Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping

• A fast PMP method based on phase-shifting and trifocal tensor is presented.
• A two-stage strategy correspondence method is proposed.
• Correspondence can be determined without phase unwrapping.
• Arbitrary shape can be measured with minimum phase-shifting image number.
• Correspondence refinement can make the 3D results insensitive to the phase error.

In fast phase measurement profilometry (PMP) systems, it is very important to use minimum image number to achieve full spatial resolution 3D measurement of arbitrary shape objects. This paper presents a fast PMP method based on phase-shifting and trifocal tensor. In this method, benefited from the trifocal tensor constraint, each pixel can explore its corresponding point independently only in the wrapped phase-map, so arbitrary shape including the discontinuous or step-like surfaces can be measured with minimum phase-shifting image number. To enhance the resistance to false correspondence caused by multiple fringe number and phase error, a two-stage strategy, using disparity range constraint and mixed consistency check successively, is proposed to reject the wrong candidates. To avoid the missing correspondence at the edge of sinusoidal fringes, the phase values of the corresponding points are properly adjusted. And the coordinate accuracy of the corresponding points is improved by performing correspondence refinement, and it will make the 3D result insensitive to the phase error. The experiments indicate that this method is simple yet works well in measuring both static and dynamic objects; and the experimental system can perform fast 3D measurement of arbitrary shape objects with full spatial and temporal resolution.