| Methods are developed for estimating aberrations on the elements of a two-element optical system based on knowledge of the input and output fields. The equation is written for the propagation of a scalar, quasi-monochromatic field through the system, and the output field is assumed measurable at a given plane. The resulting convolution integral contains the unknown aberration functions in the integrand. The integral equation is a Fredholm equation of the first kind, and the integrand is a nonlinear function of the aberrations. The integral is completed by the method of stationary phase. Methods for estimating the aberration functions are developed, and the effects of noisy measurements are considered. A computerized algorithm that will estimate the Fourier coefficients of the aberration functions is demonstrated for a simple deconvolution problem. |
