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    This study introduces overlapped Fourier coding (OFC), a new imaging method that enhances camera resolution and recovers sample phase information from multiple snapshots. OFC computationally corrects optical imperfections for improved imaging quality.

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    Area of Science:

    • Optical imaging
    • Computational photography
    • Phase retrieval

    Background:

    • Traditional imaging systems face limitations in resolution and are susceptible to optical aberrations.
    • Phase information retrieval is crucial for various imaging applications but often requires specialized setups.

    Purpose of the Study:

    • To develop a novel imaging procedure that simultaneously enhances spatial resolution and retrieves phase information.
    • To overcome inherent optical imperfections in imaging systems computationally.

    Main Methods:

    • Introduced overlapped Fourier coding (OFC), a technique using a spatial light modulator to digitally pan a small aperture across the camera's pupil plane.
    • Acquired a sequence of low-resolution images at different aperture locations.
    • Developed an OFC algorithm to fuse these images into a full-resolution complex optical field estimate.
    • Employed simulated annealing to computationally estimate and remove optical aberrations and system misalignments using data redundancies.

    Main Results:

    • Achieved a full-resolution estimate of the complex optical field incident upon the detector.
    • Successfully computationally corrected for unknown optical aberrations and system misalignments.
    • Demonstrated enhanced imaging resolution by overcoming optical imperfections.

    Conclusions:

    • Overlapped Fourier coding (OFC) offers a powerful approach to computationally improve imaging performance.
    • The technique enables simultaneous resolution enhancement and phase retrieval at the cost of requiring multiple snapshots.
    • OFC provides a method to mitigate the impact of optical imperfections in imaging systems.