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 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 Q≃r02/λz0, where r0 is Fried’s correlation scale, λ is the wavelength, and z0 is the root-mean-square distance through the atmosphere, weighted by the refractive-index structure constant Cn2. At the best astronomical sites, with an optimal adaptive-optics system, a value of Q≃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 Q6/5; hence a single-image curvature sensor should be practical whenever D/r0≲Q6/5. 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.