莫尔条纹纳米级细分关键技术研究
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摘要
光栅传感器具有量程大、适应环境能力强、成本低等优势，广泛应用在精密位移测量、数显数控、大行程精密定位、精密加工和微电子等行业中。目前各行业对光栅位移测量提出了大量程纳米级等更高要求。
莫尔条纹细分是光栅纳米级测量的关键。对于高密度光栅采用低倍细分就可以实现纳米级测量，而低密度光栅则需要高倍细分才能实现纳米级测量。低密度光栅具有量程大、成本低等优势，本文选择了线低密度光栅传感器作为研究对象。目前国内外莫尔条纹细分法主要集中在光学法和电子法，存在的主要问题是受莫尔条纹信号质量的影响大、误差修正困难等。本文针对莫尔条纹细分和栅距误差修正等关键问题进行了研究，提出了新的细分方法和栅距测量方法，完成的工作如下：
首先研究了小波细分法。该方法是对光栅传感器的输出信号进行细分，由于传感器的光学部分是固定的，因此是通过高倍电子细分实现纳米级测量。为了能够适应传感器输出的质量较差的信号，对输出信号的非等幅、非正交进行了校正。
采用菲涅尔衍射理论对光栅传感器的光学结构建模，基于透射原理的低密度光栅在实现纳米级测量时，其干涉和衍射效应的影响不能忽略，通过建立光栅调制光场的数学模型分析了低密度光栅的光强变化规律。光强与栅距、指示光栅和标尺光栅之间的距离、标尺光栅和光电转换器之间的距离等因素有直接关系，当光栅传感器运行时，这些影响因素是变化的，因此光栅传感器的输出波形非常复杂。光栅传感器在测量过程不一定是匀速运行，特别是启动、停止和换向的过程中，信号具有随机性。采用随机理论对输出信号进行了分析，结果表明信号的频率、幅值不是宽平稳的，相位是宽平稳的。本文根据光栅信号的随机性提出了小波细分法。
小波细分法先将光栅输出的信号调制到小波基的相位和频率上，再对调制后的信号进行小波变换，那么脊最大对应的相位反映位移值，脊最大对应的尺度反映频率值即速度值。调制的小波基和小波基在变换的过程中可获得最大的相似性，能够提高测量的准确性。该方法解决了选择小波基的难题，无论应用在哪个领域，无需重新选择小波基，具有较强的实用性。同时根据相邻时刻相位差的正负和调制的小波基信号频率的增减可实现辨向。基于同步数据采集卡和构建了实验系统，采集光栅传感器的输出信号并进行了非正交校正和滤波预处理，实验验证了小波细分法的可行性。因为调制相位和频率均属于相位细分，比幅值细分法具有更好的抗干扰性。
其次研究了基于采集的空间莫尔条纹信号的细分方法。该方法是利用替换传统的传感器内部的四个光电管，可获得整周期的空间莫尔条纹光强信号，同时提高了空间分辨力。在分析栅线刻划误差和采集误差的基础上，基于一个周期的空间莫尔条纹信号提出了单谱线算法和相位校正相结合的细分方法，通过计算莫尔条纹的相位差实现位移测量。基于构建了实验系统，实验验证了该方法的可行性。该方法具有只需一路信号、不受四路信号幅值不等、直流分量不等、非正交等问题影响的优点。
最后研究了栅距测量及其误差修正方法。栅距是光栅位移精密测量的基准，测出栅距值是进一步提高位移测量精度的关键。根据光栅莫尔条纹的动态特性，提出在光栅传感器运行过程中将栅距量转换为时间量的测量方法。基于高阶累积量估计莫尔条纹信号经过两个距离固定的光电管的时间延迟来获得传感器的运行速度，基于最小二乘原理确定莫尔条纹信号的相邻两个最小值来获得光栅栅距所对应的时间，由运行速度与栅距所对应时间的乘积确定栅距值。实验结果表明对栅距的光栅传感器测量，误差小于，验证了方法的可行性。该方法能够实现每个栅距的测量，通过对每个栅距的误差进行修正可减少累积误差和细分误差，为光栅大量程高精度测量奠定了基础。
Grating sensor has such advantages as long range, strong ability to adapt to the environment and low cost, which is widely used in precision displacement measurement, digital readouts and numerical controls, long stroke precision positioning, precision processing and microelectronics industry, etc. Current industries put forward higher requirements of nanoscale and long range and so on to grating displacement measurement.
