Abstract

A theoretical investigation of spatial coherence effects on imaging concentrators is conducted and a design procedure is developed for providing the best concentration of light on an array of detectors using a passive imaging system. Optical field coherence is characterized by the cross-spectral density (CSD) function of the light in the pupil which may be expressed as a correlation of individual frequency (wavelength) components in the space-frequency domain.¹ Using ratio of encircled energy and absolute encircled energy measures as criteria for concentrator performance, we develop design procedures which specify those passive pupil screens (apodizers) which provide optimal light concentration in conditions of arbitrary spatial coherence in the pupil. Our apodizer specifications require solving a homogeneous Fredholm equation of the second kind similar to that encountered in resonator mode calculations, where the integral kernel for the coherent field case is replaced with a multiplicatively perturbed kernel involving the pupil field CSD function. Numerical results for various pupil CSD functions and concentrator detector geometries confirm the validity of our design technique and indicate the range of pupil field coherence conditions over which concentrator performance will be improved through apodization.

© 1985 Optical Society of America