Stable and fast techniques for unambiguous compound phase coding

Phase shift methods have proven to be very robust and accurate for photometric 3D reconstruction. One problem of these approaches is the existence of ambiguities arising from the periodicity of the fringe patterns. While several techniques for disambiguation exist, all of them require the projection of a significant number of additional patterns. For instance, a global Gray coding sequence or supplemental sinusoidal patterns of different periods are commonly used to complement the basic phase shift technique. In this paper we propose four new coding strategies that encode the index of the projected column using several phases and that mix the resulting phases into a controllable number of projected patterns from which the position can be recovered with subpixel precision. One notable characteristic of the proposed approaches is that we can allocate the additional number of patterns specifically to improve precision or provide higher robustness to noise. The proposed approaches are analyzed and compared with the state of the art, showing their ability to be tuned towards high precision in low noise conditions or robustness with respect to noise.