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    This study introduces novel super-resolution phase retrieval models for diffractive optical imaging. The new approach enhances image resolution using coded apertures, overcoming limitations of sensor-dependent methods.

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    Area of Science:

    • Diffractive Optical Imaging
    • Computational Imaging
    • Applied Optics

    Background:

    • Super-resolution phase retrieval estimates high-resolution images from low-resolution phaseless measurements in diffractive optical imaging (DOI).
    • Existing methods often rely on sensor resolution, increasing costs, and lack theoretical guarantees.
    • Current techniques typically use near and far-field measurements, limiting flexibility.

    Purpose of the Study:

    • To derive novel super-resolution models for DOI using low-resolution coded phaseless measurements at any diffraction zone.
    • To establish theoretical guarantees for solution uniqueness and explore the impact of coded aperture design on attainable resolution.
    • To develop an efficient algorithm for reconstructing high-resolution images from coded diffraction patterns.

    Main Methods:

    • Development of super-resolution models based on coded phaseless measurements applicable to any diffraction zone.
    • Theoretical analysis guaranteeing the existence and uniqueness of solutions, with probability enhanced by coded aperture design.
    • Implementation of a super-resolution phase retrieval algorithm minimizing a smoothed non-convex least-squares objective function, involving spectral approximation and iterative refinement.

    Main Results:

    • The attainable image resolution is determined by the coded aperture, not sensor limitations, offering a cost-effective solution.
    • The existence of a unique solution is guaranteed with high probability, which can be further improved through coded aperture design.
    • The proposed algorithm demonstrates superior performance compared to state-of-the-art methods in high-resolution image reconstruction.
    • Reconstruction quality is significantly enhanced using designed coded apertures over non-designed ones.

    Conclusions:

    • The proposed models and algorithm provide a robust and theoretically grounded approach to super-resolution phase retrieval in DOI.
    • Coded aperture design is a critical factor in achieving high-resolution, cost-effective imaging solutions.
    • This work advances the field by decoupling image resolution from sensor constraints and offering improved reconstruction accuracy.