From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial

Momey, Fabien; Denis, Loïc; Thomas, O.; Fournier, Corinne

doi:10.1364/josaa.36.000d62

Cited by 26 publications

(18 citation statements)

References 68 publications

(101 reference statements)

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“…It is hard to overestimate the role of Discrete Fourier Transform (DFT) in numerical techniques used in optics, especially in areas related to Fresnel and Fraunhofer diffraction [40] that depend on the iterative use of 2D DFT. DFT is heavily used in the multiple projections methods applied in the design of diffractive elements, in deconvolution and in phase retrieval algorithms [41,42,43,44], as well as for pulse retrieval in frequency resolved optical gating etc. The best known Fast Fourier Transform (FFT) algorithm [45] is certainly most commonly used.…”

Section: Funding Informationmentioning

confidence: 99%

Far-field intensity signature of sub-wavelength microscopic objects

Bancerek,

Czajkowski,

Kotynski

2020

Preprint

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Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically depends on the level of noise. This new path to superresolution has been recently investigated with use of compressed sensing and machine learning. We demonstrate a two-stage technique based on deconvolution and genetic optimization which enables the recovery of objects with features of 1/10 of the wavelength. We indicate that l1-norm based optimization in the Fourier domain unrelated to sparsity is more robust to noise than its l2-based counterpart. We also introduce an extremely fast general purpose restricted domain calculation method for Fourier transform based iterative algorithms operating on sparse data.

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Section: Funding Informationmentioning

confidence: 99%

Far-field intensity signature of sub-wavelength microscopic objects

Bancerek,

Czajkowski,

Kotynski

2020

Preprint

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“…The concept of compressive phase retrieval was formally established by an explosion of theoretical and empirical studies following the development of compressed sensing [41][42][43]. Sparsity priors in various domains such as the spatial [44][45][46][47][48][49], gradient [50][51][52][53][54][55][56][57][58][59][60][61], wavelet [62] and other domains [63,64] or with a dictionary-learned transform [65][66][67] have been demonstrated as effective regularizers for phase recovery. More recently, implicit image priors from advanced denoisers such as BM3D [68][69][70][71][72][73] or represented by deep neural networks [74][75][76][77][78][79][80][81][82][83][84][85][86][87]…”

Section: Introductionmentioning

confidence: 99%

Iterative projection meets sparsity regularization: towards practical single-shot quantitative phase imaging with in-line holography

Gao¹,

Cao²

2023

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Holography provides access to the optical phase. The emerging compressive phase retrieval approach can achieve in-line holographic imaging beyond the information-theoretic limit or even from a single shot by exploring the signal priors. However, iterative projection methods based on physical knowledge of the wavefield suffer from poor imaging quality, whereas the regularization techniques sacrifice robustness for fidelity. In this work, we present a unified compressive phase retrieval framework for in-line holography that encapsulates the unique advantages of both physical constraints and sparsity priors. In particular, a constrained complex total variation (CCTV) regularizer is introduced that explores the well-known absorption and support constraints together with sparsity in the gradient domain, enabling practical high-quality in-line holographic imaging from a single intensity image. We developed efficient solvers based on the proximal gradient method for the non-smooth regularized inverse problem and the corresponding denoising subproblem. Theoretical analyses further guarantee the convergence of the algorithms with prespecified parameters, obviating the need for manual parameter tuning. As both simulated and optical experiments demonstrate, the proposed CCTV model can characterize complex natural scenes while utilizing physically tractable constraints for quality enhancement. This new compressive phase retrieval approach can be extended, with minor adjustments, to various imaging configurations, sparsifying operators, and physical knowledge. It may cast new light on both theoretical and empirical studies.

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“…However, as the hologram is the intensity image of the wave diffracted by the sample, the phase of the wave is not directly accessible and in-line digital holography requires numerical reconstructions that consist in a phase retrieval problem. This problem can be numerically solved by using alternating projection strategies or Inverse Problem Approaches (IPA) [5][6][7]. Even if the reconstruction of the wave is possible anywhere in the object space in in-line holographic microscopy, it is important to find a criterion that can locate a refocusing plane in a reproducible and physical meaningful way, irrespective of the method used for the reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Automatic numerical focus plane estimation in digital holographic microscopy using calibration beads

et al. 2022

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We present a new method to achieve autofocus in digital holographic microscopy. The method is based on inserting calibrated objects into a sample placed on a slide. Reconstructing a hologram using the Inverse Problems Approach makes it possible to precisely locate and measure the inserted objects and thereby derive the slide plane location. Numerical focusing can then be performed in a plane at any chosen distance from the slide plane of the sample in a reproducible manner and independently of the diversity of the objects in the sample.

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From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial

Cited by 26 publications

References 68 publications

Far-field intensity signature of sub-wavelength microscopic objects

Far-field intensity signature of sub-wavelength microscopic objects

Iterative projection meets sparsity regularization: towards practical single-shot quantitative phase imaging with in-line holography

Automatic numerical focus plane estimation in digital holographic microscopy using calibration beads

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