2019
DOI: 10.1364/josaa.36.000d62
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From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial

Abstract: This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is made on the connections between the numerous alternating projection strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gra… Show more

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Cited by 30 publications
(18 citation 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%
“…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%
“…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%
“…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%