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Curvature sensors are used in adaptive optics to measure the wave-front aberrations. In practice, their performance is limited by their nonlinear behavior, which we characterize by solving simultaneously the irradiance transport equation and the accompanying wave-front transport equation. We show how the presence of nonlinear geometric terms limits the accuracy of the sensor and how diffraction effects limit the spatial resolution. The effect of photon noise on the sensor is also quantified.doi:10.1364/josaa.19.001390 pmid:12095207 fatcat:bzqxmsglyrc4ba4frd4u73fe3y