WO2021017828A1 - High-precision method for measuring high-frequency standing wave amplitude distribution - Google Patents
High-precision method for measuring high-frequency standing wave amplitude distribution Download PDFInfo
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- the invention belongs to the technical field of optical engineering, and is specifically a method for measuring the amplitude distribution of a high-frequency standing wave.
- the hemispherical resonant gyroscope and other components achieve performance through the resonant standing wave generated by excitation, so the measurement of its vibration characteristics is an important guarantee for mechanism analysis and improvement of component performance.
- the measured component is plated with a metal film, and the formed electrode and the signal detector form a capacitance, so the vibration measurement can be realized by detecting the change of the capacitance characteristic [1].
- the average distance change at the electrode and the spatial distribution of the amplitude cannot be obtained.
- the purpose of the present invention is to provide a high-precision measurement method for the amplitude distribution of the standing wave of a smooth surface element, so as to facilitate the analysis of the vibration mode and vibration characteristics.
- the high-precision measurement method for the amplitude distribution of the standing wave of the smooth surface element provided by the present invention is based on the deflection technology, and the specific steps are as follows:
- (u 0 v 0 ) represents the entire
- the center of gravity coordinates of the feature spot, (u(i,j),v(i,j)) represents the coordinate of any pixel in the feature spot;
- step (4) Perform eigenvalue decomposition on the normal matrix M in step (4), where the eigenvector corresponding to the largest eigenvalue is the extension direction of the feature spot [5]; draw a straight line perpendicular to the extension direction from the center of the feature spot , The width of the characteristic spot along the straight line is the original circle spot diameter d;
- the normal deflection range of the measuring point caused by vibration can be obtained.
- the components in the x and y directions are written as s x , s y , and the z-direction component is normalized;
- the modal method is used for integral reconstruction to obtain the amplitude distribution z [6] in the whole area, that is, to solve the partial differential equation, so that the objective function is minimized:
- D x and D y respectively represent the differential matrix along the x and y directions, and the x and y components of the normal deflection can be approximated and optimized to obtain z.
- the system of the present invention has simple structure, high sensitivity and strong anti-interference ability, can measure the standing wave amplitude distribution in a local area of the component, and is of great significance for component vibration mechanism and characteristic analysis and component resonance performance guarantee.
- Figure 1 is a schematic diagram of the deflection measurement amplitude.
- Figure 2 is a schematic diagram of the formation of blurred spots in the deflection measurement.
- Figure 3 shows the binarization pattern displayed on the screen.
- Figure 4 shows the blurred image obtained by shooting.
- Figure 5 shows the recognition contour of the blurred spot.
- Figure 6 shows the extension direction of the blur spot and the calculation of the yaw distance.
- Figure 7 shows the normal x-direction yaw range.
- Figure 8 shows the normal y-direction yaw range.
- Figure 9 shows the actual solution of the standing wave amplitude distribution.
- Embodiment 1 In this embodiment, the measured component is a plane with a diameter of 70 mm, and the vibration is excited from the lower surface, and the frequency is 4500 Hz.
- the focal length of the camera is 55mm, and the size of a single pixel is 8 ⁇ m ⁇ 8 ⁇ m.
- the screen adopts ipad mini, the angle between the center point of the two and the excitation point is 45°, the distance between the center of the screen and the excitation point of the component is 172mm, and the distance between the optical center of the camera and the excitation point is 240mm, as shown in Figure 1. .
- the standing wave of the component under test causes the local normal to change, so the reflection optics will swing accordingly, and the corresponding image will form blurred spots, as shown in Figure 2.
- the round spot pattern is displayed on the screen, as shown in Figure 3.
- the camera exposure time is set to 0.05 seconds, and the collected images are shown in Figure 4.
- the Sobel operator is used to identify the boundary of the feature spot; for clarity, we only draw the identification boundary of a feature spot in the upper left corner in FIG. 5.
- the normal matrix of all pixels in the contour is subjected to eigenvalue decomposition, and the eigenvector corresponding to the largest eigenvalue is the AB direction shown in FIG. 6.
- the normal yaw range of the component can be obtained, and its z component is normalized to obtain the lateral component (s x , s y ), respectively As shown in Figure 7, Figure 8.
- the amplitude distribution obtained after reconstruction and fitting using the modal method is shown in Figure 9. Therefore, the method of the present invention can accurately obtain the amplitude distribution of the measurement area.
