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Related Experiment Video

Updated: Jun 5, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
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Published on: February 12, 2014

Nonlinear phase retrieval from single-distance radiograph.

Julian Moosmann1, Ralf Hofmann, Andrei Bronnikov

  • 1Laboratorium f¨ur Applikationen der Synchrotronstrahlung Karlsruher Institut für Technologie, Postfach 6980, D-76128 Karlsruhe, Germany.

Optics Express
|December 18, 2010
PubMed
Summary

This study retrieves phase contrast from a single intensity measurement. A novel method extends phase retrieval beyond linearized equations, enabling accurate reconstruction from limited data.

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Area of Science:

  • Optics and Photonics
  • Image Reconstruction
  • Wave Physics

Background:

  • Phase contrast imaging is crucial for visualizing transparent specimens.
  • Traditional methods often require multiple measurements or complex setups.
  • Linearized Transport-of-Intensity Equation (TIE) has limitations in phase retrieval.

Purpose of the Study:

  • To develop a phase retrieval method using a single intensity contrast measurement.
  • To extend phase retrieval beyond the solutions of the linearized TIE.
  • To accurately reconstruct phase information from limited spatial frequency data.

Main Methods:

  • Expanding intensity contrast and phase shift in powers of object-detector distance.
  • Utilizing the full paraxial wave equation to determine expansion coefficients.

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Last Updated: Jun 5, 2026

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  • Formulating a local expression for the phase shift's Laplacian.
  • Applying a perturbative approach to the derived expression.

    • Main Results:

    • Phase retrieval is achieved from a single object-detector distance.
    • The method successfully retrieves phase contrast beyond the linearized TIE approximation.
    • Simulated phantom data validated the accuracy of the perturbative approach.

    Conclusions:

    • A novel, single-measurement phase retrieval technique is presented.
    • The method offers a more robust approach to phase reconstruction in optics.
    • This advancement has potential applications in various imaging modalities requiring phase information.