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We describe a procedure to accurately measure ground deformations from optical satellite images. Precise orthorectification is obtained owing to an optimized model of the imaging system, where look directions are linearly corrected to compensate for attitude drifts, and sensor orientation uncertainties are accounted for. We introduce a new computation of the inverse projection matrices for which a rigorous resampling is proposed. The irregular resampling problem is explicitly addressed to avoid introducing aliasing in the ortho-rectified images. Image registration and correlation is achieved with a new iterative unbiased processor that estimates the phase plane in the Fourier domain for subpixel shift detection. Without using supplementary data, raw images are wrapped onto the digital elevation model and coregistered with a 1/50 pixel accuracy. The procedure applies to images from any pushbroom imaging system. We analyze its performance using Satellite pour l'Observation de la Terre (SPOT) images in the case of a null test (no coseismic deformation) and in the case of large coseismic deformations due to the Mw 7.1 Hector Mine, California, earthquake of 1999. The proposed technique would also allow precise coregistration of images for the measurement of surface displacements due to ice-flow or geomorphic processes, or for any other change detection applications. A complete software package, the Coregistration of Optically Sensed Images and Correlation, is available for download from the Caltech Tectonics Observatory website.