Abstract
Disclosed is a method for measuring high-frequency resonant standing wave amplitude distribution of a smooth-surface element, the method comprising: constructing a deflection measurement system, placing a camera and a projection screen symmetrically on the left and on the right relative to an element to be measured; displaying round spot patterns by means of projection and using the camera to measure fuzzy characteristic spots formed by reflection of an high-frequency vibration element; recognizing the borders of the characteristic spots by using difference operators, and obtaining a deflection distance of the round spots by means of fitting; on the basis of system geometric parameters obtained by means of calibration, calculating the amount of deflection of the normal of each part of a measured surface; and finally, reconstructing integrals to obtain a standing wave amplitude distribution. The system is simple in terms of structure, has a high sensitivity and a high capability of resisting disturbance, can measure the standing wave amplitude distribution of a local area of an element, and has substantial significance on the analysis of a vibration mechanism and property of the element, and on ensuring the resonance oscillation performance of the element.
Description
本发明属于光学工程技术领域，具体为一种测量高频驻波振幅分布的方法。The invention belongs to the technical field of optical engineering, and is specifically a method for measuring the amplitude distribution of a high-frequency standing wave.
半球谐振陀螺等元件通过激励产生的谐振驻波实现性能，因此其振动特性的测量是进行机理分析、提升元件性能的重要保障。传统上通常将被测元件上镀金属膜，所形成的电极与信号探测器构成电容，于是振动测量可以通过探测电容特性的变化来实现[1]。但是这种方法得到的是电极处的平均距离变化，无法得到振幅的空间分布。随后研究者提出基于全息干涉的时间平均法[2]，可以在多个振动周期内采用全息干板记录叠加的干涉条纹，通过光学再现得到谐振子的平均振幅。但是该方法需要全息干板记录与定影，操作复杂，而且难以数字化。为此研究者提出数字全息干涉测量方法，采用CCD记录干涉图像，再利用菲涅尔衍射重构得到振幅分布[3]。但是较大的振幅会导致干涉条纹过密，无法正确解析振幅；同时，CCD像素远远大于全息干板的显像颗粒，导致记录分辨率严重下降，影响了振幅测量的精度。因此，光滑表面元件驻波振型的高精度测量方法，是当前面临的重要难题。The hemispherical resonant gyroscope and other components achieve performance through the resonant standing wave generated by excitation, so the measurement of its vibration characteristics is an important guarantee for mechanism analysis and improvement of component performance. Traditionally, the measured component is plated with a metal film, and the formed electrode and the signal detector form a capacitance, so the vibration measurement can be realized by detecting the change of the capacitance characteristic [1]. But what this method gets is the average distance change at the electrode, and the spatial distribution of the amplitude cannot be obtained. Later, researchers proposed a time averaging method based on holographic interference [2], which can record superimposed interference fringes on a holographic dry plate in multiple vibration cycles, and obtain the average amplitude of the harmonic oscillator through optical reconstruction. However, this method requires holographic dry plate recording and fixing, which is complicated in operation and difficult to digitize. For this reason, the researchers proposed a digital holographic interferometry method, which uses CCD to record the interference image, and then uses Fresnel diffraction to reconstruct the amplitude distribution [3]. However, a large amplitude will cause the interference fringes to be too dense, and the amplitude cannot be resolved correctly; at the same time, the CCD pixels are much larger than the imaging particles of the holographic dry plate, resulting in a serious decline in recording resolution and affecting the accuracy of amplitude measurement. Therefore, the high-precision measurement method of the standing wave mode of smooth surface components is an important problem currently facing.
发明内容Summary of the invention
本发明的目的在于提供一种光滑表面元件驻波振幅分布的高精度测量方法，以便于分析振型与振动特性。The purpose of the present invention is to provide a high-precision measurement method for the amplitude distribution of the standing wave of a smooth surface element, so as to facilitate the analysis of the vibration mode and vibration characteristics.
