From subperiodic to low cardinality quadrature formulas for noncircular pupils
نویسندگان
چکیده
We discuss numerical integration formulas with polynomial exactness for noncircular pupils, based on subperiodic trigonometric Gaussian quadrature and compression of discrete measures. Such formulas can be useful in optical design (numerical ray-tracing in obscured and vignetted pupils for accurate spot size computation), and in optical diffraction theory under conditions of partial coherence (Hopkins’ 3circle integrals, trasmission cross coefficients (TCC) computation).
منابع مشابه
Product Gaussian quadrature on circular lunes
Resorting to recent results on subperiodic trigonometric quadrature, we provide three product Gaussian quadrature formulas exact on algebraic polynomials of degree n on circular lunes. The first works on any lune, and has n+O(n) cardinality. The other two have restrictions on the lune angular intervals, but their cardinality is n/2 +O(n). 2000 AMS subject classification: 65D32.
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