Aberration correction of segmented-aperture telescopes by using phase diversity

There is currently much interest in deploying large space-based telescopes for various applications including fine-resolution astronomical imaging and earth observing. Often a large primary mirror is synthesized by the precise alignment of several smaller mirror segments. Misalignment or misfigure of these segments results in phase errors which degrade the resolution of collected imagery. Phase diversity (PD) is a technique used to infer unknown phase aberrations from image data. It requires the collection of two or more images of the same object, each incorporating a known phase perturbation in addition to the unknown aberrations. Statistical estimation techniques are employed to identify a combination of object and aberrations that is consistent with all of the collected images. The wavefront-sensing performance of PD is evaluated through simulation for a variety of signal and aberration strengths. The aberrations are parameterized by piston and tilt misalignment of each segment. An unknown extended scene is imaged, complicating the estimation procedure. Since wavefront correction is often an iterative process, moderate estimation errors can be corrected by subsequent estimates. The interpretation of iterative wavefront adjustments as creating new phase-diversity channels suggests a more sophisticated processing approach, called Actuated Phase Diversity. This technique is shown to significantly improve PD wavefront-sensing performance.