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Aspherical surface construction methods based on extended Jacobi polynomials
Abstract:
We propose an aspherical surface representation based on extended Jacobi polynomials to mitigate high-order oscillations and limited edge-fitting capability encountered in conventional polynomial descriptions of large-aperture annular optical systems. By extending the orthogonal interval and introducing adjustable weighting parameters, independent control of the aperture range and fitting weights is achieved, improving numerical stability. Effective suppression of oscillations and enhanced edge-fitting accuracy are demonstrated for large and small apertures. The proposed method, applied to a refractive-reflective panoramic imaging system with a field of view of (36-98∘)×360∘, achieved a modulation transfer function above 0.5 at 60 lp/mm.
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