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Phase reconstruction from intensity measurements in linear systems.

Martin J Bastiaans1, Kurt Bernardo Wolf

  • 1Technische Universiteit Eindhoven, Faculteit Elektrotechniek, Postbus 513, 5600 MB Eindhoven, The Netherlands. M.J.Bastiaans@tue.nl

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|June 13, 2003
PubMed
Summary

Signal phase is reconstructed using intensity profiles from two parallel screens and a canonical transform. This method generalizes Fresnel and fractional Fourier transforms for linear systems.

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Area of Science:

  • Optics and Photonics
  • Wave Propagation
  • Signal Processing

Background:

  • Reconstructing signal phase from intensity measurements is crucial in various optical and wave propagation scenarios.
  • Existing methods often rely on specific linear transformations like Fresnel or fractional Fourier transforms.

Purpose of the Study:

  • To develop a generalized method for signal phase reconstruction applicable to a broader range of linear systems.
  • To analyze the relationship between spatial frequency and signal intensity derivatives within canonical transforms.

Main Methods:

  • Utilizing intensity profiles from two closely spaced parallel planes.
  • Employing a small abcd canonical transform to connect the planes.
  • Analyzing the derivative of the signal's squared modulus with respect to the transform parameter.

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Main Results:

  • Successfully reconstructed the phase of a signal from intensity profiles.
  • Demonstrated the applicability of the method to harmonic and repulsive fibers, as well as free-space propagation.
  • Generalized previous findings for Fresnel and fractional Fourier transforms to all linear systems.

Conclusions:

  • The proposed method offers a unified approach to phase reconstruction in diverse linear optical systems.
  • The analysis provides a deeper understanding of the interplay between signal phase, intensity, and spatial frequency in canonical transformations.