P. Hickson, WAVE-FRONT CURVATURE SENSING FROM A SINGLE DEFOCUSED IMAGE, Journal of the Optical Society of America. A, Optics, image science,and vision., 11(5), 1994, pp. 1667-1673
The possibility of sensing the curvature and the slope of a distorted
wave front from a single defocused star image is investigated. The sug
gested technique is similar to the differential curvature-sensing meth
od of Roddier [R&D note 87-3 (National Optical Astronomy Observatories
, Tucson, Ariz., 1987)] but uses only a single sensor at a point eithe
r before or after the focus. The signal-to-noise ratio that is achieva
ble with such a sensor is ultimately limited by atmospheric scintillat
ion to a value of the order of Q congruent-to r02/lambdaz0, where r0 i
s Fried's correlation scale, lambda is the wavelength, and z0 is the r
oot-mean-square distance through the atmosphere, weighted by the refra
ctive-index structure constant C(n)2. At the best astronomical sites,
with an optimal adaptive-optics system, a value of Q congruent-to 50 s
hould be achievable. Adaptive-optics systems that use such a sensor sh
ould be capable of achieving an increase in the effective atmospheric
correlation scale of a factor of Q6/5; hence a single-image curvature
sensor should be practical whenever D/r0 less than or similar Q6/5. Th
is condition is shown to hold at good astronomical sites even for tele
scopes as large as 8 m and wavelengths as short as 0.5 mum. In additio
n to optical and mechanical simplicity, the single-image sensor offers
the advantage of reduced detector read noise and potentially higher e
fficiency compared with those from a differential system.