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    Area of Science:

    • Optical engineering
    • Computational physics

    Background:

    • Zernike polynomials are standard for optical performance prediction.
    • Numerical methods offer an alternative for optical surface analysis.

    Purpose of the Study:

    • To introduce and validate a numerical iterative method for predicting optical mirror performance.
    • To assess the efficiency and applicability of the iterative method across different mirror shapes.

    Main Methods:

    • Iterative application of rotation transformation and paraboloid graph subtraction.
    • Finite Element Method (FEM) used for surface deformation analysis.
    • Removal of piston, tip, tilt, and defocus aberrations.

    Main Results:

    • The iterative method achieved results comparable to Zernike polynomial fitting for a 30 cm concave circular mirror.
    • The computational time for the iterative method was significantly faster.
    • The method successfully visualized deformation maps for a concave square mirror, demonstrating shape independence.

    Conclusions:

    • The numerical iterative method provides an efficient and accurate alternative to Zernike polynomials for optical performance prediction.
    • This method is versatile and applicable to various mirror aperture shapes.
    • The speed and accuracy make it suitable for complex optical system analysis.