球面光栅干涉式表面测量仪若干关键技术研究
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摘要
大量程、高分辨率、高精度表面测量技术是计量测试领域的重要研究内容。特别是随着纳米科学与技术的发展,将表面量仪的分辨力提高到纳米级已成为现实的需求。同时,面向工程表面的测量要求量仪具有更大的量程,这些都对现有的传感技术和测量方法提出了新的挑战。
本文在分析近年来国内外这一领域技术发展的基础上,提出了球面光栅干涉测量方法,为表面轮廓测量提供了一个新的思路和方法。并针对球面光栅干涉式传感器原理、光栅干涉仪的光路结构、高分辨率的电子系统、传感器非线性特性的校准方法、表面的分离技术等这几个关键问题展开研究,为建立一种新型的表面测量与分析系统做好理论和技术方面的准备。
(1)给出了球面光栅的复振幅透过率函数,用标量衍射理论,对球面正弦相位光栅的菲涅耳衍射和夫琅禾费衍射的复振幅分布和光强分布进行了分析,并与平面正弦相位光栅进行了比较。通过Matlab仿真给出了二者的光强分布,仿真结果与实验结果相吻合。
(2)为降低干涉条纹对光栅偏摆的敏感性,提出了一种新的光栅干涉仪光路结构。利用非标准的猫眼逆反射器将一次衍射光逆反射回光栅上,产生二次衍射,利用二次衍射光产生干涉条纹。该光路结构对光栅偏摆不敏感。对这种光路结构进行了理论分析,通过实验证实该光路结构能够在一定程度上提高干涉条纹的质量。
(3)基于只读存储器细分方法研制出一种具有高细分倍数和高频响特性的细分电路。该电路基于高速A/D和CPLD实现,具有防误计数的功能。对其细分误差进行分析,分别研究了直流漂移、两路信号不等幅、两路信号不正交、奇次谐波和偶次谐波对细分精度的影响。在此基础上,提出一种实时的细分误差补偿算法,该算法可以补偿由直流漂移、两路信号不等幅和非正交导致的细分误差。最多只需要3个光栅信号周期,就能对上述三种误差依次实现补偿。算法计算简单,所需存储空间小,适合于实时处理。通过实验证实了算法的有效性。
(4)触针式大量程传感器存在由杠杆结构和触针针尖半径不为零所导致的非线性问题,会引起表面测量信号的畸变。在分析了不同校准方法的优缺点之后,采用标准球对传感器进行校准。建立了传感器传输特性的校准模型,用最小二乘拟合的方法得到了模型系数的解。实验结果表明当标准球半径为80.029mm时校准后残余轮廓误差不超过2μm,相对偏差不超过0.0025%;当标准球半径为12.5086mm时校准后残余轮廓误差不超过0.5μm,相对偏差不超过0.004%。
(5)基于中心极限定理,提出了一种新的高斯滤波器逼近数学模型,在8级级联的条件下,幅度偏差只有0.25%。给出了快速分离表面粗糙度、波纹度、形状的递归计算方法。将这种方法推广到三维表面测量的情形,利用二维高斯滤波器的可分离性,将二维高斯滤波器分解成两个一维高斯滤波器并分别实现,提高了三维表面的滤波效率。
实验结果验证了上述理论、技术、方法的正确性,为发展新型的表面测量仪奠定了良好的基础。
Large range, high resolution and high precision surface measurement technique is an important research field of metrology. Especially with development of nano-science and technology, the resolution of instruments raised to nano-scale has bacome a reality demand. At the same time, measurement for engineering surface requires instruments with greater range. Those are challenge to existing sensor technique and measurement methods.
After analyzing the development in this field in the recent years, a new kind of grating interferometer called spherical grating interferometer is proposed, which is a new technique for surface measurement. These key problems, such as theory of the spherical grating interferometric sensor, optical path configuration of the grating interferometer, high resolution electronic system, calibration method on the non-liner characteristics of the sensor, surface separation technologies, were researched. Solving these problems can help to build a new system of surface measurement and analysis.
(1) The complex amplitude transmissivity function of spherical grating is given. In Fresnel diffraction and Fraunhofer diffraction using spherical sinusoidal phase grating, the distribution of the complex amplitude and light intensity of diffraction light are analyzed and compared with that using plane sinusoidal phase grating based on the theory of scalar diffraction. The result of the distributions of the light intensity using the two instruments in the Matlab simulation is the same as that in experiment.
