A comparison of n-ary simple code and n-ary gray code phase unwrapping in high-speed fringe projection profilometry

Abstract

Binary defocusing technique has been widely used in fringe projection profilometry for high-speed measurement. This technique projects designed binary patterns with a defocused projector to generate fringes for wrapped phase calculation, and n-ary simple codes (nSC) or n-ary gray codes (nGC) for phase unwrapping. The unwrapped phase reflecting the object surface profile is calculated by a phase-shifting algorithm with nSC/nGC phase unwrapping. However, it remains unclear which phase unwrapping method, nSC or nGC, is more appropriate for high-accuracy and high-speed measurement. This paper comprehensively compares nSC and nGC with the consideration of various factors, including the strategies for error removal, the base n, the step heights and invalid regions on the measured objects, defocusing level and noise level of the system. From simulations and experiments, we conclude that, (i) in general, nSC with a proposed identification and binary classification (IBC) method has a similar result as nGC; (ii) when accuracy is critical, binary simple code (nSC with n = 2) and binary gray code (nGC with n = 2) methods are recommended; (iii) when speed is critical, quaternary simple code (nSC with n = 4) method with continuity/geometry constraints is recommended.