The conventional way of measuring the average slope of the phase of a wave front is from the centroid of the image formed at the focal plane. We show the limitations of using the centroid and present an optimal estimator along with the derivation of its lower error bound for a diffraction-limited image. The method is extended to slope estimation in the case of a random aberration introduced by atmospheric turbulence. It was found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the minimum mean-square-error estimator instead of the centroid.
© 2000 Optical Society of America
Original Manuscript: August 3, 1999
Revised Manuscript: March 23, 2000
Manuscript Accepted: March 23, 2000
Published: July 1, 2000
Marcos A. van Dam and Richard G. Lane, "Wave-front slope estimation," J. Opt. Soc. Am. A 17, 1319-1324 (2000)