Phase retrieval from one or more intensity measurements is a potential
ly powerful and appealing technique for real-time adaptive-optics wave
-front sensors. Under the assumption of small wave-front phase excursi
ons, one is able to derive an exact solution to the inverse problem gi
ven three or more intensity measurements with known phase offsets. App
lications include a high-order wave-front sensor to correct for residu
al aberrations in an adaptive-optics system in tandem with a low-resol
ution Hartmann-Shack wave-front sensor. The formula can also furnish m
athematical insights into the full nonlinear phase-retrieval task. (C)
1998 Optical Society of America.