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Short and accurate formulae for the Seidel coefficients of gradient-index lenses with arbitrary radial refractive index distributions have been obtained.
F. Bociort
"Seidel aberration coefficients for radial gradient-index lenses", Proc. SPIE 1983, 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, 19832E (26 July 1993); https://doi.org/10.1117/12.2308505
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F. Bociort, "Seidel aberration coefficients for radial gradient-index lenses," Proc. SPIE 1983, 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, 19832E (26 July 1993); https://doi.org/10.1117/12.2308505