本发明提供的光滑表面元件驻波振幅分布的高精度测量方法，是基于偏折技术的，具体步骤如下：The high-precision measurement method for the amplitude distribution of the standing wave of the smooth surface element provided by the present invention is based on the deflection technology, and the specific steps are as follows:
(1)搭建偏折测量光路，投影屏幕和相机相对于被测元件左右对称放置；(1) Set up the deflection measurement optical path, and place the projection screen and camera symmetrically with respect to the component under test;
(2)在屏幕上显示二值化圆斑图样，经过振动元件反射后在相机成像；(2) Display the binarized round spot pattern on the screen, which will be imaged on the camera after being reflected by the vibrating element;
(3)采用Sobel微分算子对图像进行处理，并采用二值化识别图像中特征斑的边界[4]，以灰度w(u,v)为权重计算斑点中心：(3) Use the Sobel differential operator to process the image, and use binarization to identify the boundary of the feature spot in the image [4], and calculate the spot center with the gray level w(u,v) as the weight:
(4)对特征斑中所有点坐标构造正规矩阵：(4) Construct a normal matrix for the coordinates of all points in the feature spot:
M＝∑w(i,j)δ(i,j)
Tδ(i,j),
M=∑w(i,j)δ(i,j) T δ(i,j),
其中，δ(i,j)＝(u(i,j)-u
0,v(i,j)-v
0)，表示特征斑中每个像素的坐标偏差，(u
0v
0)表示 整个特征斑的重心坐标，(u(i,j),v(i,j))表示特征斑中任意像素的坐标；
Among them, δ(i,j)=(u(i,j)-u 0 ,v(i,j)-v 0 ), represents the coordinate deviation of each pixel in the feature spot, (u 0 v 0 ) represents the entire The center of gravity coordinates of the feature spot, (u(i,j),v(i,j)) represents the coordinate of any pixel in the feature spot;
(5)对步骤(4)中的正规矩阵M进行特征值分解，其中最大特征值对应的特征向量即为特征斑的延伸方向[5]；从特征斑重心画出一条垂直于延伸方向的直线，特征斑沿该直线方向的宽度即为原始圆斑直径d；(5) Perform eigenvalue decomposition on the normal matrix M in step (4), where the eigenvector corresponding to the largest eigenvalue is the extension direction of the feature spot [5]; draw a straight line perpendicular to the extension direction from the center of the feature spot , The width of the characteristic spot along the straight line is the original circle spot diameter d;
(6)从特征斑重心沿其延伸方向画一条直线，与特征斑边界的两个交点记为A、B；线段AB长度与圆斑直径d之差的一半即为该点极限振幅引起的成像偏差；(6) Draw a straight line from the center of gravity of the characteristic spot along its extension direction, and mark the two intersection points with the boundary of the characteristic spot as A and B; the half of the difference between the length of the line segment AB and the diameter d of the spot is the imaging caused by the limit amplitude at this point deviation;
(7)利用偏折标定的几何参数，便可得到振动引起的测量点法向偏摆范围，将其x,y方向的分量分别写作s
x,s
y，并将z向分量归一化；
(7) Using the geometric parameters calibrated by deflection, the normal deflection range of the measuring point caused by vibration can be obtained. The components in the x and y directions are written as s x , s y , and the z-direction component is normalized;
(8)采用modal法进行积分重构，得到全区域振幅分布z[6],也即解偏微分方程，使得目标函数最小：(8) The modal method is used for integral reconstruction to obtain the amplitude distribution z [6] in the whole area, that is, to solve the partial differential equation, so that the objective function is minimized:
E(z)＝‖zD
x-s
x‖
2+||D
yz-s
y||
2 (2)
E(z)=‖zD x -s x ‖ 2 +||D y zs y || 2 (2)
其中，D
x、D
y分别表示沿x、y方向的微分矩阵，和法向偏摆的x、y方向分量进行逼近优化，就可以解得z。
Among them, D x and D y respectively represent the differential matrix along the x and y directions, and the x and y components of the normal deflection can be approximated and optimized to obtain z.
由于此方程的解不唯一，求解后将振幅分布整体偏移，使得驻点振幅为零。Since the solution of this equation is not unique, the amplitude distribution is shifted as a whole after the solution is solved, so that the stationary point amplitude is zero.
本发明的系统结构简单，灵敏度高，抗干扰能力强，可以测量元件局部区域的驻波振幅分布，对于元件振动机理与特性分析、元件谐振性能保障有重要意义。The system of the present invention has simple structure, high sensitivity and strong anti-interference ability, can measure the standing wave amplitude distribution in a local area of the component, and is of great significance for component vibration mechanism and characteristic analysis and component resonance performance guarantee.