Moire fringe subdivision is the key to the grating nanoscale measurement. High density grating can achieve nanoscale measurement only with low subdivision, but the low density grating needs high subdivision to achieve nanoscale measurement. Low density grating has such advantages as long range and low cost, low density grating sensor of50lines/mm is chosen as the research object. At present, Moire fringe subdivision methods at home and abroad mainly focus on the optical and electronic method, which has such main problems as serious effect by Moire fringe signal quality and difficult error correction, etc. The key problems of Moire fringe subdivision and pitch error correction are studied, and the new subdivision method and the pitch measurement method are proposed, completed work as follows:
Firstly, wavelet subdivision method is studied. The method subdivides grating sensor's output signal, because the optical part of sensor is fixed, the nanoscale measurement is achieved by high electronic subdivision. The unequal amplitude and non-orthogonality are corrected in order to adapt to the poor quality signal of sensor output.
The optical structure model of grating sensor is built with Fresnel diffraction theory, low density grating based on the transmission principle can't ignore the influence of interference and diffraction effect when it achieves nanoscale measurement, and the light intensity variation law of low density grating is analyzed by establishing the mathematical model of modulated light field by grating. Light intensity has directly relationship with such factors as the pitch, the distance between index grating and scale grating, the distance between scale grating and the photoelectric converter and so on, those influence factors are change with the movement of the grating sensor, so the output waveform of grating sensor is very complicated. The moving speed of grating sensor is not always a constant speed in the measuring process, especially in the process of start, stop and the reversing process, the signal is random. The output signals are analyzed with random theory, the results show that the frequency and amplitude is not wide-sense stationary and phase is wide-sense stationary. The wavelet subdivision method is proposed based on the randomness of grating signal.
Wavelet subdivision method modulates the phase and frequency of the wavelet base function with grating output signal and then completes wavelet transform to modulated signal, phase corresponding to the maximum ridge reflects the displacement, and scale corresponding to the maximum ridge reflects the frequency that is the speed value. Modulated wavelet base and wavelet base can obtain the biggest similarity in the process of transform, which can improve the measurement accuracy. The method solves the problem to choose wavelet base, it is not necessary to choose the wavelet base again, whatever the method is applied in any the field, practicability is strong. At the same time identification direction can be realized according to the positive and negative of the phase difference of the adjacent moments and increase and decrease of modulated wavelet base signal frequency. The experiment system is constructed based on the synchronous data acquisition card and Lab VIEW, which can acquire the grating sensor output signal and preprocess the non-orthogonal correction and filtering, experiments verify the feasibility of wavelet subdivide method. The phase modulation and frequency modulation belong to phase subdivision, which has better anti-interference performance than the amplitude subdivision.
Secondly, subdivision method is studied based on the space Moire fringe signal acquired by CCD. The method uses CCD to replace the four photoelectric cells inside traditional sensor, which can obtain the integral period space Moire fringe light intensity signal, and improve the space resolution. On the basis of the analysis of the pitch lines error and CCD acquisition error, subdivision method of the single spectral line algorithm and phase correction is proposed with a period of space Moire fringe signal, which realizes the displacement measurement through calculating the phase difference of Moire fringe. The experiment system is constructed based on FPGA, experiments verify the feasibility of subdivide method. This method has advantages of calculating with one way signal and unaffecting by unequal amplitude, non-orthogonal problems of the four way signals.
Finally, measurement and error correction method of grating pitch are studied. Grating pitch is the benchmark of accurate grating displacement measurement, and the pitch value is the key to further improve displacement measurement accuracy. According to the dynamic characteristic of the grating Moire fringe, the measurement method to convert pith quantity to time quantity is proposed in the movement process of grating sensor. Based on the high order cumulant principle the time delay within which the Moire fringe signal passes through the two fixed distance photoelectric cells is measured, and then the sensor moving speed can be obtained, the time corresponding to grating pitch can be obtained according to the two adjacent minimum values of the Moire fringe signal that are determined based on the least square principle, the pitch value is determined according to the product of the moving speed and the corresponding time of pitch. The experimental results show that the measuring error is less than0.08μm for the grating sensor with the pitch of20μm, which verifies the feasibility of the method. This method can measure each pitch, and reduce the accumulation error and subdivision error based on each pitch error correction, which laid a foundation for large range and high precision measurement.
