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Geometrical optics and optimal transport.

Jacob Rubinstein, Gershon Wolansky

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |October 17, 2017
    PubMed
    Summary

    The Fermat principle is extended to ray systems, revealing multiple solutions for light

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    Area of Science:

    • Optics
    • Mathematical Physics

    Background:

    • The Fermat principle describes light's path as minimizing travel time.
    • Understanding wave propagation from intensity measurements is crucial in optics.

    Purpose of the Study:

    • Generalize the Fermat principle for ray systems.
    • Investigate the uniqueness of solutions in the phase retrieval problem from intensity data.

    Main Methods:

    • Generalized Fermat principle for systems of rays.
    • Analysis of canonical functionals and stationary points.
    • Investigation of caustic structures.

    Main Results:

    • Ray mappings compatible with intensity data are stationary points of a canonical functional.
    • Demonstrated at least two distinct stationary points exist.
    • Identified inherent multiplicity of solutions in geometrical optics phase retrieval.

    Conclusions:

    • The phase from intensity problem in geometrical optics is inherently multi-valued.
    • The generalized Fermat principle provides a framework for analyzing these multiple solutions.
    • Caustic structures are linked to the multiplicity of solutions.

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