参考文献references
[1]万泉.微型半球谐振陀螺检测与控制系统研究，苏州大学硕士学位论文，2018[1] Wan Quan. Research on the detection and control system of miniature hemispherical resonant gyroscope, Master's thesis of Soochow University, 2018
[2]樊尚春.轴对称壳谐振陀螺,国防工业出版社，2013[2] Fan Shangchun. Axisymmetric shell resonant gyroscope, National Defense Industry Press, 2013
[3]A Asundi,VR Singh.Time-averaged in-line digital holography interferometry for vibration analysis.Applied Optics 2006；45(11):2391-2395[3]A Asundi, VR Singh. Time-averaged in-line digital holography interferometry for vibration analysis. Applied Optics 2006; 45(11):2391-2395
[4]L Li,X Zhang,H Xiao and M Xu.Segmentation of non-stochastic surfaces based on non-subsampled contourlet transform and mathematical morphologies.Measurement2016；79:137-146[4]L Li,X Zhang,H Xiao and M Xu.Segmentation of non-stochastic surfaces based on non-subsampled contourlet transform and mathematical morphologies.Measurement2016;79:137-146
[5]GH Golub and CF van Loan.Matrix Computations.4Edition.The John Hopkins University Press,2013[5] GH Golub and CF van Loan. Matrix Computations. 4 Edition. The John Hopkins University Press, 2013
[6]I Mochi and KA Goldberg.Modal wavefront reconstruction from its gradient.Applied Optics 2015；54:3780–3785.。[6] I Mochi and KA Goldberg. Modal wavefront reconstruction from its gradient. Applied Optics 2015; 54: 3780-3785..
图1为偏折测量振幅示意图。Figure 1 is a schematic diagram of the deflection measurement amplitude.
图2为偏折测量模糊斑形成原理图。Figure 2 is a schematic diagram of the formation of blurred spots in the deflection measurement.
图3为屏幕显示的二值化图样。Figure 3 shows the binarization pattern displayed on the screen.
图4为拍摄得到的模糊斑图像。Figure 4 shows the blurred image obtained by shooting.
图5为模糊斑的识别轮廓。Figure 5 shows the recognition contour of the blurred spot.
图6为模糊斑的延伸方向及偏摆距离计算。Figure 6 shows the extension direction of the blur spot and the calculation of the yaw distance.
图7为法向的x方向偏摆范围。Figure 7 shows the normal x-direction yaw range.
图8为法向的y方向偏摆范围。Figure 8 shows the normal y-direction yaw range.
图9为实际解得的驻波振幅分布。Figure 9 shows the actual solution of the standing wave amplitude distribution.
下面通过实施例结合附图进一步说明本发明。The present invention will be further described below through embodiments in combination with the drawings.
实施例1：本实施例中被测元件为口径70mm的平面，从下表面进行振动激励，频率为4500Hz。相机焦距为55mm，单个像素的尺寸为8μm×8μm。屏幕采用ipad mini，二者的中心点和激励点连线的夹角都是45°，屏幕中心到元件激励点的距离为172mm，相机光心到激励点的距离为240mm，如图1所示。被测元件驻波引起局部法向变化，因此反射光学随之发生偏摆，对应图像就会形成模糊斑，如图2所示。在屏幕上显示圆斑图样，如图3所示。相机曝光时间设为0.05秒，所采集的图像如图4所示。采用本发明中的方法，利用Sobel算子识别特征斑边界；为了清晰起见，我们在图5中只画出左上角一个特征斑的识别边界。将轮廓内的所有像素的正规矩阵进行特征值分解，最大特征值对应的特征向量即为图6所示的AB方向。得到圆斑的偏摆距离之后，结合相机、屏幕、元件直径的相对距离，可以得到元件法向的偏摆范围，将其z分量归一化，得到横向分量(s
x,s
y)，分别如图7、图8所示。利用modal法经过重构拟合后得到的振幅分布如图9所示。因此本发明中的方法可以准确得到测量区域的振幅分布。
Embodiment 1: In this embodiment, the measured component is a plane with a diameter of 70 mm, and the vibration is excited from the lower surface, and the frequency is 4500 Hz. The focal length of the camera is 55mm, and the size of a single pixel is 8μm×8μm. The screen adopts ipad mini, the angle between the center point of the two and the excitation point is 45°, the distance between the center of the screen and the excitation point of the component is 172mm, and the distance between the optical center of the camera and the excitation point is 240mm, as shown in Figure 1. . The standing wave of the component under test causes the local normal to change, so the reflection optics will swing accordingly, and the corresponding image will form blurred spots, as shown in Figure 2. The round spot pattern is displayed on the screen, as shown in Figure 3. The camera exposure time is set to 0.05 seconds, and the collected images are shown in Figure 4. Using the method of the present invention, the Sobel operator is used to identify the boundary of the feature spot; for clarity, we only draw the identification boundary of a feature spot in the upper left corner in FIG. 5. The normal matrix of all pixels in the contour is subjected to eigenvalue decomposition, and the eigenvector corresponding to the largest eigenvalue is the AB direction shown in FIG. 6. After the yaw distance of the circular spot is obtained, combined with the relative distance of the camera, screen, and component diameter, the normal yaw range of the component can be obtained, and its z component is normalized to obtain the lateral component (s x , s y ), respectively As shown in Figure 7, Figure 8. The amplitude distribution obtained after reconstruction and fitting using the modal method is shown in Figure 9. Therefore, the method of the present invention can accurately obtain the amplitude distribution of the measurement area.
