The transfer function can be determined by convolution of the pupil function over the aperture. The pupil function itself is a function of the design data of the lens system (i.e., refractive indices, radii of curvature, etc.) Of particular importance, both practically and theoretically, is the frequency response on-axis where only rotationally symmetric aberrations are present. The aberration function is obtained from an integration over the ray-trace data and is curve-fitted by Chebyschev interpolation. Unlike the least-squares method, the Chebyschev approach allows a <i>uniform</i> approximation over the interval. This data is substituted into the transfer function which is numerically evaluated by application of very high-order Gauss quadrature theory.
RICHARD BARAKAT, "Computation of the Transfer Function of an Optical System from the Design Data for Rotationally Symmetric Aberrations. Part I. Theory," J. Opt. Soc. Am. 52, 985-990 (1962)