Optical misalignment sensing and image reconstruction using phase diversity

TLDR

Segmented‑aperture telescopes, such as the Multiple‑Mirror Telescope, suffer phase errors unless segments are aligned to within a fraction of a wavelength, and real‑time coherent alignment is difficult, so images degraded by these errors are instead recorded and later restored using phase‑retrieval techniques. The authors employ Gonsalves’s phase‑diversity method to correct imagery blurred by a misaligned segmented‑aperture telescope. They record a focused and an out‑of‑focus image simultaneously, use an iterative gradient‑search algorithm to estimate the telescope’s phase error from both images, and then apply Wiener–Helstrom filtering with the retrieved phase to reconstruct the corrected image. Simulated reconstruction experiments with random piston phase errors on six segments, including noise, demonstrate that the method can recover the image.

Abstract

A segmented-aperture telescope such as the Multiple-Mirror Telescope 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 difficult to achieve in real time. An alternative is to record the images degraded by phase errors and to restore them after detection by using phase-retrieval techniques. In this paper we describe the use of Gonsalves's phase-diversity method (which was previously used to combat atmospheric turbulence) to correct imagery blurred by a misaligned segmented-aperture telescope. Two images are recorded simultaneously: 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. We refer to this technique as the method of multiple-plane measurements with iterative reconstruction. The final image is obtained by a Wiener–Helstrom filtering of the degraded image using the retrieved phase errors. The results of reconstruction experiments performed with simulated data including the effects of noise are shown for the case of random piston phase errors on each of six segments.