Linear algorithms for phase retrieval in the Fresnel region. 3. Validity conditions

T. E. Gureyev, Ya I. Nesterets

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2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)394-399
Number of pages6
JournalOptics Communications
Publication statusPublished - 15 Dec 2017


  • Fresnel diffraction
  • Phase contrast
  • Phase retrieval
  • X-ray imaging

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