This paper demonstrates how to derive analytical expressions for aberration coefficients for refraction at curved interfaces between rotationally symmetric gradient-index (GRIN) media. The expansion formulas are encoded using the Lie algebraic method. Previous results about aberrations during propagation in GRIN media can be readily combined with the formulas in this paper and allow us to completely describe ray paths through rotationally symmetric inhomogeneous media with curved end-surfaces. The presented aberration coefficients are used to optimize the front surface of a focusing GRIN rod together with its refractive index parameters with promising results.
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Barion et al. (2024) studied this question.
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