Date of Award


Document Type


Degree Name

Master of Science


Department of Electrical and Computer Engineering

First Advisor

Byron Welsh, PhD


Current methods for estimating the wavefront slope at the aperture of a telescope using a Hartmann wavefront sensor are based upon a centroid shift estimator. The centroid shift estimator determines the displacement, or shift, of the centroid off the optical axis using a moment calculation of the intensity distributions recorded in each subaperture. This centroid shift is proportional to the average slope of the wavefront in each subaperture. A maximum a-posteriori (MAP) slope estimator takes advantage of a-priori knowledge of the wavefront slope statistics and total irradiance falling on the subaperture detector arrays when determining the shift estimate. In order to derive a closed form solution for the MAP estimator, several assumptions were made: infinite resolution on the detector arrays, no read noise in the detection process, and no intensity spillover into adjacent subapertures. By implementing the Hartmann wavefront sensor and MAP estimator in simulation, the performance of the MAP estimator was evaluated using realizable wavefront sensor parameters. While the MAP estimator mean square error (MSE) performance decreased relative to the centroid estimator MSE performance as a result of spillover, finite detector resolution, and read noise, the MAP estimator MSE performance was found to be upper bounded by the centroid estimator MSE in all cases.

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