Zonal processing of Hartmann or Shack–Hartmann patterns

Instead of measuring the wavefront deformations, Hartmann and Shack–Hartmann tests, we measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this paper, we describe a proposed new zonal procedure. This method finds a different analytical expression for each square cell formed by four sampling points in the pupil of the system. In this manner, a full single analytical expression for the wavefront is not obtained. The advantage is that small localized errors that cannot be adjusted by a single polynomial function can be represented with this method. A second advantage is that the analytical function for each cell is obtained in an exact manner, without the errors in a trapezoidal integration.