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Fast and accurate computation of normalized Bargmann transform.

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    |January 7, 2017
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    Summary
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    This study normalizes the Bargmann transform for optical systems, enabling bounded analysis near infinity. New computational methods are proposed for this normalized transform and its inverse.

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    Area of Science:

    • Optics and Photonics
    • Signal Processing
    • Mathematical Physics

    Background:

    • The complex linear canonical transform (LCT) models wave propagation in optical systems.
    • The Bargmann transform is a specific type of complex LCT.
    • Existing Bargmann transform formulations can be unbounded.

    Purpose of the Study:

    • To normalize the Bargmann transform for boundedness near infinity.
    • To establish relationships between the normalized Bargmann transform and other integral transforms.
    • To develop efficient computational methods for the normalized Bargmann transform.

    Main Methods:

    • Normalization of the Bargmann transform.
    • Derivation of relationships to Gabor transform, Hermite-Gaussian functions, gyrator transform, and 2D nonseparable LCT.
    • Development of fast and accurate computational algorithms.

    Main Results:

    • A normalized Bargmann transform that is bounded near infinity.
    • Established connections between the normalized Bargmann transform and related mathematical tools.
    • Proposed novel computational techniques for the normalized Bargmann transform and its inverse.

    Conclusions:

    • The normalized Bargmann transform offers a more robust framework for optical system analysis.
    • The derived relationships facilitate a deeper understanding of these integral transforms.
    • The proposed computational methods enhance the practical applicability of the normalized Bargmann transform.