Abstract

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

Maximum a posteriori estimation of wave-front slopes using a Shack–Hartmann wave-front sensor

Scott A. Sallberg, Byron M. Welsh, and Michael C. Roggemann
J. Opt. Soc. Am. A 14(6) 1347-1354 (1997)

Wave-front estimation from wave-front slope measurements

W.H. Southwell
J. Opt. Soc. Am. 70(8) 998-1006 (1980)

Characterization of atmospheric turbulence phase statistics using wave-front slope measurements

Eric E. Silbaugh, Byron M. Welsh, and Michael C. Roggemann
J. Opt. Soc. Am. A 13(12) 2453-2460 (1996)

Tip/tilt estimation from defocused images

Marcos A. van Dam and Richard G. Lane
J. Opt. Soc. Am. A 19(4) 745-752 (2002)

Wave-front phase estimation from Fourier intensity measurements

J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R. Robinson, and D. Kryskowski
J. Opt. Soc. Am. A 6(7) 1020-1026 (1989)