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摘要:
在相位测量轮廓术中，测量系统中投影仪等存在的非线性响应大大影响了相位测量的精度，因此，如何快速高效地消除系统中的非线性误差是提高测量精度的关键。本文建立了相位误差的精确模型，并提出了一种基于相位误差精确模型的相位提取方法，利用高步数相移算法预先标定各频谱分量的比例关系，再通过迭代运算即可得到高精度的相位分布。实验结果表明，该方法可有效补偿非线性误差，从而大大提高相位测量精度，同时，由于各频谱分量是通过高步数相移预先标定的，仅三步相移即可得到高精度相位分布，满足了快速、实时的测量要求。
Abstract:In the phase measuring profilometry, the phase measuring accuracy could be heavily affected by the nonlinearity effects of the projecting and imaging devices. Therefore, it is very important to reduce the nonlinear errors fast and efficiently. An analytic model of nonlinear errors is introduced. Then we propose a phase compensation method which is based on the accurate mathematical model of the phase error. The proportion of each harmonic component is collected by using a large-step phase-shifting algorithm to measure a reference plane. Then the phase errors of the measured object could be compensated by an iterative algorithm. The experimental results show that the proposed method can realize nonlinear error compensation effectively and improve the precision of phase measurement. Meanwhile, since all the harmonic components are pre-calibrated, there is no extra fringe needed, which can meet the requirements of fast and real-time measurement.
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Overview: The phase-shifting method uses multiple grating fringe images to solve the phase value pixel by pixel. This method has the advantages of high measurement accuracy and low cost, and is widely used in phase-based 3D topography measurement. Generally, it includes random error and systematic error. The former is usually represented by random noise, while the latter can be divided into phase-shifting error and nonlinear error. Among them, the nonlinear phase error is mainly caused by the nonlinear response in the measurement system, which is inevitable. Therefore, how to quickly and efficiently eliminate the nonlinear error in the system is the key to improve the measurement accuracy. This paper, which takes the three-step phase-shifting method as an example, proposes a phase compensation method based on the accurate mathematical model of phase error. We project a set of large phase shift fringe patterns in the calibration process, and collect all the harmonic components by using a large-step phase-shifting algorithm to measure a reference plane. In the actual measurement, the real phase is calculated by the three-step phase-shifting method, and then the phase compensation can be realized by iteration according to the phase error model and the known amplitude coefficients of all the harmonic components. In order to verify the effectiveness of this algorithm. We project a set of 18-step phase-shifting fringe patterns to obtain the ideal phase distributions and use three of them to get the nonlinear error-inclusive phase distributions. Then we use Pan's method and our method to compensate the phase error of the object respectively, and both methods are quantitatively evaluated by the residual errors. The experimental results show that the standard deviation of the residual errors without compensation is 0.1662 rad, which is reduced to 0.0581 rad by using Pan's method and 0.0193 rad by using our proposed method. The maximum phase error decreased from 0.2676 rad to 0.0807 rad. The original phase error without compensation is mainly 3-fold frequency characteristic, and the residual phase error is mainly 6-fold frequency characteristic after using Pan's method. It means that there are still uncompensated periodic errors, and the residual errors do not have obvious periodic distribution after compensated by our method. The experimental results show that this method is feasible and effective in three-dimensional measurement. The algorithm only needs three sinusoidal fringes to realize high-precision phase error compensation, which has the advantages of high precision and fast speed.
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图 2 高次谐波对条纹正弦性的影响。(a) 条纹强度；(b) 条纹的傅里叶频谱
Figure 2. The influence of higher harmonics on the sinusoidality of fringes. (a) The intensity of the fringe; (b) Fourier spectrum of the fringe
图 5 剩余相位误差展开图。(a) 变形条纹；(b) 未补偿相位误差；(c) Pan的方法；(d) LUT法；(e) 本文方法
Figure 5. Residual phase error. (a) Deformation fringe; (b) Phase without compensation; (c) Phase compensated by Pan's method; (d) Phase compensated by LUT; (e) Phase compensated by our method
图 6 三种方法模拟补偿后的剩余相位误差
Figure 6. The residual phase difference of simulation experiment by three methods
图 7 三种方法对平面补偿后的剩余相位误差
Figure 7. The residual phase difference of plane by three methods
图 8 葫芦的补偿实验。(a) 变形条纹；(b) 未补偿相位误差；(c) Pan的方法；(d) LUT法；(e) 本文方法
Figure 8. Object compensation experiment. (a) Deformation fringe; (b) Phase without compensation; (c) Phase compensated by Pan's method; (d) Phase compensated by LUT; (e) Phase compensated by our method
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