An optimal principal component analysis method for carrier removal in Fourier transform profilometry

To improve the reconstruction accuracy in the fringe projection profilometry (FPP), a bidimensional empirical mode decomposition and principal component analysis (BEMD&PCA) algorithm are proposed to directly acquire the object phase from fundamental-frequency component which includes the carrier phase and object phase. BEMD is employed to remove the zero frequency to reduce the spectrum overlapping. A reduced-size spectrum is adopted to limit the size of the spectrum for principal component analysis. PCA is used to decompose the phase into several principal components and extract the carrier phase from the first dominant component, and the object phase can be acquired by multiplying with the carrier phase conjugation. The experiment and analysis results illustrate that the proposed method has the merit of less error distribution and single-frame acquisition.