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The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
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Fourier processing with partially coherent fields.

Taco D Visser, Govind P Agrawal, Peter W Milonni

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    Fourier signal processing is generalized for partially coherent fields. Spatial filtering in a 4f system tunes beam coherence, controlling directionality, spectrum, and polarization.

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    Area of Science:

    • Optics and Photonics
    • Signal Processing

    Background:

    • Partially coherent light sources are crucial in various optical applications.
    • Understanding and controlling the coherence properties of light is essential for advanced optical systems.

    Purpose of the Study:

    • To generalize Fourier signal processing techniques for partially coherent fields.
    • To investigate how optical systems modify and control the coherence properties of light beams.

    Main Methods:

    • Application of standard coherence theory to analyze beam focusing.
    • Utilizing a 4f imaging system with spatial filtering in the Fourier plane.

    Main Results:

    • Focusing a partially coherent beam with a lens alters its coherence properties.
    • Spatial filtering enables tuning of beam coherence, directionality, spectrum, and polarization.

    Conclusions:

    • Fourier signal processing can be effectively extended to partially coherent light.
    • 4f imaging systems offer a method to manipulate beam characteristics by controlling coherence.