(2) A new optical path configuration used in grating interferometer is proposed in order to reduce the sensitivity of the interference fringe to the disturbing shifts and tilts of scale due to additional motion of the grating. Use the cat’s-eye retroreflector to reflect the first diffraction light to the grating to generate the second diffraction light, then the interference fringe can be generated using the second diffraction light. This new method is not much less sensitive to the additional movement of the grating. This new method is analyzed in theory and it has been proved to be able to improve the quality of the interfere fringe in the experiment.
(3) The ROM subdivision circuit system is developed which has high subdivision multiple and high frequency response. This circuit is based on high-speed A/D and CPLD and also has the function of preventing counting error. Then the subdivision error is analyzed. The influence of the zero offset, unequal amplitude of two channels, quadrature phase shift, odd harmonics and even harmonics on subdivision precision are also investigated. A real-time subdivision error compensation algorithm is developed, this algorithm can compensate on the subdivision error caused by zero offset, unequal amplitude of two channels and quadrature phase shift. The three above errors can be totally compensated in no more than three grating signal periods. The influence on the algorithm from harmonics is analyzed and developed. Through experiments the effect of this algorithm is proved. The advantage of this algorithm is simple, requiring little memory, easy to be real time processed.
(4) The large-range surface measuring sensor has a problem of non-liner which leads signal distortion because of lever and finite ball tip radius.
After analyzing several calibration technologies and methods, we used the standard ball to calibrate the sensor and build a calibration model of the transmission characteristic of the sensor. Then we got the solution using the least squares fitting method. The result showed that when the radius of the standard ball is 80.029mm, the residual form error is no more than 2μm after calibration, relative error is 0.0025%. When the radius of the standard ball is 12.5086mm, the residual form error is no more than 0.5μm after calibration, relative error is 0.004%.
(5) A new approximate mathematic model of Gaussian filter is proposed on the basis of central limit theorem. The amplitude deviation is approximate to 0.25% when 8 approximate filter cascaded. A fast algorithm of Gaussian filtering is given to separate the surface roughness, waviness and form deviation. This algorithm can be also used in 3-D surface measurement. Depending on the separability of the 2-D Gaussian filter, a 2-D Gaussian filter is separated into two 1-D Gaussian filter. The realization of the 2-D Gaussian filter is predigested and the filtering efficiency is improved in 3-D surface measurement.
The result of the experiment showed that the theories, technologies and methods are correct which is affording a stable foundation to developing a new instrument for surface measurement.
本文在分析近年来国内外这一领域技术发展的基础上,提出了球面光栅干涉测量方法,为表面轮廓测量提供了一个新的思路和方法。并针对球面光栅干涉式传感器原理、光栅干涉仪的光路结构、高分辨率的电子系统、传感器非线性特性的校准方法、表面的分离技术等这几个关键问题展开研究,为建立一种新型的表面测量与分析系统做好理论和技术方面的准备。
(1)给出了球面光栅的复振幅透过率函数,用标量衍射理论,对球面正弦相位光栅的菲涅耳衍射和夫琅禾费衍射的复振幅分布和光强分布进行了分析,并与平面正弦相位光栅进行了比较。通过Matlab仿真给出了二者的光强分布,仿真结果与实验结果相吻合。
(2)为降低干涉条纹对光栅偏摆的敏感性,提出了一种新的光栅干涉仪光路结构。利用非标准的猫眼逆反射器将一次衍射光逆反射回光栅上,产生二次衍射,利用二次衍射光产生干涉条纹。该光路结构对光栅偏摆不敏感。对这种光路结构进行了理论分析,通过实验证实该光路结构能够在一定程度上提高干涉条纹的质量。
(3)基于只读存储器细分方法研制出一种具有高细分倍数和高频响特性的细分电路。该电路基于高速A/D和CPLD实现,具有防误计数的功能。对其细分误差进行分析,分别研究了直流漂移、两路信号不等幅、两路信号不正交、奇次谐波和偶次谐波对细分精度的影响。在此基础上,提出一种实时的细分误差补偿算法,该算法可以补偿由直流漂移、两路信号不等幅和非正交导致的细分误差。最多只需要3个光栅信号周期,就能对上述三种误差依次实现补偿。算法计算简单,所需存储空间小,适合于实时处理。通过实验证实了算法的有效性。
(4)触针式大量程传感器存在由杠杆结构和触针针尖半径不为零所导致的非线性问题,会引起表面测量信号的畸变。在分析了不同校准方法的优缺点之后,采用标准球对传感器进行校准。建立了传感器传输特性的校准模型,用最小二乘拟合的方法得到了模型系数的解。实验结果表明当标准球半径为80.029mm时校准后残余轮廓误差不超过2μm,相对偏差不超过0.0025%;当标准球半径为12.5086mm时校准后残余轮廓误差不超过0.5μm,相对偏差不超过0.004%。
(5)基于中心极限定理,提出了一种新的高斯滤波器逼近数学模型,在8级级联的条件下,幅度偏差只有0.25%。给出了快速分离表面粗糙度、波纹度、形状的递归计算方法。将这种方法推广到三维表面测量的情形,利用二维高斯滤波器的可分离性,将二维高斯滤波器分解成两个一维高斯滤波器并分别实现,提高了三维表面的滤波效率。
实验结果验证了上述理论、技术、方法的正确性,为发展新型的表面测量仪奠定了良好的基础。
Large range, high resolution and high precision surface measurement technique is an important research field of metrology. Especially with development of nano-science and technology, the resolution of instruments raised to nano-scale has bacome a reality demand. At the same time, measurement for engineering surface requires instruments with greater range. Those are challenge to existing sensor technique and measurement methods.
