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    A new mathematical formula precisely calculates point source signals in imaging arrays. This involves understanding distance distributions within square domains for improved signal analysis.

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    Area of Science:

    • Optics and Imaging Science
    • Mathematical Physics

    Background:

    • Imaging arrays are crucial for detecting faint signals.
    • Accurate signal quantification is essential for data interpretation.

    Purpose of the Study:

    • To derive a closed-form expression for pixel-averaged point source signals.
    • To determine the probability distribution of squared Euclidean distances in a 2D square domain.

    Main Methods:

    • Derivation of a novel mathematical expression.
    • Analysis of probability distributions for Euclidean distances.

    Main Results:

    • A closed-form expression for pixel-averaged point source signals has been obtained.
    • The probability distribution of squared Euclidean distances within a square domain was determined.

    Conclusions:

    • The derived expression offers a precise method for analyzing point source signals.
    • This work provides a foundational mathematical tool for imaging array applications.