基于傅里叶变换的改进圆形条纹投影轮廓术

Improved Circular Fringe Projection Profilometry Based on Fourier Transform

圆形正弦条纹在条纹圆心处具有恒定相位(常编码为零相位),其圆心可以作为相位展开的参考点,据此得到的绝对相位用于计算被测物体的高度信息。由于圆形条纹的载波相位为非线性函数,已有的圆形条纹投影傅里叶变换法需要求解一元二次方程,进行判根操作,再使用拟合来得到对应物面高度信息的像素位移量,鲁棒性差。提出并研究了一种基于傅里叶变换的改进圆形条纹投影轮廓术,该技术通过多投影一帧具有水平移动量的条纹,简化了圆形条纹投影方式的像素位移量的计算,将像素位移量的计算从解一元二次方程降维为解一元一次方程,提高了基于傅里叶变换圆形条纹投影轮廓术的鲁棒性和面形重建精度。计算机仿真和实验验证了所提方法重建物体三维面形的有效性,特别适合全平面离面测量。

The circular sinusoidal fringe has a constant phase(encoded as zero phase)at the circular center,and its center can be used as a reference point for phase unwrapping to obtain absolute phase for calculating the height information of the measured object.As the carrier phase of the circular fringe is a non-linear function,the existing Fourier transform method based on circular fringe projection needs to solve a quadratic equation,judge roots,and fit to obtain the pixel displacement corresponding to height information of object surface.The robustness of the algorithm is not good in fact.In this paper,an improved circular fringe projection profilometry based on Fourier transform is proposed and investigated.By projecting another fringe with horizontal movement,the calculation of pixel displacement in circular fringe profilometry is simplified,and the calculation of pixel displacement is changed from solving a first-order equation to solving a quadratic equation.The robustness and surface reconstruction accuracy of circular fringe profilometry based on Fourier transform are improved.Computer simulation and experiments validate the effectiveness of proposed method in 3D measurement,which is especially suitable for out-of-plane measurement of the whole plane.