Phase Sensitivity-Based Fringe Angle Optimization in Telecentric Fringe Projection Profilometry

Telecentric fringe projection profilometry (TFPP) is an important solution for 3-D measurement of micro-objects. In a TFPP system, the fringe projection angle affects the sensitivity of the phase-to-depth changes, thus affecting the 3-D measurement accuracy. Considering the particularity of the affine projection model of a telecentric lens, this article proposes a phase sensitivity-based fringe angle optimization method for TFPP. First, the telecentric epipolar geometry is analyzed in detail using the special imaging model of the telecentric lens, revealing a key characteristic that the epipolar lines are parallel to each other. Second, it is theoretically derived that the maximum phase sensitivity can be achieved when the fringe direction is perpendicular to the parallel epipolar lines, and the fringe angle can be optimized based on this conclusion. Finally, the optimized fringe pattern is projected onto the object to be measured. Quantitative tests and qualitative verification are performed through 3-D measurement and reconstruction. Experimental results demonstrate that the proposed fringe angle optimization method is feasible and effective for improving phase sensitivity and measurement accuracy.