WAVE-FRONT CURVATURE SENSING FROM A SINGLE DEFOCUSED IMAGE

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.