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On inverse problem with phase retrieval for an inclined line in the parabolic approximation

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R.M. Feshchenko, I.A. Artyukov, A.V. Vinogradov

Numerical Analysis · Submitted 10 Apr 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed.

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arXiv ID1804.04718 (version 2)
Pith IDRXF4NJHV, Pith's permanent record of this paper and its review
CitationA.V. Vinogradov, I.A. Artyukov, R.M. Feshchenko. "On inverse problem with phase retrieval for an inclined line in the parabolic approximation." arXiv:1804.04718 (2018). https://pith.science/paper/RXF4NJHV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,299 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.79 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D parabolic equation. It is demonstrated that this inverse problem, in case when the complex image plane amplitude is known, can be reduced to a singular Cauchy type integral equation. The existence of its solutions requires that certain conditions be met but if a solution exists it is necessary unique. The obtained integral equation is then approximated piece-wisely and the resulting linear algebraic system is solved numerically while applying necessary regularization procedures to enhance the stability of its solutions. Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D parabolic equation. contribution 0.50 0.66 0.07 asserted 0.95
s1 It is demonstrated that this inverse problem, in case when the complex image plane amplitude is known, can be reduced to a singular Cauchy type integral equation. result 0.44 0.89 0.30 asserted 1.00
s2 The existence of its solutions requires that certain conditions be met but if a solution exists it is necessary unique. result 0.95 0.77 0.21 asserted 1.00
s3 The obtained integral equation is then approximated piece-wisely and the resulting linear algebraic system is solved numerically while applying necessary regularization procedures to enhance the stability of its solutions. method 1.00 0.93 0.09 asserted 1.00
s4 Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed. contribution 0.63 0.95 0.17 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.80 · evidence from simulation or computation 0.60.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D parabolic equation. It is demonstrated that this inverse problem, in case when the complex image plane amplitude is known, can be reduced to a singular Cauchy type integral equation. The existence of its solutions requires that certain conditions be met but if a solution exists it is necessary unique. The obtained integral equation is then approximated piece-wisely and the resulting linear algebraic system is solved numerically while applying necessary regularization procedures to enhance the stability of its solutions. Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed.

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