An exact formulation of a filter for rotations in phase gradients and its applications to wavefront reconstruction problems

A non-singular and explicit method of constructing a filter exactly for the rotational gradient vector is shown. Such a filter is expected to be useful in phase reconstruction and related problems in adaptive optics with Hartmann sensors. In the deduction of this method, great care is taken in the arrangement of coordinates in order to make the mathematical implementation exact and consistent. The most notable consequence of the deduction is that, after the rotation is eliminated on coordinates shifted a half-period from the original, integral paths should once more be shifted a half-period from the centre of rotations to obtain a consistent wavefront reconstruction. Differences from conventional least methods are shown with experimental results. This formula would be effective for accurate decomposition of the rotation component, which is useful for phase reconstruction and related problems.