Differential 3D shape measurement without phase unwrapping

A differential three-dimensional (3D) shape measurement method without phase unwrapping is proposed and applied for profilometry based on fringe projection. Firstly, four frames of phase-shifting sinusoidal fringes designed and generated by computer are projected onto the tested object surface by a digital-light-processing (DLP) projector. Then a CCD camera captures four frames of fringe patterns modulated by the tested object's surface shape. Two partial derivatives of the phase of tested object with respect to horizontal and vertical spatial coordinates are derived from four frames of phase-shifted fringe patterns by numerical calculation of the intensity distribution patterns. Thus, integrating the partial derivatives of the phase is equivalent to finding the solution of the Poisson's equation. Discrete cosine transform (DCT) is introduced to solve Poisson's equation with the Neumann boundary condition. The 3D surface information of the tested object is reconstructed completely. Finally, the experimental evaluation is conducted to prove the validity of the proposed method. The standard deviation of phase demodulation is less than 0.031 7 rad, which shows that the method has high precision. The feasibility of the proposed algorithm is also demonstrated by the experimental results. ©, 2015, Board of Optronics Lasers. All right reserved.