Extreme shearing interferometry: theoretical limits with practical consequences

In this work we analyze the frequency response, the spatial distribution and continuity of the recovered phase in Lateral Shearing Interferometry (LSI). This frequency content and topology of the recovered phase is analyzed for the forward LSI operator as well as its inverse LSI operator using one, two, or n two-dimensional sheared interferograms. The spatial frequency response of the shearing interferometer is well known and for the reader's convenience, it is briefly revisited in a new perspective. It is however less well-known and more interesting to analyze the spatial distribution of the sheared data as well as the spatial topology of the recovered phase produced by some inverse LSI operators. Also we define a useful space of functions S with the property that any sheared data available, along any direction, may be used to recovered a smooth continuous phase with the bonus property of fully covering the pupil of the wavefront being tested. These combined aspects allow us to find the best possible wave-front reconstruction from the available sheared data using one, two or n sheared interferograms.