<title>Single-image wavefront curvature sensing</title>

Abstract

A single defocused star image contains sufficient information to uniquely determine the spatial phase fluctuations \nof the incident wavefront. A sensor which responds to the intensity distribution in the image produces signals \nproportional to the wavefront curvature within the pupil and the radial slope at the pupil boundary. Unlike Roddier's \ndifferential curvature sensing technique, a single-image sensor does not cancel intensity fluctuations due to atmospheric \nscintillation. However, it has been shown that at typical astronomical sites the scintillation signal is negligibly small. \nA single-image curvature sensor can theoretically achieve a signal-to-noise ratio of order Q approximately equals r20/(lambda) z0 \nwhere r0 is Fried's correlation length, (lambda) is the wavelength, and z0 is the root-mean-square distance through \nthe atmosphere, weighted by the refractive index structure constant C2n. This is more than adequate for AO systems \nwhenever D/r0 <EQ Q6/5. Such a sensor can be very simple, optically and mechanically, and has lower detector read \nnoise than a comparable differential system. The concept has been tested in the laboratory by introducing, and \ndetecting, spherical aberration in a simple optical system.\n\nCopyright 1994 Society of Photo-Optical Instrumentation Engineers. \nOne print or electronic copy may be made for personal use only. Systematic reproduction and distribution, \nduplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.