光谱共焦法厚度测量系统中抖动补偿算法研究

Research on jitter compensation algorithm in spectral confocal thickness measurement system

为获得样品多点数据,光谱共焦位移传感系统在移动测量时会产生抖动效应,引起测量数据发生漂移,文中基于已实现的光谱共焦厚度测量系统,研究抖动的影响并探究抖动补偿算法。首先,基于光谱共焦厚度测量模型及抖动存在时探头相对于光轴发生一定倾斜,推导了抖动对厚度测量影响的关系模型,并采用蒙特卡洛法分析了4种样品在不同程度随机抖动下的厚度概率密度函数,将解析结果与蒙特卡洛仿真结果进行比较,验证了厚度概率密度函数表达式的正确性。结果表明:抖动效应导致测量性能下降,尤其在样品厚度较大时;而抖动标准差较大时,较薄的样品具有更好的抗抖动性能;为补偿抖动的影响,提出采用Savitzky-Golay滤波及高斯拟合实现滤波和光谱信号峰值波长的提取,并建立了抖动误差补偿算法;最后,对厚度为(1.0±0.1) mm的样品进行实验测量,测得平均厚度为1.064 0 mm,补偿后的相对标准偏差为0.29%,验证了抖动补偿算法的有效性。文中的研究内容对提高系统测量稳定性及测量精度有一定的指导意义。

In order to obtain multi-point data of the sample,the spectral confocal displacement sensing system will produce jitter effect when moving the measurement,causing the drift of the measurement data.Based on the realized spectral confocal thickness measurement system,the effect of jitter is studied and the jitter compensation algorithm is explored;Firstly,based on the spectral confocal thickness measurement model and the presence of jitter when the probe is tilted to a certain extent relative to the optical axis,the relational model of the effect of jitter on the thickness measurement is deduced,and the thicknesses of four kinds of samples with different degrees of random jitter are analyzed by Monte Carlo simulation method.The analyzed results are compared with the Monte Carlo simulation results to verify the correctness of the expression of the thickness probability density function.The results show that the jitter effect leads to a degradation of the measurement performance,especially when the sample thickness is large;In the case of a large standard deviation of jitter,the measurement of thinner samples has a better anti-jitter performance.Then,in order to compensate the effect of jitter on the measurement results,it is proposed to use Savitzky-Golay filtering and Gaussian fitting to realize the filtering and the extraction of the peak wavelength of the spectral signal,and the jitter error compensation algorithm is established;Finally,experimental measurements were conducted on a sample with a thickness of(1.0±0.1)mm,and the average thickness was measured to be 1.0640 mm.The compensated relative standard deviation was 0.29%,verifying the effectiveness of the jitter compensation algorithm.This research has some guiding significance to improve the system measurement stability and measurement accuracy.Objective With the development of miniature integrated optical instruments such as optical communications and optical sensing,the use of transparent materials is becoming more and more stringent.Highly accurate thickness measurement parameters help guide their precise application and control the performance of related ultra-precision optical instruments,making accurate thickness inspection necessary.Spectral confocal method uses a broad-spectrum light source to irradiate the surface of the object,uses the principle of optical dispersion to make the dispersive objective lens produce axial chromatic aberration,establishes the correspondence between the dispersive distance and the wavelength,and uses a spectrometer to detect the peak wavelength of the spectrum that is focused on the surface of the object and reflected back to get the accurate axial position or microdisplacement data.Such an approach allows to break through the diffraction limit of ordinary optical microscopes.It achieves ultra-high ranging resolution on the nanometer scale and has wide adaptability to environments and materials.When measuring the thickness of transparent materials using the spectral confocal method,the jitter effect alters the refractive properties of the beam entering the sample and random noise is present in the received spectral response curve reflected from the sample surface,which leads to drift of the measurement data.On this basis,the relationship model of the effect of jitter on the spectral confocal thickness measurement is firstly derived in this paper,and the distribution of the thickness probability density function of the sample under different degrees of random jitter is simulated and analyzed by Monte Carlo method.In order to compensate for the effect of jitter on the measurement results,it was proposed in this paper to use Savitzky-Golay filtering and Gaussian fitting to extract the peak wavelength of the spectral signal,and a jitter compensation algorithm was established.Finally,the stability of the measurement results is improved by experimental measurements,and the effectiveness of the algorithm is verified.Methods The effect of jitter on thickness measurement of transparent materials is studied in this paper.First,the thickness measurement models of the probe with respect to the optical axis were derived when the probe was not tilted(Fig.2)and tilted(Fig.3),and the influence of jitter on the thickness measurement results was characterized by the optical axis tilt,and simulation analysis was carried out(Fig.4).Then,by comparing thickness measurement errors and jitter standard deviation at different wavelengths(Fig.5),after comparative analysis of various algorithms,spectral noise was filtered by Savitzky-Golay filtering algorithm(Fig.7-8),and peak wavelength of spectral signal was extracted by Gaussian fitting algorithm(Tab.1).An optimized jitter compensation algorithm is constructed.Finally,the validity of Savitzky-Golay filtering algorithm and Gaussian fitting algorithm for jitter compensation in spectral confocal thickness measurement is verified(Tab.2).Results and Discussions The thickness of the sample under static conditions depends only on the focusing wavelength,the angle of incidence and the refractive index of the transparent material.Random jitter angle is the main source of thickness measurement error,and the thickness measurement error caused by sensor probe jitter should not be neglected.By analyzing the effect of random jitter angle on the measurement error,a jitter compensation mechanism is established to reduce the measurement error.Thickness measurement data is noncentral cardinality distribution,the jitter effect will lead to the measurement performance degradation,especially in the case of larger sample thickness;In the case of larger jitter standard deviation,thinner samples have better anti-jitter performance.The peak wavelength of the spectral signal is extracted by S-G filtering and Gaussian fitting,which can reduce the error caused by the mechanical vibration of the probe and improve the measurement stability of the confocal spectroscopy measurement system.Conclusions In this paper,based on the spectral confocal method to realize the thickness measurement of transparent materials,the jitter effect generated by the movement will make the measurement data drift,and the influence of the jitter effect on the thickness measurement is systematically studied.Firstly,the relationship model of the effect of jitter on thickness measurement is established based on the principle of spectral confocal thickness measurement system,theoretical derivation is carried out,and MC simulation is used for simulation verification.Secondly,the thickness PDF and MC simulation results are compared and analyzed to verify the correctness of the thickness PDF expression.The results show that the jitter effect leads to a degradation of the measurement performance,especially when the sample thickness is large;In the case of a large standard deviation of jitter,the measurement of thinner samples has a better anti-jitter performance.In order to correct or compensate the effect of jitter on the measurement results,it is proposed to use S-G filtering and Gaussian fitting to realize the random noise filtering and the extraction of the peak wavelength of the spectral signal,and the jitter error compensation algorithm is modeled.Finally,experimental measurements were conducted on a sample with a thickness of(1.0±0.1)mm.Under stable conditions,the average thickness was measured to be 1.0640 mm.The relative standard deviation of the moving measurement results was reduced from 1.86%before compensation to 0.29%after compensation,verifying the effectiveness of the jitter error compensation algorithm proposed in this paper and proposing improvement measures.The results of this paper have certain guiding significance for optimizing the system structure and further improving the performance of the system,and have certain advancing effect on the practical application of the spectral confocal displacement sensing system for stable measurement.