Influence of sampling on three-dimensional surface shape measurement

In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.

非线性系统中双频光栅相位测量

为了在非线性测量系统中获得更好的相位测量结果,提出了一种在几乎消除非线性影响后使用双频光栅投影的相位测量方法。首先,讨论了相位测量系统的非线性效应,分析了频域中存在高阶频谱成份的基本原因,给出了减小非线性效应并分离基频信息的基本方法。然后,在减小系统非线性效应影响的基础上,分析了使用双频光栅投影测量被测物体条纹图像的相位基本原理。为验证所提出的相位测量方法的有效性,进行了计算机仿真和实际实验,获得了良好结果。在仿真实验中,该方法的误差值为有非线性影响方法的27.97%,为几乎没有非线性影响方法的52.51%;在实际实验中,该方法的相位恢复效果最好。表明采用本文方法所测量的相位效果好,误差较小。

基于系统非线性校正与滤波的相位测量

相位测量系统中投影仪输出与CCD输入变形条纹光强之间的非线性导致频谱混叠,影响测量精度,为了消除他们之间的非线性关系,提高相位测量精度,分析了系统非线性产生的基本原因,提出了一种基于系统非线性校正与滤波的相位测量方法.首先校正由投影仪中伽马畸变产生的系统非线性,然后采用低通滤波器对校正后输出的频谱进行滤波,只保留频谱中的基频成份,最后采用四步相移法对变形条纹进行相位测量.MATLAB仿真与实际实验结果表明,所提方法的系统非线性校正与滤波效果较好,有助于提高相位测量精度.

CCD非线性效应对双频光栅三维面形测量的影响

在测量系统中,CCD的非线性效应会影响复杂光学三维面形的测量精度,针对这一问题,提出采用双频光栅投影消除CCD的非线性效应以提高测量精度。首先,分析了CCD非线性效应对三维面形测量的影响,给出了该情况下出现频谱混叠的解析推导和物理解释。然后,讨论了CCD非线性效应下的双频光栅测量原理,分析了此时变形条纹的光强分布及其经傅立叶变换后得到混叠频谱的原理。最后,给出了由等效波长来衡量测量精度的方法,推出了使用双频光栅投影测量三维面形高度信息的基本公式,并进行了理论分析。对最大绝对值与平均绝对值分别为24.3181 mm和1.0839 mm的物体进行仿真分析,测量值与实际值之间的最大绝对高度误差与平均绝对高度误差分别为0.8950 mm和0.0622 mm,提高双频光栅基频后,其对应值分别减小为0.3710 mm和0.0232 mm;在实验结果显示,当双频光栅的基频都增加2.5倍后,频谱中的基频与高级频谱间分离较好,测量精度提高。因此,采用双频光栅投影消除CCD非线性效应具有较强的实用性和很好的发展前景。