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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Beam Physics

    Background:

    • The point spread function (PSF) is crucial for understanding optical system performance.
    • Traditional optical systems have limitations in real-time image manipulation and beam generation.

    Purpose of the Study:

    • To analyze the PSF of a 4f optical system using a spatially variable half-wave plate.
    • To explore the system's capability for performing radial Hilbert transforms for image processing.
    • To investigate the generation of vector beams with arbitrary configurations.

    Main Methods:

    • Utilized a spatially variable half-wave plate as a spatial filter in a 4f optical system.
    • Conducted theoretical analysis and experimental verification.
    • Employed a polarization analyzer for selective edge enhancement.

    Main Results:

    • Identified the PSF as an elementary vector beam.
    • Demonstrated the system's ability to perform a radially symmetric Hilbert transform.
    • Achieved selective 2D edge enhancement of input images.
    • Showcased real-time generation of arbitrary vector beams.

    Conclusions:

    • The 4f optical system with a spatially variable half-wave plate offers a versatile platform for advanced image processing.
    • The system facilitates selective edge enhancement and dynamic vector beam generation.
    • This approach provides a convenient method for manipulating optical information in real time.