The possibility of sensing the curvature and the slope of a distorted wave front from a single defocused star image is investigated. The suggested technique is similar to the differential curvature-sensing method of Roddier [R&D note 87-3 (National Optical Astronomy Observatories, Tucson, Ariz., 1987)] but uses only a single sensor at a point either before or after the focus. The signal-to-noise ratio that is achievable with such a sensor is ultimately limited by atmospheric scintillation to a value of the order of Զ C r<sub>0</sub><sup>2</sup>/λz<sub>0</sub>, where r<sub>0</sub> is Fried's correlation scale, λ is the wavelength, and z<sub>0</sub> is the root-mean-square distance through the atmosphere, weighted by the refractive-index structure constant C<sub>n</sub><sup>2</sup>. At the best astronomical sites, with an optimal adaptive-optics system, a value of Զ C 50 should be achievable. Adaptive-optics systems that use such a sensor should be capable of achieving an increase in the effective atmospheric correlation scale of a factor of Զ<sup>6/5</sup>; hence a single-image curvature sensor should be practical whenever D/r<sub>0</sub> ≤ C Զ <sup>6/5</sup>. This condition is shown to hold at good astronomical sites even for telescopes as large as 8 m and wavelengths as short as 0.5 μm. In addition to optical and mechanical simplicity, the single-image sensor offers the advantage of reduced detector read noise and potentially higher efficiency compared with those from a differential system.
© 1994 Optical Society of America
Paul Hickson, "Wave-front curvature sensing from a single defocused image," J. Opt. Soc. Am. A 11, 1667-1673 (1994)