中文摘要：

提出了一种无需相位去包裹的微分算法,应用于投影栅三维形貌测量。首先由计算机设计并生成4幅四步相移正弦条纹图,利用DLP投影仪将其投影到待测物体上;然后由CCD相机采集受待测物体面型调制的变形光栅条纹图。再利用4幅四步相移变形条纹图,经数值运算求得沿水平和垂直方向上待测物体相位的偏导数,而相位偏导数的积分过程相当于求解泊松方程,于是利用离散余弦变换（DCT）求解泊松方程就可得到待测物体三维形貌对应的相位数据,从而重构待测物体的三维形貌。测量结果表明,相位解调的标准差小于0.0317rad,验证了本文方法的有效性。

英文摘要：

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 objectls 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 Poissonrs equation. Discrete cosine trans- form （DCT） is introduced to solve Poissonls 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. 0317 rad,which shows that the method has high precision. The feasibility of the proposed algorithm is also demonstrated by the experimental results.