莫尔条纹细分是光栅纳米级测量的关键。对于高密度光栅采用低倍细分就可以实现纳米级测量，而低密度光栅则需要高倍细分才能实现纳米级测量。低密度光栅具有量程大、成本低等优势，本文选择了线低密度光栅传感器作为研究对象。目前国内外莫尔条纹细分法主要集中在光学法和电子法，存在的主要问题是受莫尔条纹信号质量的影响大、误差修正困难等。本文针对莫尔条纹细分和栅距误差修正等关键问题进行了研究，提出了新的细分方法和栅距测量方法，完成的工作如下：
首先研究了小波细分法。该方法是对光栅传感器的输出信号进行细分，由于传感器的光学部分是固定的，因此是通过高倍电子细分实现纳米级测量。为了能够适应传感器输出的质量较差的信号，对输出信号的非等幅、非正交进行了校正。
采用菲涅尔衍射理论对光栅传感器的光学结构建模，基于透射原理的低密度光栅在实现纳米级测量时，其干涉和衍射效应的影响不能忽略，通过建立光栅调制光场的数学模型分析了低密度光栅的光强变化规律。光强与栅距、指示光栅和标尺光栅之间的距离、标尺光栅和光电转换器之间的距离等因素有直接关系，当光栅传感器运行时，这些影响因素是变化的，因此光栅传感器的输出波形非常复杂。光栅传感器在测量过程不一定是匀速运行，特别是启动、停止和换向的过程中，信号具有随机性。采用随机理论对输出信号进行了分析，结果表明信号的频率、幅值不是宽平稳的，相位是宽平稳的。本文根据光栅信号的随机性提出了小波细分法。
小波细分法先将光栅输出的信号调制到小波基的相位和频率上，再对调制后的信号进行小波变换，那么脊最大对应的相位反映位移值，脊最大对应的尺度反映频率值即速度值。调制的小波基和小波基在变换的过程中可获得最大的相似性，能够提高测量的准确性。该方法解决了选择小波基的难题，无论应用在哪个领域，无需重新选择小波基，具有较强的实用性。同时根据相邻时刻相位差的正负和调制的小波基信号频率的增减可实现辨向。基于同步数据采集卡和构建了实验系统，采集光栅传感器的输出信号并进行了非正交校正和滤波预处理，实验验证了小波细分法的可行性。因为调制相位和频率均属于相位细分，比幅值细分法具有更好的抗干扰性。
其次研究了基于采集的空间莫尔条纹信号的细分方法。该方法是利用替换传统的传感器内部的四个光电管，可获得整周期的空间莫尔条纹光强信号，同时提高了空间分辨力。在分析栅线刻划误差和采集误差的基础上，基于一个周期的空间莫尔条纹信号提出了单谱线算法和相位校正相结合的细分方法，通过计算莫尔条纹的相位差实现位移测量。基于构建了实验系统，实验验证了该方法的可行性。该方法具有只需一路信号、不受四路信号幅值不等、直流分量不等、非正交等问题影响的优点。
最后研究了栅距测量及其误差修正方法。栅距是光栅位移精密测量的基准，测出栅距值是进一步提高位移测量精度的关键。根据光栅莫尔条纹的动态特性，提出在光栅传感器运行过程中将栅距量转换为时间量的测量方法。基于高阶累积量估计莫尔条纹信号经过两个距离固定的光电管的时间延迟来获得传感器的运行速度，基于最小二乘原理确定莫尔条纹信号的相邻两个最小值来获得光栅栅距所对应的时间，由运行速度与栅距所对应时间的乘积确定栅距值。实验结果表明对栅距的光栅传感器测量，误差小于，验证了方法的可行性。该方法能够实现每个栅距的测量，通过对每个栅距的误差进行修正可减少累积误差和细分误差，为光栅大量程高精度测量奠定了基础。
Grating sensor has such advantages as long range, strong ability to adapt to the environment and low cost, which is widely used in precision displacement measurement, digital readouts and numerical controls, long stroke precision positioning, precision processing and microelectronics industry, etc. Current industries put forward higher requirements of nanoscale and long range and so on to grating displacement measurement.