Claims (1)
- 一种高频驻波振幅分布精密测量方法，基于偏折技术的，其特征在于，具体步骤如下：A precision measurement method for the amplitude distribution of high-frequency standing waves, based on deflection technology, is characterized in that the specific steps are as follows:(1)搭建偏折测量光路，投影屏幕和相机相对于被测元件左右对称放置；(1) Set up the deflection measurement optical path, and place the projection screen and camera symmetrically with respect to the component under test;(2)在屏幕上显示二值化圆斑图样，经过振动元件反射后在相机成像；(2) Display the binarized round spot pattern on the screen, which will be imaged on the camera after being reflected by the vibrating element;(3)采用Sobel微分算子对图像进行差分计算，对算子进行二值化处理，识别所采集图像中特征斑的边界，以灰度w(u,v)为权重计算斑点中心：(3) The Sobel differential operator is used to calculate the difference of the image, and the operator is binarized to identify the boundary of the characteristic spot in the collected image, and calculate the spot center with the gray level w(u,v) as the weight:
(4)对特征斑中所有点坐标构造正规矩阵：(4) Construct a normal matrix for the coordinates of all points in the feature spot:M＝∑w(i,j)δ(i,j) Tδ(i,j), M=∑w(i,j)δ(i,j) T δ(i,j),其中，δ(i,j)＝(u(i,j)-u 0,v(i,j)-v 0)表示特征斑中每个像素的坐标偏差，(u 0 v 0)表示整个特征斑的重心坐标，(u(i,j),v(i,j))表示特征斑中任意像素的坐标； Among them, δ(i,j)=(u(i,j)-u 0 ,v(i,j)-v 0 ) represents the coordinate deviation of each pixel in the feature spot, (u 0 v 0 ) represents the entire feature The center of gravity coordinates of the spot, (u(i,j),v(i,j)) represents the coordinates of any pixel in the feature spot;(5)对步骤(4)中的正规矩阵M进行特征值分解，其中最大特征值对应的特征向量即为特征斑的延伸方向；从特征斑重心画出一条垂直于延伸方向的直线，特征斑沿该直线方向的宽度即为原始圆斑直径d；(5) Perform eigenvalue decomposition on the normal matrix M in step (4), where the eigenvector corresponding to the largest eigenvalue is the extension direction of the feature spot; draw a straight line perpendicular to the extension direction from the center of the feature spot, the feature spot The width along the straight line is the original circle diameter d;(6)从特征斑重心沿其延伸方向画一条直线，与特征斑边界的两个交点记为A、B；线段AB长度与圆斑直径d之差的一半即为该点极限振幅引起的成像偏差；(6) Draw a straight line from the center of gravity of the characteristic spot along its extension direction, and mark the two intersection points with the boundary of the characteristic spot as A and B; the half of the difference between the length of the line segment AB and the diameter d of the spot is the imaging caused by the limit amplitude at this point deviation;(7)利用偏折标定的几何参数便可得到振动引起的测量点法向偏摆范围，将其x,y方向的分量分别写作s x,s y，并将z向分量归一化； (7) The normal deflection range of the measuring point caused by vibration can be obtained by using the geometric parameters calibrated by deflection. The components in the x and y directions are respectively written as s x and s y , and the z-direction component is normalized;(8)采用modal法进行积分重构得到全区域振幅分布z,也即解偏微分方程，使得目标函数最小：(8) Use the modal method to perform integral reconstruction to obtain the amplitude distribution z in the whole region, that is, to solve the partial differential equation, so that the objective function is minimized:E(z)＝‖zD x-s x‖ 2+||D yz-s y|| 2 (2) E(z)=‖zD x -s x ‖ 2 +||D y zs y || 2 (2)其中，D x、D y分别表示沿x、y方向的微分矩阵，和法向偏摆的x、y方向分量进行逼近优化，解得z；求解后振幅分布整体偏移，使得驻点振幅为零。 Among them, D x and D y respectively represent the differential matrix along the x and y directions, and the x and y components of the normal yaw are approximated and optimized to obtain z; after the solution, the overall amplitude distribution is shifted so that the stationary point amplitude is zero.
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| CN113686360B (en) * | 2021-08-27 | 2023-05-26 | 中国科学院西安光学精密机械研究所 | Global measurement method and system for hemispherical harmonic oscillator standing wave drift |
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