Abstract

A phased-array telescope will suffer from phase errors unless the subtelescopes are mutually aligned to within a small fraction of a wavelength. In this presentation we describe the use of Gonsalves' phase-diversity method to sense misalignments in a phased-array telescope. The technique requires the simultaneous collection of two images. The first is the conventional focal-plane image that has been degraded by the unknown misalignments. The second image is collected in an out-of-focus plane so that there is an additional (known) degradation due to defocus. Conventional nonlinear optimization methods are employed to estimate misalignment parameters that are consistent with both degraded images. One of the dangers of nonlinear optimization is the possibility of entrapment by local minima, which are known to exist in the phase-diversity objective function. An extensive Monte Carlo simulation was performed to quantify the probability of undesirable entrapment for a particular phased-array telescope. The results suggest that the probability of convergence to within a prescribed tolerance is large.

© 1992 Optical Society of America