In this paper, we present a mathematical model that describes a general relationship between the projected signal and the deformed signal in fringe pattern profilometry (FPP) systems. The derived mathematical model proves that in theory any kind of fringe pattern could be utilized for profilometry. Based on the derived mathematical model, this paper also proposes a new algorithm, referred to as inverse function analysis (IFA) method, to reconstruct 3-D surfaces using the FPP technique. Compared with traditional methods, our algorithm has neither the requirement for the structure of projected fringe patterns nor the prior knowledge of the distortion characteristics of projection systems. The correctness of the proposed mathematical model and IFA method has been confirmed by simulation results, which are provided to demonstrate that compared with the conventional analysis methods, the measurement accuracy has been significantly improved by the IFA method, particularly when the expected sinusoidal fringe patterns are distorted by unknown factors.