Image reconstruction for misaligned optics using phase diversity

Abstract

A segmented-aperture telescope such as the Multiple Mirror Telescope (MMT) will suffer from phase errors unless the segments are aligned to within a small fraction of a wavelength. Such a coherent alignment of the segments is very difficult to achieve in real time. An alternative is to record the images degraded by phase errors and restore them after detection using phase-retrieval techniques. This paper describes the use of Gonsalves’ phase-diversity method (which was previously used to combat atmospheric turbulence) to correct imagery blurred by a misaligned MMT. Two images are simultaneously recorded: the usual degraded image in the focal plane and a second degraded image in an out-of-focus plane. An iterative gradient-search algorithm finds the phase error of the telescope that is consistent with both degraded images. The final image is obtained by a Wiener-Helstrom filtering of the degraded image using the retrieved phase errors. The results of reconstruction experiments using simulated data including the effects of noise are shown for the case of random piston phase errors on each of six segments.