Extrapolation, interpolation, and identification of spots in Hartmann patterns

Based on Fourier analysis, we propose a simple method to extrapolate spots outside an aperture that bounds a Hartmann pattern, and interpolate spots in those regions where some spots are lost or damaged. It allows us to smoothen or remove the discontinuities of the wavefront slopes at the border of the aperture or in those inner regions where some spots are lost. The method changes the spot pattern by a fringe pattern. The extrapolated or interpolated spots are obtained from the intersection of the fringe maxima. The fringe pattern is also used to identify the spots, and it is particularly useful in highly distorted Hartmann patterns. Experimental results show how the method works.