results from the numerical method are compared with graphical and analytical forms of the newly suggested method. Moreover, under a specific condition, the numerical results and the analytical results are compared to analyze the evolution of the Ex SI phenomenon.

Phase Retrieval By Enforcing the Off-Axis Holographic Condition

김우식 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.52 No.2

The phase retrieval problem is concerned with the reconstruction of a Fourier transform phase or the signal itself from its Fourier transform magnitude and occurs in various physical fields, including astronomy, optics, X-ray crystallography, etc. In this paper, we address a one-dimensional phase retrieval by using a window function to enforce an off-axis holographic condition. We show that, by choosing an appropriate window function, we can make the windowed signal satisfy the off-axis holographic condition and reconstruct the unknown signal from the magnitudes of two Fourier transforms; the magnitude of the Fourier transform of an original unknown signal and that of the windowed signal. We show that this problem has a unique solution to within a sign ambiguity and present a closed-form solution. The phase retrieval problem is concerned with the reconstruction of a Fourier transform phase or the signal itself from its Fourier transform magnitude and occurs in various physical fields, including astronomy, optics, X-ray crystallography, etc. In this paper, we address a one-dimensional phase retrieval by using a window function to enforce an off-axis holographic condition. We show that, by choosing an appropriate window function, we can make the windowed signal satisfy the off-axis holographic condition and reconstruct the unknown signal from the magnitudes of two Fourier transforms; the magnitude of the Fourier transform of an original unknown signal and that of the windowed signal. We show that this problem has a unique solution to within a sign ambiguity and present a closed-form solution.

Large-Scale Phase Retrieval via Stochastic Reweighted Amplitude Flow

( Zhuolei Xiao ),( Yerong Zhang ),( Jie Yang ) 한국인터넷정보학회 2020 KSII Transactions on Internet and Information Syst Vol.14 No.11

Phase retrieval, recovering a signal from phaseless measurements, is generally considered to be an NP-hard problem. This paper adopts an amplitude-based nonconvex optimization cost function to develop a new stochastic gradient algorithm, named stochastic reweighted phase retrieval (SRPR). SRPR is a stochastic gradient iteration algorithm, which runs in two stages: First, we use a truncated sample stochastic variance reduction algorithm to initialize the objective function. The second stage is the gradient refinement stage, which uses continuous updating of the amplitude-based stochastic weighted gradient algorithm to improve the initial estimate. Because of the stochastic method, each iteration of the two stages of SRPR involves only one equation. Therefore, SRPR is simple, scalable, and fast. Compared with the state-of-the-art phase retrieval algorithm, simulation results show that SRPR has a faster convergence speed and fewer magnitude-only measurements required to reconstruct the signal, under the real- or complex- cases.

Dual-path Phase Unwrapping Algorithm Based on Geodesic Curvature for Interferometric Fringe Analysis

Ohgan Kim,Bong Ju Lee,Hyug-Gyo Rhee,이윤우,양호순 한국물리학회 2020 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.76 No.3

We present a path-dependent phase unwrapping algorithm with the dual-path scheme. The proposed algorithm removes the inconsistency between the true phase and its wrapped phase by rolling up a 1D wrapped phase array around a cylindrical surface. The dual-path scheme entails phase unwrapping by using two different paths linked from an arbitrary position to other points in 2D wrapped phase images. The proposed algorithm is confirmed to be as fast as the UNWRAP in MATLAB, and its noise resistance is comparable to that of the conventional algorithms up to a signal-to-noise ratio (SNR) of 6 dB.

Closed-form Algorithms for Phase Retrieval with an Additive Linear Phase Signal

김우식 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.57 No.4

The phase retrieval problem is a problem of reconstruction of a signal from the magnitude of its Fourier transform. In this paper, we consider the problem of reconstructing an unknown onedimensional signal from the magnitude of its Fourier transform and the magnitude of the Fourier transform of another signal that is made by the addition of a linear phase signal at the center of the original signal. Since there are two kinds of linear phase signals, i.e., symmetric and antisymmetric, we consider the two cases separately. After showing that there are exactly two solution signals that satisfy the given condition, we develop a closed-form algorithm that may reconstruct the two solution signals.