In this paper we demonstrate that the amplitude and phase of the
principle eigenfunction for the pupil-plane mutual intensity
can be used to specify a beam that concentrates its intensity
at the brightest point on the target in a target-in-the-loop system with a spatially incoherent reflected field. In addition, we discuss two methods for beam control: a method for which the beam amplitude and phase are determined as the principle eigenfunction for the measured (but incomplete) pupil-plane mutual intensity; and a method for which the beam amplitude and phase are determined to maximize a window-based image-plane sharpness measure. We demonstrate that the two methods are similar, and that both result in beams that correspond to the principle eigenfunction for an apodized mutual intensity function.
In this paper we consider the optimal coherence for beam propagation through random media. First, we demonstrate that a beam that maximizes the average receiver intensity is fully coherent, and that the upper bounds on received intensity are nearly attained by a beam that is focused for clear air. Second, we demonstrate that a beam that maximizes the scintillation index (along with other criteria that trade-off the mean and standard deviation for the received intensity) is, in general, partially coherent. We conclude with an example in which modal intensities are optimized for a beam that is constructed from Hermite-Gaussian modes.