Theoretical considerations on aperiodic sinusoidal fringes in comparison to phase-shifted sinusoidal fringes for high-speed three-dimensional shape measurement.

The demand for optically reconstructing the three-dimensional (3D) surface shape of moving objects or deformation processes makes the development of high-speed projectors necessary. Our 3D sensor containing an array projector can achieve frame rates of several tens of kilohertz and is based on the projection of aperiodic sinusoidal fringes. This approach is compared with phase-shifting fringe projection as probably the most widely used technique. Theoretical considerations as well as extensive simulations are conducted to derive criteria for the design of optimal sequences of aperiodic sinusoidal fringes and to compare the number of patterns of both approaches necessary for comparable accuracies.