Measurement depth modeling and extension for geometric constraint phase unwrapping method

As an important phase unwrapping method in Fringe Projecting Profilometry, the geometric constraint enables pixel-by-pixel computation while avoiding the projection of additional patterns. However, its measurement depth is limited and influenced by multiple factors in the camera-projector system. There is still a lack of a generalized model that can describe the measurement depth. In this paper, to completely understand the variables related to the measurement depth, we analyze the unwrapping process of geometric constraint and derive a generalized model. Then, by compare the results calculated by the model and obtained from the experiments, the effectiveness of the model is verified. To further validate the key variables in the model, we establish a virtual camera-projector system and conduct simulations. Based on the simulation results, we propose four ways to extend the measurement depth, including (a) selecting a reference plane farther away from the camera, ( b) designing the fringe patterns with fewer periods, (c) using the shorter focal lens and (d) reducing the camera-projector distance.