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Retrieval of refractive index fields in two-dimensional gradient-index elements from external deflectometry data.

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    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
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    This study develops a new method to determine the refractive index of optical elements using external beam slopes. This technique requires minimal data, enabling accurate reconstruction of complex index fields.

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    Area of Science:

    • Optical physics
    • Materials science
    • Computational optics

    Background:

    • Previous work established methods for refractive index retrieval using internal boundary slopes.
    • Determining refractive index fields in gradient-index (GRIN) elements is crucial for optical design.
    • Existing methods often require extensive data or knowledge of surface refractive indices.

    Purpose of the Study:

    • To extend refractive index field retrieval methods to utilize external boundary beam slopes.
    • To develop a technique requiring minimal additional information, such as a single known internal index point.
    • To accurately reconstruct inhomogeneous refractive index fields in optical elements.

    Main Methods:

    • Formulating the inverse problem as a linear algebraic system based on probe beam deflection.
    • Employing an iterative inversion algorithm to generate the index field.
    • Incorporating Snell's law into the system equation using surface values from tentative index reconstructions.

    Main Results:

    • The extended method successfully retrieves refractive index fields using external boundary slopes.
    • Simulations demonstrate accurate recovery of the original index profile.
    • The approach requires only beam position, slope data, and one known internal index point.

    Conclusions:

    • The developed method offers a robust and efficient way to characterize gradient-index optical elements.
    • This technique advances the non-destructive evaluation of optical materials.
    • The findings have implications for designing and manufacturing advanced optical components.