Fringe projection profilometry using model-free distorted patterns

Currently, many fringe projection profilometry (FPP) systems are based on expensive multi-media or scientific projectors (such as digital micromirror devices, spatial light modulators, etc.) and need an explicit math model for the projection system when performing measurements. This paper presents a method to use model-free distorted fringe patterns for 3-D profilometry, which can significantly loosen requirements on projector optics quality and open the door to low-cost projector designs. Without loss of generality, we chose hyperbolic and circular patterns as examples in our experiments and did 3-D shape measurements with these two distorted patterns without using any of their mathematical models. Experimental results show that the root mean square error (RMSE) of the 3-D reconstruction for a flat plane was 0.047 mm and 0.049 mm for the circular and hyperbolic patterns, respectively, which are both comparable to the error (0.036 mm) obtained with a horizontal pattern. Our method can be extended to any other aberrated and distorted fringe patterns and accelerate the application of fringe projection profilometry technologies in cost-sensitive fields, such as consumer electronics.