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    Area of Science:

    • Optics and Photonics
    • Wavefront Engineering

    Background:

    • Aberrations limit optical system performance.
    • Precise wavefront manipulation is crucial for imaging and optical metrology.

    Purpose of the Study:

    • To derive an exact analytical refractive surface for arbitrary wavefronts.
    • To achieve perfect focusing into a single image point without approximations.

    Main Methods:

    • Analytical derivation of the refractive surface equation.
    • No paraxial or numerical approximations were used.

    Main Results:

    • An exact analytical solution for the refractive surface was obtained.
    • The derived surface successfully focuses arbitrary wavefronts into a single point.
    • Performance evaluation confirmed expected results.

    Conclusions:

    • The derived analytical surface provides a method for perfect wavefront focusing.
    • This work advances the design of optical elements for aberration correction and beam shaping.