Theoretical analysis and experimental investigation of the Floyd-Steinberg-based fringe binary method with offset compensation for accurate 3D measurement.

Digital fringe projection (DFP) with defocused binary fringe patterns has the ability to overcome the projector nonlinearity and achieve a high-speed 3D measurement. The Floyd-Steinberg (FS) dithering technique is one of the most commonly adopted binary fringe coding methods due to its relatively high measurement accuracy. Nevertheless, we found that the FS binary fringe would cause a fixed error in the recovered phase, which is proven to be invariable for various defocusing levels and various phase-shift steps according to the analysis of the phase error based on noise model of phase-shifting profilometry. It means that FS binary fringe would have a certain offset in space, compared with standard sinusoidal fringe, which is verified to be essentially constant for different fringe pitches through simulation and experiment. This offset would distort the 3D geometry of the tested target for monocular systems relying on triangulation, which needs to be compensated to improve 3D measurement accuracy. Experiments are presented to demonstrate the enhanced 3D result after compensation.