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Algorithm for Wavefront Sensing Using an Extended Scene
 Created: Wednesday, 01 October 2008
The restriction to a point source has been removed.
A recently conceived algorithm for processing image data acquired by a ShackHartmann (SH) wavefront sensor is not subject to the restriction, previously applicable in SH wavefront sensing, that the image be formed from a distant star or other equivalent of a point light source. That is to say, the image could be of an extended scene. (One still has the option of using a point source.) The algorithm can be implemented in commercially available software on ordinary computers.
The steps of the algorithm are the following:
 Suppose that the image comprises M subimages. Determine the x,y Cartesian coordinates of the centers of these subimages and store them in a 2×M matrix.
 Within each subimage, choose an N×Npixel cell centered at the coordinates determined in step 1. For the ith subimage, let this cell be denoted as s_{i}(x,y). Let the cell of another subimage (preferably near the center of the whole extendedscene image) be designated a reference cell, denoted r(x,y).
 Calculate the fast Fourier transforms of the subsubimages in the central N’×N’ portions (where N’ < N and both are preferably powers of 2) of r(x,y) and s_{i}(x,y).
 Multiply the two transforms to obtain a crosscorrelation function C_{i}(u,ν), in the Fourier domain. Then let the phase of C_{i}(u,ν) constitute a phase function, Φ(u,ν).
 Fit u and ν slopes to Φ(u,ν) over a small u,ν subdomain.
 Compute the fast Fourier transform, S_{i}(u,ν) of the full N×N cell s_{i}(x,y). Multiply this transform by the u and ν phase slopes obtained in step 4. Then compute the inverse fast Fourier transform of the product.
 Repeat steps 4 through 6 in an iteration loop, cumulating the u and ν slopes, until a maximum iteration number is reached or the change in image shift becomes smaller than a predetermined tolerance.
 Repeat steps 4 through 7 for the cells of all other subimages.
This work was done by Erkin Sidick, Joseph Green, Catherine Ohara, and David Redding of Caltech for NASA’s Jet Propulsion Laboratory.
The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 3952322. Refer to NPO44770.
This Brief includes a Technical Support Package (TSP).
Algorithm for Wavefront Sensing Using an Extended Scene (reference NPO44770) is currently available for download from the TSP library.
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