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    This study presents a novel, simple, and exact numerical method for reconstructing gradient-index (GRIN) media from light ray paths. The technique leverages system symmetries and invariants for robust 3D GRIN distribution derivation.

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    Area of Science:

    • Optics
    • Photonics
    • Applied Physics

    Background:

    • Ray tracing in gradient-index (GRIN) media is well-established.
    • The inverse problem of determining GRIN from ray paths is challenging.
    • Existing methods for GRIN reconstruction vary in complexity.

    Purpose of the Study:

    • To introduce a new, simplified method for deriving symmetric GRIN distributions.
    • To provide an exact numerical solution based on physical principles.
    • To demonstrate the method's robustness in reconstructing GRIN from ray paths.

    Main Methods:

    • Utilizing invariants derived from system symmetries and Fermat's principle.
    • Developing an exact numerical approach, avoiding physical system approximations.
    • Applying the method to reconstruct known GRIN media from 2D and 3D ray data.

    Main Results:

    • A novel, straightforward method for GRIN reconstruction is presented.
    • The method is exact and numerically robust.
    • Successful reconstruction of various symmetric GRIN media was achieved.

    Conclusions:

    • The proposed method offers the simplest implementation for deriving symmetric GRIN distributions to date.
    • The invariant-based approach provides an exact and robust solution for GRIN reconstruction.
    • This technique is effective for both 2D and 3D ray propagation scenarios.