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    This study provides a formula for the average overlap area between a blur spot and a square pixel. This is crucial for improving the accuracy of detecting faint point sources in imaging systems.

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    Area of Science:

    • Image processing
    • Computational imaging
    • Optical engineering

    Background:

    • Accurate point source detection is vital in various scientific fields.
    • Blurring is an inherent challenge in image acquisition.
    • Understanding blur-pixel intersection is key to mitigating its effects.

    Purpose of the Study:

    • To derive a mathematical expression for the average intersection area between a circular blur spot and a square pixel.
    • To analyze the implications of this derived expression for point source detection algorithms.

    Main Methods:

    • Derivation of an analytical expression for the average area of intersection.
    • Uniform probability distribution assumption for the blur center within the pixel.

    Main Results:

    • An explicit formula for the average intersection area was obtained.
    • The derived expression quantifies the impact of blur radius and pixel size on signal overlap.

    Conclusions:

    • The results offer a quantitative basis for optimizing point source detection strategies.
    • This work contributes to improved signal-to-noise ratio and detection sensitivity in imaging applications.