The linear condition, spatial resolution and filter model of a curvature sensor are obtained by a brief and intelligible frequency analysis approach. The bounded interval of propagation distance is given by considering the linear condition and the noise in intensity measurement. The effects of nonlinearity and measurement noise on different frequency aberrations are discussed. We provide a guide to choose the propagation distance of a curvature sensor. The propagation distance should be large for low-frequency aberrations, which are greatly affected by the measurement noise, and small for high-frequency aberrations, which are greatly limited by the nonlinear effect. For a wavefront composed of various frequencies, it is important to select a proper propagation distance for less nonlinear effects and better noise suppression.