Both the analysis of phase errors which occur at the abrupt discontinuities in the profilometry based on fringe projection and the identification method are presented in this paper. The sampling effect of CCD will cause a dilution of accuracy, especially at abrupt discontinuities on the object surface. We analyze the relationship among the phase, the height and the equivalent wavelength. By viewing the phase as the argument of a vector, we find out that, CCD sampling introduces error into the measurement, and the phase is nonlinear to the equivalent wavelength. Therefore Temporal Phase Unwrapping (TPU) is introduced into the measurement to identify the abrupt discontinuities. Computer simulations and practical experiment validate the feasibility of this method. The study provides the theoretical support for the reduction of errors caused by CCD sampling.