Reconstruction of missing information in diffraction patterns and holograms by iterative phase retrieval

Latychevskaia, Tatiana

doi:10.1016/j.optcom.2019.07.021

Cited by 9 publications

(3 citation statements)

References 25 publications

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“…In holography, this condition is typically fulfilled, since the area occupied by the reference wave is always larger that of the object wave [5]. In fact, some pixels in the acquired distribution can be missing, thus reducing the number of equations, and such a hologram can still be successfully reconstructed by applying iterative phase retrieval [43]. For a 2D real-valued object distribution sampled with M × M pixels, there are M 2 unknowns, and a solution can exist if M N  .…”

Section: N mentioning

confidence: 99%

Iterative phase retrieval for digital holography: tutorial

Latychevskaia

2019

J. Opt. Soc. Am. A

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101

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This paper provides a tutorial of iterative phase retrieval algorithms based on the Gerchberg-Saxton (GS) algorithm applied in digital holography. In addition, a novel GSbased algorithm that allows reconstruction of 3D samples is demonstrated. The GS-based algorithms recover complex-valued wavefront-by-wavefront back-and forth propagation between two planes with constraints superimposed in these two planes. Iterative phase retrieval allows quantitatively correct and twin-image-free reconstructions of object amplitude and phase distributions from its in-line hologram. The present work derives the quantitative criteria on how many holograms are required to reconstruct a complex-valued object distribution, be it a 2D or 3D sample. It is shown that for a sample that can be approximated as a 2D sample, a single-shot in-line hologram is sufficient to reconstruct the absorption and phase distributions of the sample. Previously, the GS-based algorithms have been successfully employed to reconstruct samples that are limited to a 2D plane. However, realistic physical objects always have some finite thickness and therefore are 3D rather than 2D objects. This study demonstrates that 3D samples, including 3D phase objects, can be reconstructed from two or more holograms. It is shown that in principle, two holograms are sufficient to recover the entire wavefront diffracted by a 3D sample distribution. In this method, the reconstruction is performed by applying iterative phase retrieval between the planes where intensity was measured. The recovered complex-valued wavefront is then propagated back to the sample planes, thus reconstructing the 3D distribution of the sample. This method can be applied for 3D samples such as 3D distribution of particles, thick biological samples, and other 3D phase objects. Examples of reconstructions of3Dobjects, including phase objects, are provided. Resolution enhancement obtained by iterative extrapolation of holograms is also discussed.

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Section: N mentioning

confidence: 99%

Iterative phase retrieval for digital holography: tutorial

Latychevskaia

2019

J. Opt. Soc. Am. A

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101

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“…The object distribution can be also reconstructed from a single in-line hologram (defocus image) by applying iterative reconstruction, as explained in detail in the literature [53,[72][73][74][75][76]. We provide only a brief summary of the reconstruction steps here.…”

Section: Single In-line Hologram and Its Reconstructionmentioning

confidence: 99%

Holography and Coherent Diffraction Imaging with Low-(30–250 eV) and High-(80–300 keV) Energy Electrons: History, Principles, and Recent Trends

Latychevskaia

2020

Materials

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In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

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“…Nanoscale applications of CDI often necessitate imaging in the low-photon regime, where measurements are highly corrupted by noise. CDI measurements are also typically lacking low-frequency data, due to the presence of a beamstop apparatus which occludes direct measurement of these values (He et al, 2015;Latychevskaia, 2019;.…”

Section: Holographic Coherent Diffraction Imaging and Phase Retrievalmentioning

confidence: 99%

Phase Retrieval with Holography and Untrained Priors: Tackling the Challenges of Low-Photon Nanoscale Imaging

Lawrence,

Barmherzig,

et al. 2020

Preprint

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Phase retrieval is the inverse problem of recovering a signal from magnitude-only Fourier measurements, and underlies numerous imaging modalities, such as Coherent Diffraction Imaging (CDI). A variant of this setup, known as holography, includes a reference object that is placed adjacent to the specimen of interest before measurements are collected. The resulting inverse problem, known as holographic phase retrieval, is well-known to have improved problem conditioning relative to the original. This innovation, i.e. Holographic CDI, becomes crucial at the nanoscale, where imaging specimens such as viruses, proteins, and crystals require low-photon measurements. This data is highly corrupted by Poisson shot noise, and often lacks low-frequency content as well. In this work, we introduce a dataset-free deep learning framework for holographic phase retrieval adapted to these challenges. The key ingredients of our approach are the explicit and flexible incorporation of the physical forward model into an automatic differentiation procedure, the Poisson log-likelihood objective function, and an optional untrained deep image prior. We perform extensive evaluation under realistic conditions. Compared to competing classical methods, our method recovers signal from higher noise levels and is more resilient to suboptimal reference design, as well as to large missing regions of low frequencies in the observations. To the best of our knowledge, this is the first work to consider a dataset-free machine learning approach for holographic phase retrieval.

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Reconstruction of missing information in diffraction patterns and holograms by iterative phase retrieval

Cited by 9 publications

References 25 publications

Iterative phase retrieval for digital holography: tutorial

Iterative phase retrieval for digital holography: tutorial

Holography and Coherent Diffraction Imaging with Low-(30–250 eV) and High-(80–300 keV) Energy Electrons: History, Principles, and Recent Trends

Phase Retrieval with Holography and Untrained Priors: Tackling the Challenges of Low-Photon Nanoscale Imaging

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