Noise-induced phase error comparison in multi-frequency phase-shifting profilometry based on few fringes

For fringe projection profilometry (FPP), the combination of phase-shifting profilometry (PSP) and multi frequency temporal phase unwrapping (MFTPU) is a phase extraction scheme with high accuracy and robustness, which is widely used in three dimensional (3D) measurement equipment. To make it suitable for real-time or dynamic objects 3D measurement, reducing the number of fringes is an effective method. To this end, this paper introduces four phase extraction algorithms based on few fringes. We introduce the unit phase accuracy, and analyze the phase extraction accuracy and reliability of the above four algorithms. Experiments are carried out to confirm the theoretical analysis conclusions. Our theoretical and experimental results include that the wrapped phase error variance is inversely proportional to the number of phase-shifting steps, and that the phase unwrapping reliability is proportional to the wrapped phase accuracy and inversely proportional to the frequency ratio between fringe sequences. Compared with the existing four standard multi-frequency phase-shifting methods, the measurement efficiency of the four non-standard multi-frequency phase-shifting methods supplemented in this paper are improved by 16.7%, 37.5%, 22.2% and 41.7%, respectively. However, the phase unwrapping reliability decreases. The balance between phase extraction accuracy and efficiency needs to be determined according to the actual application. This paper can provide a reference for the selection of phase extraction algorithm.