Optimization of a DIY parallel-optical-axes profilometer for compensation of fringe divergence

In profilometry systems, the conventional optical configuration of fringe projection with the oblique projection and camera axis perpendicular to the field of view requires complicated calculus and exact ray trace designs to get the 3D shape under question accurately. Moreover, when the optical components of the camera and projector and their internal placement are unknown, as is the case with commercial digital video projectors, the correct alignment of these components is uncertain, needing complex methods of calibration to correct the measured shape. In this work, we re-introduce a parallel-optical-axes configuration for a DIY profilometer that simplifies the calibration by a simple trigonometric relationship obtaining the topography with a resolution and accuracy similar to conventional arrangements that require non-simple relationships among phase and height. Furthermore, an experimental method is presented to locate the divergence point within the projector, which allows optimizing the projection and observation distances. The proposed calibration procedure allows proper compensation for the apparent scale change caused by perspective. The performance of the proposed method is tested in an optimized configuration and a non-optimized one, comparing the measurements with a Coordinate-measuring machine. The optimized optical system using simple spatial phase unwrapping shows an improved RMS error of 53µm versus 203µm of the non-optimized.