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    This study introduces overall comparison optimization (OCO) to efficiently design freeform phase diffractive optical elements. The novel method simplifies ray mapping as a quadratic assignment problem (QAP), accelerating convergence and reducing computational load for complex illumination patterns.

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    Area of Science:

    • Optics and Photonics
    • Computational Physics

    Background:

    • Designing freeform phase diffractive optical elements is computationally intensive.
    • Existing methods often rely on complex differential equations or numerous iterative calculations.

    Purpose of the Study:

    • To propose a novel, efficient method for designing freeform phase diffractive optical elements.
    • To accelerate the convergence of the cost function in the design process.

    Main Methods:

    • Introduced overall comparison optimization (OCO) for fast cost function convergence.
    • Framed the design of freeform phase diffraction optics as a quadratic assignment problem (QAP).
    • Simplified ray mapping calculations in geometric optics to a QAP.

    Main Results:

    • OCO ensures rapid progression of the cost function in the non-negative direction.
    • The proposed approach significantly reduces computational burden and accelerates design convergence.
    • Simulations demonstrated swift realization of complex illumination patterns using OCO-constructed holographic masks.

    Conclusions:

    • The OCO method offers a computationally efficient solution for designing freeform phase diffractive optical elements.
    • The approach shows good performance for complex illumination tasks.
    • Findings are extendable to phase-only holography and freeform surface illumination design.