Iterative phase retrieval in coherent diffractive imaging: practical issues

Latychevskaia, Tatiana

doi:10.1364/ao.57.007187

Cited by 62 publications

(40 citation statements)

References 37 publications

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“…As a result, research in this field is still active and new approaches are often proposed. In the past 30 decades, it has benefited from many practical improvements [6,10,11,13,49] and theoretical studies [9,41,50]. Recent approaches include new constraint enforcement strategies using sparsity constraints in the object or data spaces [51,52] or in the wavelets domain [16,53] .…”

Section: Fienup's Alternating Projections Strategiesmentioning

confidence: 99%

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

Momey¹,

Denis²,

Thomas³

et al. 2019

J. Opt. Soc. Am. A

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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 gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projection techniques to the inverse problems formulation is straightforward and advantageous.

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Section: Fienup's Alternating Projections Strategiesmentioning

confidence: 99%

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

Momey¹,

Denis²,

Thomas³

et al. 2019

J. Opt. Soc. Am. A

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“…A CDI experiment is prepared in such a way that the oversampling condition is fulfilled, and a certain oversampling ratio is achieved [12,13]. The extent of the reconstructed area 00 SS  is provided from the Fourier transform:…”

Section: Oversampling Condition and "Missing" Intensity Valuesmentioning

confidence: 99%

“…The diffraction patterns were simulated and reconstructed as described in detail in [12], here we provide the main details.…”

Section: Simulated Examplesmentioning

confidence: 99%

“…Although the correct information in these pixels is missing, it can be recovered during the iterative phase retrieval reconstruction procedure. It has been noted that although the acquired intensity distribution may be incomplete, or in other words have missing intensity values, a good quality reconstruction of the object can still be achieved [6,12]. This study attempts to answer the question of how much information can be missing from the acquired diffraction pattern or hologram so that the imaged object can be still reconstructed without error by using conventional iterative phase retrieval algorithms.…”

Section: Introductionmentioning

confidence: 99%

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

Latychevskaia

2019

Optics Communications

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It is demonstrated that an object distribution can be successfully retrieved from its diffraction pattern or hologram, even if some of the measured intensity samples are missing. The maximum allowable number of missing values depends on the linear oversampling ratio , where the higher the value of , the more intensity samples can be missing. For a real-valued object, the ratio of missing pixels to the total number of pixels should not exceed (1 -2/ 2 ) or (1 -1/ 2 ) in the acquired diffraction pattern or hologram, respectively. For example, even 5% of the measured intensity values at an oversampling ratio of  = 8 are sufficient to simultaneously retrieve the object distribution and the missing intensity values. It is important that the missing intensity values should not be concentrated in the centre, but should be randomly distributed over the acquired diffraction pattern.

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“…Here, the diffraction pattern     2 00 F I k k  was simulated by solving the analytical integral for far-field diffraction as given by Eq. (5), without applying fast Fourier transform (FFT) to avoid wrapping effects [27]. The diffraction pattern shown in Fig.…”

Section: Fiber Diffraction Imaging (Fdi)mentioning

confidence: 99%

Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval

Latychevskaia¹,

Fink²

2018

Opt. Express

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Coherent diffraction imaging (CDI) allows the retrieval of the structure of an isolated object, such as a macromolecule, from its diffraction pattern. CDI requires the fulfilment of two conditions: the imaging radiation must be coherent and the object must be isolated. We discuss that it is possible to directly retrieve the molecular structure from its diffraction pattern which was acquired neither with coherent radiation nor from an individual molecule, provided the molecule exhibits periodicity in one direction, as in the case of fiber diffraction. We demonstrate that by applying iterative phase retrieval methods to a fiber diffraction pattern, the repeating unit, that is, the molecule structure, can directly be reconstructed without any prior modeling. As an example, we recover the structure of the DNA double helix in three-dimensions from its two-dimensional X-ray fiber diffraction pattern, Photograph 51, acquired in the famous experiment by Raymond Gosling and Rosalind Franklin, at a resolution of 3.4 Å.

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Iterative phase retrieval in coherent diffractive imaging: practical issues

Cited by 62 publications

References 37 publications

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

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

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

Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval

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