Suppressing anomalous localized waffle behavior in least-squares wavefront reconstructors

A major difficulty with wavefront slope sensors is their insensitivity to certain phase aberration patterns, the classic example being the waffle pattern in the Fried sampling geometry. As the number of degrees of freedom in AO systems grows larger, the possibility of troublesome waffle-like behavior over localized portions of the aperture is becoming evident. Reconstructor matrices have associated with them, either explicitly or implicitly, an orthogonal mode space over which they operate, called the singular mode space. If not properly preconditioned, the reconstructor's mode set can consist almost entirely of modes that each have some localized waffle-like behavior. In this paper we analyze the behavior of least-squares reconstructors with regard to their mode spaces. We introduce a new technique that is successful in producing a mode space that segregates the waffle-like behavior into a few "high order" modes, which can then be projected out of the reconstructor matrix. This technique can be adapted so as to remove any specific modes that are undesirable in the final recontructor (such as piston, tip, and tilt for example) as well as suppress (the more nebulously defined) localized waffle behavior.