Exhaustive dithering algorithm for 3D shape reconstruction by fringe projection profilometry

Three-dimensional (3D) shape reconstruction by projection of defocused binary patterns overcomes the nonlinearity introduced by the projector. Current patch-based procedures that generate dithered patterns are time consuming and are affected by the harmonics introduced through the tiling process. To overcome this problem, we propose a novel idea, to the best of our knowledge, to generate dithering patterns using the composition of two-dimensional patches as a stack of one-dimensional arrays obtained through an efficient deterministic approach. This procedure is a one-dimension optimization problem in the intensity domain, employing only a quarter of the fringe pitch. Furthermore, the unwanted distorting harmonics are eliminated using a Hilbert transform method. Both numerical simulations and experimental results verify the effectiveness of the proposal.