In three-dimensional shape measurement by fringe projection, the calibration of the measurement system is an essential procedure to determine the relationship between the retrieval phase and the object height. In this work, we present an analysis of three calibration methods that had been proposed in the literature. These are based on three mathematical models: linear, quadratic and nonlinear. The linear and nonlinear mathematical models were deduced from the geometry of the measurement system, and parameters of the model were estimated by employing the ordinary least-squares method. The implementation of this calibration method was performed by translating a reference plane at different positions with known depths. The measurement accuracy for these three models was compared by numerical simulations, and the nonlinear model was employed to measure data.