Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear algorithms for phase retrieval in the Fresnel region: validity
  conditions   We describe the relationship between different forms of linearized
expressions for the spatial distribution of intensity of X-ray projection
images obtained in the Fresnel region. We prove that under the natural validity
conditions some of the previously published expressions can be simplified
without a loss of accuracy. We also introduce modified validity conditions
which are likely to be fulfilled in many relevant practical cases, and which
lead to a further significant simplification of the expression for the
image-plane intensity, permitting simple non-iterative linear algorithms for
the phase retrieval.

13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th