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    This summary is machine-generated.

    This study introduces a model-free method to accurately correct vignetting distortion in star-sky images from large telescopes. The technique enhances image quality without needing complex optical system parameters.

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    Area of Science:

    • Astronomy
    • Image Processing
    • Optical Engineering

    Background:

    • Vignetting distortion is a common issue in large-aperture optical systems.
    • Accurate modeling of complex optical systems is challenging.
    • Existing vignetting correction methods often rely on detailed optical models.

    Purpose of the Study:

    • To develop a robust, model-free method for determining the vignetting function from single star-sky images.
    • To correct vignetting distortion without prior knowledge of the optical system's parameters.
    • To improve the accuracy of vignetting correction for astronomical images.

    Main Methods:

    • A model-free approach utilizing a polynomial regular term within the expectation-maximization algorithm.
    • Application of the method to single star-sky images.
    • Validation using real-world data from a 2-m telescope.

    Main Results:

    • Successfully determined the vignetting function from single images.
    • Achieved accurate vignetting distortion correction without an optical model.
    • Demonstrated superior accuracy compared to prior single-image vignetting correction techniques.

    Conclusions:

    • The proposed model-free method provides an effective solution for vignetting correction in large-aperture optical systems.
    • This technique offers a significant advancement for astronomical image processing.
    • The method's accuracy was validated on real observational data.