Curvature sensing is an intensity-based technique for wavefront reconstruction using two defocused images located on the opposite sides of the focal plane. It requires either one detector placed at two consecutive axial locations or a dual path with a pair of detectors from which the sensor signal is obtained. The method yields sensitivity comparable to that of the Hartmann test in the adjustment and evaluation of ground-based optical telescopes. We introduce the analytical framework underlying the function of a curvature sensor which operates from a single defocused image. A series of twin images is computed from the propagation law of the mutual intensity along the optical axis. The polynomial decomposition of the wavefront allows retrieval of Zernike coefficients by means of the standard least-squares algorithm. The paper concludes with a review of image sampling requirements and a discussion on the signal-to-noise ratio.