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Spatial sub-Rayleigh imaging analysis via speckle laser illumination.

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    This study demonstrates a breakthrough in optical imaging beyond the Rayleigh limit using first-order intensity measurements with speckle laser illumination. High-order algorithms, while achieving sub-Rayleigh imaging for binary objects, distort gray objects, revealing limitations in their underlying physics.

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    Area of Science:

    • Optics
    • Imaging Science
    • Photonics

    Background:

    • Optical sub-Rayleigh imaging offers significant potential across various scientific and technological fields.
    • Existing high-order correlation imaging algorithms can achieve sub-Rayleigh resolution but are limited to binary objects.

    Purpose of the Study:

    • To investigate and demonstrate a method for achieving optical imaging beyond the Rayleigh limit.
    • To analyze the limitations of high-order correlation algorithms in sub-Rayleigh imaging.
    • To explain the physical principles governing high-order correlation imaging.

    Main Methods:

    • Confining the divergence of the optical field.
    • Controlling the size of the illumination source.
    • Utilizing first-order averaged intensity measurement with speckle laser illumination.
    • Analyzing the cross-correlation function for high-order algorithms.

    Main Results:

    • A breakthrough beyond the Rayleigh limit was achieved using first-order averaged intensity measurements.
    • High-order algorithms using autocorrelation functions were found to be limited to binary objects, causing image distortion for gray objects.
    • The cross-correlation function was identified as a key element in the physics of high-order algorithms.

    Conclusions:

    • First-order averaged intensity measurements offer a viable path for sub-Rayleigh optical imaging.
    • The limitations of high-order algorithms stem from their reliance on specific correlation functions.
    • Understanding the role of the cross-correlation function is crucial for advancing high-order imaging techniques.