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1

Phase retrieval without phase unwrapping for white blood cells in deep-learning phase-shifting digital holography

Jin Shuyang, Xu Xiaoqing, Chen Jili, Ni Yudan

Optica Applicata

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2023

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Vol. 53, nr 1

127--140

EN

Phase retrieval and phase unwrapping are the two important problems for enabling quantitative phase imaging of cells in phase-shifting digital holography. To simultaneously cope with these two problems, a deep-learning phase-shifting digital holography method is proposed in this paper. The proposed method can establish the continuous mapping function of the interferogram to the ground-truth phase using the end-to-end convolutional neural network. With a well-trained deep convolutional neural network, this method can retrieve the phase from one-frame blindly phase-shifted interferogram, without phase unwrapping. The feasibility and applicability of the proposed method are verified by the simulation experiments of the microsphere and white blood cells, respectively. This method will pave the way to the quantitative phase imaging of biological cells with complex substructures.

2

Simultaneous intensity projection for projector response computation with application to an active radiometric calibration

Filio-Aguilar Pedro-David, López-García Lourdes, Rueda-Paz Juvenal, Ávila-Aoki Manuel

Optica Applicata

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2022

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Vol. 52, nr 4

521--533

EN

One of the most important sources of errors in digital fringe projection (DFP) systems is the nonlinearity in the response of the projector when it uses the three-step phase retrieval algorithm. Thus, it is necessary to increase the accuracy without affecting the efficiency. In this sense, the radiometric rectification methods are used. In this paper, an active radiometric rectification method for digital fringe projection is proposed. This proposal consists in two improvements of traditional active techniques: first, parallel intensity projection is used to obtain the projector response which requires only four dot patterns; and second, a method is provided for the calculation of the inverse polynomial that guarantees symmetry with respect to the response of the projector. Experimental results, in a digital fringe projection system, show that the root-mean-square phase error improves 6.3 times using this proposal.

3

Two-step blind phase-shifting interferometry based on the extreme value of interference and least-squares iterative algorithm

Xu Xiaoqing, Xie Ming, Ji Ying, Wang Yawei

Optica Applicata

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2021

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Vol. 51, nr 4

513--527

EN

To improve the measuring accuracy in two-step phase-shifting interferometry (PSI), a new approach combining the extreme value of interference (EVI) and the least-squares iterative algorithm (LSIA) is proposed to extract the phase from two-frame blind phase-shifting interferograms. This method first evaluates the phase shift between two interferograms by the EVI algorithm, and then constructs the fitted interferogram by the addition of two interferograms after filtering the corresponding background intensities, so the phase with high precision can be retrieved by combining two real interferograms and this fitted interferogram using the LSIA method. The proposed algorithm expands the flexibility of the LSIA method and has the high-precision performance compared with the existing algorithms in two-step PSI. Simulation and experiment are performed to verify the feasibility of the proposed algorithm.

4

The effect of noise, a constant background, and bit depth on the phase retrieval of pure phase objects

Karitans Varis, Tokmakovs Andrejs, Antonuka Adele

Optica Applicata

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2021

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Vol. 51, nr 2

257--269

EN

In the current study, we investigate the effect of uniform white noise, Poisson noise and a constant background on the phase retrieval of pure phase objects. We also study the influence of the aforementioned factors on phase retrieval at different bit depths of intensity measurements. An algorithm called PhaseLift is used for phase retrieval as it requires a small number of modulating masks and can retrieve the phase of an object from sparse intensity measurements of low bit depth. A test object is modulated by eight random masks generated from a single mask and the phase of the object is retrieved from coded diffraction patterns. Different levels of uniform white noise, Poisson noise and constant background are superimposed on the diffraction patterns and the root-mean-square error (RMSE) of the retrieved object is calculated at each level. The results suggest that Poisson noise and a constant background at the same level cause similar RMSE compared to uniform white noise. Lowering the bit depth from 18-bits to 14-bits resulted in the decrease of the RMSE caused by Poisson noise and a constant background. We conclude that the effects of noise and constant background can be reduced by lowering the bit depth.

5

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

Chen Lung-Hui

Journal of Applied Analysis

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2021

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Vol. 27, nr 2

259--268

EN

In this paper, we discuss how to partially determine the Fourier transform F(z) = 1 ∫ −1 f(t)eizt dt, z ∈ ℂ, given the data |F(z)| or arg F(z) for z ∈ ℝ. Initially, we assume [−1, 1] to be the convex hull of the suport 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). 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.

6

Fast phase reconstruction in off-axis digital holography with zero-order term suppression

Luan Guangyu, Shan Mingguang, Zhong Zhi, Xia Bai

Optica Applicata

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2020

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Vol. 50, nr 3

425--432

EN

A fast phase reconstruction method (FPRM) employing a free-sample hologram can improve the efficiency of phase reconstruction in off-axis digital holography. However, the space-bandwidth product is still confined by spectrum aliasing in the hologram owing to the zero-order term. In this paper, we propose an FPRM that features an efficient zero-order term suppression method called the average gray that can eliminate spectrum shifting. We can implement phase reconstruction by considering both speed and the space-bandwidth product. We verified the validity of our approach for off-axis digital holography using laser and white-light illumination.

7

Deflectometry for phase retrieval using a composite fringe

Liu T., Zhou C., Liu Y, Si S, Lei Z.

Optica Applicata

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2014

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Vol. 44, nr 3

451--461

EN

An improved deflectometry for wavefront measurement using a composite fringe is proposed to reduce the projection fringes and improve the accuracy. The single composite fringe contains four fringes in different directions. It goes through the tested objects and then is captured by a CCD camera. Two high frequency orthogonal fringe patterns and two single period orthogonal fringe patterns can be obtained from the composite fringe by fast Fourier transform. The unwrapping of the wrapped phase of the high frequency fringe is accomplished by the corresponding single period fringe using a heterodyne method. The wavefront is reconstructed by the integration of partial derivatives. Using only one fringe, the proposed method is more applicable to dynamic wavefront measurement. The experimental results demonstrate that the proposed method can retrieve the complex wavefronts more accurately.

8

Dispersion error of a beam splitter cube in white-light spectral interferometry

Hlubina P., Luňáček J., Ciprian D., Chlebus R.

Opto-Electronics Review

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2008

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Vol. 16, No. 4

439-443

EN

We revealed that the phase function of a thin-film structure measured by a white-light spectral interferometric technique depends on the path length difference adjusted in a Michelson interferometer. This phenomenon is due to a dispersion error of a beam splitter cube, the effective thickness of which varies with the adjusted path length difference. A technique for eliminating the effect in measurement of the phase function is described. In a first step, the Michelson interferometer with same metallic mirrors is used to measure the effective thickness of the beam splitter cube as a function of the path length difference. In a second step, one of the mirrors of the interferometer is replaced by a thin-film structure and its phase function is measured for the same path length differences as those adjusted in the first step. In both steps, the phase is retrieved from the recorded spectral interferograms by using a windowed Fourier transform applied in the wavelength domain.