Moire fringe subdivision is the key to the grating nanoscale measurement. High density grating can achieve nanoscale measurement only with low subdivision, but the low density grating needs high subdivision to achieve nanoscale measurement. Low density grating has such advantages as long range and low cost, low density grating sensor of50lines/mm is chosen as the research object. At present, Moire fringe subdivision methods at home and abroad mainly focus on the optical and electronic method, which has such main problems as serious effect by Moire fringe signal quality and difficult error correction, etc. The key problems of Moire fringe subdivision and pitch error correction are studied, and the new subdivision method and the pitch measurement method are proposed, completed work as follows:
Firstly, wavelet subdivision method is studied. The method subdivides grating sensor's output signal, because the optical part of sensor is fixed, the nanoscale measurement is achieved by high electronic subdivision. The unequal amplitude and non-orthogonality are corrected in order to adapt to the poor quality signal of sensor output.
The optical structure model of grating sensor is built with Fresnel diffraction theory, low density grating based on the transmission principle can't ignore the influence of interference and diffraction effect when it achieves nanoscale measurement, and the light intensity variation law of low density grating is analyzed by establishing the mathematical model of modulated light field by grating. Light intensity has directly relationship with such factors as the pitch, the distance between index grating and scale grating, the distance between scale grating and the photoelectric converter and so on, those influence factors are change with the movement of the grating sensor, so the output waveform of grating sensor is very complicated. The moving speed of grating sensor is not always a constant speed in the measuring process, especially in the process of start, stop and the reversing process, the signal is random. The output signals are analyzed with random theory, the results show that the frequency and amplitude is not wide-sense stationary and phase is wide-sense stationary. The wavelet subdivision method is proposed based on the randomness of grating signal.
Wavelet subdivision method modulates the phase and frequency of the wavelet base function with grating output signal and then completes wavelet transform to modulated signal, phase corresponding to the maximum ridge reflects the displacement, and scale corresponding to the maximum ridge reflects the frequency that is the speed value. Modulated wavelet base and wavelet base can obtain the biggest similarity in the process of transform, which can improve the measurement accuracy. The method solves the problem to choose wavelet base, it is not necessary to choose the wavelet base again, whatever the method is applied in any the field, practicability is strong. At the same time identification direction can be realized according to the positive and negative of the phase difference of the adjacent moments and increase and decrease of modulated wavelet base signal frequency. The experiment system is constructed based on the synchronous data acquisition card and Lab VIEW, which can acquire the grating sensor output signal and preprocess the non-orthogonal correction and filtering, experiments verify the feasibility of wavelet subdivide method. The phase modulation and frequency modulation belong to phase subdivision, which has better anti-interference performance than the amplitude subdivision.
Secondly, subdivision method is studied based on the space Moire fringe signal acquired by CCD. The method uses CCD to replace the four photoelectric cells inside traditional sensor, which can obtain the integral period space Moire fringe light intensity signal, and improve the space resolution. On the basis of the analysis of the pitch lines error and CCD acquisition error, subdivision method of the single spectral line algorithm and phase correction is proposed with a period of space Moire fringe signal, which realizes the displacement measurement through calculating the phase difference of Moire fringe. The experiment system is constructed based on FPGA, experiments verify the feasibility of subdivide method. This method has advantages of calculating with one way signal and unaffecting by unequal amplitude, non-orthogonal problems of the four way signals.
Finally, measurement and error correction method of grating pitch are studied. Grating pitch is the benchmark of accurate grating displacement measurement, and the pitch value is the key to further improve displacement measurement accuracy. According to the dynamic characteristic of the grating Moire fringe, the measurement method to convert pith quantity to time quantity is proposed in the movement process of grating sensor. Based on the high order cumulant principle the time delay within which the Moire fringe signal passes through the two fixed distance photoelectric cells is measured, and then the sensor moving speed can be obtained, the time corresponding to grating pitch can be obtained according to the two adjacent minimum values of the Moire fringe signal that are determined based on the least square principle, the pitch value is determined according to the product of the moving speed and the corresponding time of pitch. The experimental results show that the measuring error is less than0.08μm for the grating sensor with the pitch of20μm, which verifies the feasibility of the method. This method can measure each pitch, and reduce the accumulation error and subdivision error based on each pitch error correction, which laid a foundation for large range and high precision measurement.
引文
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