基于光栅衍射光干涉的位移测量技术研究
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摘要
为了研制结构紧凑的高精度纳米分辨力位移测量装置,对基于光栅衍射光干涉的位移测量技术进行了理论研究并研制了原理样机。
系统地分析了光栅位移测量理论及方法。基于标量衍射理论,建立了透射式单光栅系统数学模型,分析了光栅栅距等参数对莫尔干涉的影响;利用矢量衍射理论给出了任意斜入射条件下的广义光栅方程,分析了光栅栅距等参数对衍射级次和衍射效率的影响,讨论了有限尺寸高斯光束入射时的衍射特性。
提出和实现了一种采用长度为100mm、刻线密度为400lp/mm的高密度单光栅衍射光干涉的位移测量系统,两衍射光进行差频干涉,实现了光学四倍频,原始信号周期达到0.6μm。采用偏振移相的方法获得四路空间相位相差90°的原始信号,系统进行1024倍电子细分,细分后系统分辨率达到0.586nm。
利用三光栅理论建立了反射式双光栅系统的光强模型,分析了系统参数对调制光强的影响并与双光栅理论结果进行了对比,讨论了光源尺寸等因素对系统输出信号的影响;针对典型Littrow模式建立了输出信号之间相位关系的模型,分析了光栅栅距等参数对相位关系的影响。
分析了影响光栅位移测量系统精度的各种误差因素,针对环境变化造成的随机误差进行了相应的滤波处理。根据信号特点设计了FIR数字滤波器,能够有效地抑制低频噪声的影响;基于平稳卡尔曼滤波理论,在典型的电机控制情况下,给出了卡尔曼滤波的一般模型,通过仿真和实验证明了方法的有效性。
In order to develop compact high-precision nano-resolution displacement measuring device, diffraction grating-based optical interferometry measuring displacement theory and prototype machine was developed.
Grating displacement measurement theory and methods was systematically analyzed. Based on the scalar diffraction theory, single-grating transmission system model was established and the effect of parameters such as grating pitch on the Moore fringe was analyzed. Using vector diffraction theory, generalized grating equation under the condition of any oblique incidence is given. The impact of Grating pitch and other parameters on diffraction orders and the diffraction efficiency was analyzed. The diffraction characteristics when the finite-size Gaussian beam incidence was discussed.
A diffraction interference displacement measuring system was proposed and implemented which use a high-density single-grating whose length is 100mm, groove density is 400lp/mm. When the two diffracted beam with small frequency difference meet and interfere, the interference fringes changes four periods when the grating is moving a grating period relative the reading head, so the original signal period is 0.6μm. Stable signal phase difference was obtained by polarized light interference. The resolution of the system is 0.586nm after 1024-fold subdivision.
Reflective intensity double-grating system model was established by three grating theory. The effect of system parameters on light intensity modulation was analyzed and the result was compared with two grating theory. The impact of Source size and other factors on system output signal was discussed. For the typical Littrow mode, the model of phase relationship between the output signal was established. The effect of parameters such as grating pitch on phase relationship was analyzed.
Factors which affect the precision grating displacement measuring system were analyzed. The random error caused by environmental changes was processed by filtering. FIR digital filter was designed according to the signal characteristics which can effectively reduce the effect of low frequency noise. The general Kalman filter was given in a typical case of motor control. The simulation and experimental results showed the effectiveness of the method.
系统地分析了光栅位移测量理论及方法。基于标量衍射理论,建立了透射式单光栅系统数学模型,分析了光栅栅距等参数对莫尔干涉的影响;利用矢量衍射理论给出了任意斜入射条件下的广义光栅方程,分析了光栅栅距等参数对衍射级次和衍射效率的影响,讨论了有限尺寸高斯光束入射时的衍射特性。
提出和实现了一种采用长度为100mm、刻线密度为400lp/mm的高密度单光栅衍射光干涉的位移测量系统,两衍射光进行差频干涉,实现了光学四倍频,原始信号周期达到0.6μm。采用偏振移相的方法获得四路空间相位相差90°的原始信号,系统进行1024倍电子细分,细分后系统分辨率达到0.586nm。
利用三光栅理论建立了反射式双光栅系统的光强模型,分析了系统参数对调制光强的影响并与双光栅理论结果进行了对比,讨论了光源尺寸等因素对系统输出信号的影响;针对典型Littrow模式建立了输出信号之间相位关系的模型,分析了光栅栅距等参数对相位关系的影响。
分析了影响光栅位移测量系统精度的各种误差因素,针对环境变化造成的随机误差进行了相应的滤波处理。根据信号特点设计了FIR数字滤波器,能够有效地抑制低频噪声的影响;基于平稳卡尔曼滤波理论,在典型的电机控制情况下,给出了卡尔曼滤波的一般模型,通过仿真和实验证明了方法的有效性。
In order to develop compact high-precision nano-resolution displacement measuring device, diffraction grating-based optical interferometry measuring displacement theory and prototype machine was developed.
Grating displacement measurement theory and methods was systematically analyzed. Based on the scalar diffraction theory, single-grating transmission system model was established and the effect of parameters such as grating pitch on the Moore fringe was analyzed. Using vector diffraction theory, generalized grating equation under the condition of any oblique incidence is given. The impact of Grating pitch and other parameters on diffraction orders and the diffraction efficiency was analyzed. The diffraction characteristics when the finite-size Gaussian beam incidence was discussed.
A diffraction interference displacement measuring system was proposed and implemented which use a high-density single-grating whose length is 100mm, groove density is 400lp/mm. When the two diffracted beam with small frequency difference meet and interfere, the interference fringes changes four periods when the grating is moving a grating period relative the reading head, so the original signal period is 0.6μm. Stable signal phase difference was obtained by polarized light interference. The resolution of the system is 0.586nm after 1024-fold subdivision.
Reflective intensity double-grating system model was established by three grating theory. The effect of system parameters on light intensity modulation was analyzed and the result was compared with two grating theory. The impact of Source size and other factors on system output signal was discussed. For the typical Littrow mode, the model of phase relationship between the output signal was established. The effect of parameters such as grating pitch on phase relationship was analyzed.
Factors which affect the precision grating displacement measuring system were analyzed. The random error caused by environmental changes was processed by filtering. FIR digital filter was designed according to the signal characteristics which can effectively reduce the effect of low frequency noise. The general Kalman filter was given in a typical case of motor control. The simulation and experimental results showed the effectiveness of the method.
引文
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