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

•Noise_induced phase accuracy and reliability for four typical multi-frequency phase-shifting algorithms based on few fringes are introduced and compared.•We take the unit unwrapped phase accuracy as the standard, and discuss the main factors that affect the phase accuracy and reliability.•Noise_induced phase error between the standard-fringe-based MFPSP and the few-fringe-based MFPSP are compared in deteail, which provides a reference for the selection of phase extraction algorithm.