Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry

•We describe how to combine co-phased profilometry with 2-step temporal phase-unwrapping to digitize discontinuous solids.•This technique minimizes the problem of self-generated shadows in profilometry of discontinuous solids.•This 3D profilometer of discontinuous solids uses 2-steps temporal phase unwrapping of two widely separated phase sensitivities.

In this work we review and combine two techniques that have been recently published for three-dimensional (3D) fringe projection profilometry and phase unwrapping, namely: co-phased profilometry and 2-steps temporal phase-unwrapping. By combining these two methods we get a more accurate, higher signal-to-noise 3D profilometer for discontinuous industrial objects. In single-camera single-projector (standard) profilometry, the camera and the projector must form an angle between them. The phase-sensitivity of the profilometer depends on this angle, so it cannot be avoided. This angle produces regions with self-occluding shadows and glare from the solid as viewed from the camera׳s perspective, making impossible the demodulation of the fringe-pattern there. In other words, the phase data is undefined at those shadow regions. As published recently, this limitation can be solved by using several co-phased fringe-projectors and a single camera. These co-phased projectors are positioned at different directions towards the object, and as a consequence most shadows are compensated. In addition to this, most industrial objects are highly discontinuous, which precludes the use of spatial phase-unwrappers. One way to avoid spatial unwrapping is to decrease the phase-sensitivity to a point where the demodulated phase is bounded to one lambda, so the need for phase-unwrapping disappears. By doing this, however, the recovered non-wrapped phase contains too much harmonic distortion and noise. Using our recently proposed two-step temporal phase-unwrapping technique, the high-sensitivity phase is unwrapped using the low-frequency one as initial gross estimation. This two-step unwrapping technique solves the 3D object discontinuities while keeping the accuracy of the high-frequency profilometry data. In scientific research, new art are derived as logical and consistent result of previous efforts in the same direction. Here we present a new 3D-profilometer combining these two recently published methods: co-phased profilometry and two-steps temporal phase-unwrapping. By doing this, we obtain a new and more powerful 3D profilometry technique which overcomes the two main limitations of previous fringe-projection profilometers namely: high phase-sensitivity digitalization of discontinuous objects and solid׳s self-generated shadow minimization. This new 3D profilometer is demonstrated by an experiment digitizing a discontinuous 3D industrial-solid where the advantages of this new profilometer with respect to previous art are clearly shown.