Single-shot circular fringe projection for the profiling of objects having surface discontinuities

Fringe projection profilometry (FPP) is a widely used non-contact optical method for 3D profiling of objects. The commonly used linear fringe pattern in FPP has periodic intensity variations along the lateral direction. As a result, the linear fringe pattern used in FPP cannot uniquely represent the lateral shift induced by the objects having surface discontinuities. Thus, unambiguous surface profiling of objects, especially with surface discontinuities, using a single linear fringe image having a single fringe frequency, is unfeasible. This paper proposes using a radially symmetric circular fringe pattern as the structured light pattern for accurate unambiguous surface profiling of sudden height-discontinuous objects. To the best of our knowledge, this is the only method that can reconstruct discontinuous height profiles with the help of a single fringe image having a single frequency. The performance of the proposed algorithm is evaluated on several synthetic and real objects having smooth variations and discontinuities. Compared to the well-known fringe projection methods, the results depict that for a tolerable range of error, the proposed method can be applied for the reconstruction of objects with 4 times higher dynamic range and even at much lower fringe frequencies.