A single defocused star image contains sufficient information to uniquely determine the spatial phase fluctuations of the incident wavefront. A sensor which responds to the intensity distribution in the image produces signals proportional to the wavefront curvature within the pupil and the radial slope at the pupil boundary. Unlike Roddier's differential curvature sensing technique, a single-image sensor does not cancel intensity fluctuations due to atmospheric scintillation. However, it has been shown that at typical astronomical sites the scintillation signal is negligibly small. A single-image curvature sensor can theoretically achieve a signal-to-noise ratio of order Q approximately equals r20/(lambda) z0 where r0 is Fried's correlation length, (lambda) is the wavelength, and z0 is the root-mean-square distance through the atmosphere, weighted by the refractive index structure constant C2n. This is more than adequate for AO systems whenever D/r0 <EQ Q6/5. Such a sensor can be very simple, optically and mechanically, and has lower detector read noise than a comparable differential system. The concept has been tested in the laboratory by introducing, and detecting, spherical aberration in a simple optical system.