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Relating wavefront error, apodization, and the optical transfer function: general case.

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    This study generalizes a method to decompose the optical transfer function (OTF) using basis functions, enabling analysis of arbitrary wavefront errors and apodization for improved optical system characterization.

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    Area of Science:

    • Optics and Optical Engineering
    • Image Science and Systems

    Background:

    • A previous method decomposed the incoherent optical transfer function (OTF) into basis functions.
    • The prior technique was limited to rotationally symmetric wavefront errors and apodization.

    Purpose of the Study:

    • To generalize the OTF decomposition technique for arbitrary wavefront errors and apodization.
    • To provide analytic expressions for the new basis functions.

    Main Methods:

    • Developed a generalized mathematical framework for OTF decomposition.
    • Derived analytic expressions for basis functions applicable to non-rotationally symmetric cases.
    • Demonstrated the technique with an example expansion.

    Main Results:

    • The generalized technique successfully decomposes OTFs with arbitrary wavefront errors and apodization.
    • Analytic expressions for the basis functions were derived.
    • An example expansion validated the generalized approach.

    Conclusions:

    • The generalized OTF decomposition method enhances the analysis of optical systems with complex aberrations and pupil functions.
    • This technique offers a more comprehensive tool for optical system characterization and performance evaluation.