After analyzing the development in this field in the recent years, a new kind of grating interferometer called spherical grating interferometer is proposed, which is a new technique for surface measurement. These key problems, such as theory of the spherical grating interferometric sensor, optical path configuration of the grating interferometer, high resolution electronic system, calibration method on the non-liner characteristics of the sensor, surface separation technologies, were researched. Solving these problems can help to build a new system of surface measurement and analysis.
(1) The complex amplitude transmissivity function of spherical grating is given. In Fresnel diffraction and Fraunhofer diffraction using spherical sinusoidal phase grating, the distribution of the complex amplitude and light intensity of diffraction light are analyzed and compared with that using plane sinusoidal phase grating based on the theory of scalar diffraction. The result of the distributions of the light intensity using the two instruments in the Matlab simulation is the same as that in experiment.
(2) A new optical path configuration used in grating interferometer is proposed in order to reduce the sensitivity of the interference fringe to the disturbing shifts and tilts of scale due to additional motion of the grating. Use the cat’s-eye retroreflector to reflect the first diffraction light to the grating to generate the second diffraction light, then the interference fringe can be generated using the second diffraction light. This new method is not much less sensitive to the additional movement of the grating. This new method is analyzed in theory and it has been proved to be able to improve the quality of the interfere fringe in the experiment.
(3) The ROM subdivision circuit system is developed which has high subdivision multiple and high frequency response. This circuit is based on high-speed A/D and CPLD and also has the function of preventing counting error. Then the subdivision error is analyzed. The influence of the zero offset, unequal amplitude of two channels, quadrature phase shift, odd harmonics and even harmonics on subdivision precision are also investigated. A real-time subdivision error compensation algorithm is developed, this algorithm can compensate on the subdivision error caused by zero offset, unequal amplitude of two channels and quadrature phase shift. The three above errors can be totally compensated in no more than three grating signal periods. The influence on the algorithm from harmonics is analyzed and developed. Through experiments the effect of this algorithm is proved. The advantage of this algorithm is simple, requiring little memory, easy to be real time processed.
(4) The large-range surface measuring sensor has a problem of non-liner which leads signal distortion because of lever and finite ball tip radius.
After analyzing several calibration technologies and methods, we used the standard ball to calibrate the sensor and build a calibration model of the transmission characteristic of the sensor. Then we got the solution using the least squares fitting method. The result showed that when the radius of the standard ball is 80.029mm, the residual form error is no more than 2μm after calibration, relative error is 0.0025%. When the radius of the standard ball is 12.5086mm, the residual form error is no more than 0.5μm after calibration, relative error is 0.004%.
(5) A new approximate mathematic model of Gaussian filter is proposed on the basis of central limit theorem. The amplitude deviation is approximate to 0.25% when 8 approximate filter cascaded. A fast algorithm of Gaussian filtering is given to separate the surface roughness, waviness and form deviation. This algorithm can be also used in 3-D surface measurement. Depending on the separability of the 2-D Gaussian filter, a 2-D Gaussian filter is separated into two 1-D Gaussian filter. The realization of the 2-D Gaussian filter is predigested and the filtering efficiency is improved in 3-D surface measurement.
The result of the experiment showed that the theories, technologies and methods are correct which is affording a stable foundation to developing a new instrument for surface measurement.
引文
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