Adaptive Periodic-Correlation Algorithm for Shack-Hartmann Wavefront Sensing
- Created: Monday, 31 March 2014
- NASA’s Jet Propulsion Laboratory, Pasadena, California
Conventional Shack-Hartmann Wavefront Sensing requires a point source such as a star to perform wavefront sensing. This software allows one to conduct such sensing using an extended-scene or scene-based image. The software allows a Shack-Hartmann Wavefront Sensor (SH-WFS) to be used with an extended scene. It estimates the shift between the positions of a reference and test extended-scene sub-images or cells.
It runs a series of six steps:
- It determines the centers of all of the sub-images, and stores these x and y positions in a [2×Ncell] matrix. Usually, the centroids of the point-source spot-images measured in the same system can serve this purpose.
- It chooses an N×N-pixels subaperture, S(x,y), within each sub-image with the x and y positions determined in step 1 as its center, where N is preferentially a power of two for this algorithm (e.g., N=32). Such a subaperture is referred to as a test cell. It also chooses one M×M-pixels reference cell, r(x,y), preferably near the center of the whole extended scene image, where M<N is preferentially also a power of two (e.g., M=16).
- It calculates the cross-correlation (CC) of r(x,y) and s(x,y), where s(x,y) is the central M×M-pixels portion of S(x,y), using FFT (fast Fourier transform). It determines the location of the CC-peak by fitting a quadratic curve to three points near and including the CC-peak in the xdirection, and doing the same in the y-direction. This is done analytically since there are three data for three unknown parameters in such a fit.
- It shifts the test cell S(x,y)by the amount determined in the previous step to match it with the reference cell.
- It repeats Steps 3 and 4 in an iteration loop, while accumulating the sub-image offsets dx and dy between the test and the reference cells, until a maximum iteration number is reached or the incremental change in sub-image offset becomes smaller than a pre-determined tolerance.
- It repeats Steps 2 to 5 for all of the test cells.
This work was done by Erkin Sidick of Caltech for NASA’s Jet Propulsion Laboratory.
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Adaptive Periodic-Correlation Algorithm for Shack-Hartmann Wavefront Sensing (reference NPO-48003) is currently available for download from the TSP library.
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