CN103105285B - Shadow-rejection based test method and test instrument for optical fiber panel limiting resolution - Google Patents

Shadow-rejection based test method and test instrument for optical fiber panel limiting resolution Download PDF

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CN103105285B
CN103105285B CN201310023618.5A CN201310023618A CN103105285B CN 103105285 B CN103105285 B CN 103105285B CN 201310023618 A CN201310023618 A CN 201310023618A CN 103105285 B CN103105285 B CN 103105285B
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optical fiber
resolution
fiber panel
integrating sphere
shadow
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CN103105285A (en
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张淑琴
陈亮
杨润光
金尚忠
杨琳
吴军法
徐珍宝
张林波
徐强
毛世挺
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China Jiliang University
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Abstract

本发明公开了一种基于暗影剔除的光纤面板极限分辨率测试仪器,包括:标准光源(1)及其稳流源(2),聚光镜(3),积分球(4)及其移动机构,分辨率靶(5),和CCD数据采集和微机处理系统(8),所述分辨率靶(5)设置在所述积分球(4)的均匀漫射出口上;本发明还公开了一种基于暗影剔除的光纤面板极限分辨率测试方法。本发明补充当前对光纤面板极限分辨率测试技术的空白,利用一种分辨率靶剔除暗影点来精确的系统测量光纤面板各个部分的极限分辨率,可以给出不同光纤面板各个部分的分辨率分布,还能定位出光纤面板存在的暗影坐标。

The invention discloses an optical fiber panel limit resolution test instrument based on shadow elimination, comprising: a standard light source (1) and its steady current source (2), a condenser lens (3), an integrating sphere (4) and its moving mechanism, a resolution rate target (5), and CCD data acquisition and microcomputer processing system (8), the resolution target (5) is set on the uniform diffusion outlet of the integrating sphere (4); the invention also discloses a Test method for limit resolution of optical fiber panels with shadow removal. The present invention supplements the blank of the current limit resolution testing technology for optical fiber panels, uses a resolution target to eliminate shadow points to accurately and systematically measure the limit resolution of each part of the optical fiber panel, and can give the resolution distribution of each part of different optical fiber panels , and can also locate the shadow coordinates of the optical fiber panel.

Description

基于暗影剔除的光纤面板极限分辨率测试方法及仪器Optical fiber panel limit resolution test method and instrument based on shadow removal

技术领域 technical field

本发明涉及一种测量光纤面板、光学镜头的极限分辨率的光学仪器,具体涉及一种基于暗影补偿原理的分辨率的测试装置,属于光学领域。 The invention relates to an optical instrument for measuring the limit resolution of an optical fiber panel and an optical lens, in particular to a resolution test device based on the principle of shadow compensation, which belongs to the field of optics.

背景技术                                                                 Background technique

    光纤面板具有传光效率高,级间耦合损失小,传像清晰、真实,具有零厚度等特点。广泛的应用于各种阴极射线管、摄像管、CCD耦合及其他需要传送图像的仪器和设备中。光纤面板是实现光纤到桌面解决方案的用户终端产品,内部空间设计合理。因而逐渐走向一些家庭和工作区。光纤面板的好与坏与该面板的分辨率是分不开的,因此对其极限分辨率的参数也提出了测试需要。由于光纤面板在实际制造过程中各种不可控因素的影响( 如红外响应、温度等),光纤面板会产生一定数量的瑕疵点,称之为暗影,因此在测量光纤面板的分辨率时必须找出这些暗影点。目前国内还没有深入开展光纤面板暗影检测方法的研究,而系统测试光纤面板各个部分的极限分辨率的技术几乎为零。而对于检测光纤面板中暗影的检测有一种叫利用最优算子Canny算子实现暗影的检测。但该方案存在以下问题: The optical fiber panel has the characteristics of high light transmission efficiency, small inter-stage coupling loss, clear and real image transmission, and zero thickness. Widely used in various cathode ray tubes, camera tubes, CCD couplings and other instruments and equipment that need to transmit images. The fiber optic panel is a user terminal product that realizes the fiber-to-the-desktop solution, and the internal space design is reasonable. Thus gradually moving towards some home and work areas. The quality of the fiber optic panel is inseparable from the resolution of the panel, so the parameters of its limit resolution also need to be tested. Due to the influence of various uncontrollable factors (such as infrared response, temperature, etc.) out of these shadow spots. At present, there is no in-depth research on the shadow detection method of optical fiber panels in China, and the technology for systematically testing the limit resolution of various parts of optical fiber panels is almost zero. As for the detection of the shadow in the optical fiber panel, there is a method called using the optimal operator Canny operator to realize the detection of the shadow. But this solution has the following problems:

1)Canny 算子是用数学模拟的方法去接近实际问题,其定位精度和宽度无法无法直观的描述。 1) The Canny operator uses mathematical simulation to approach practical problems, and its positioning accuracy and width cannot be described intuitively.

2)Canny 算子的调用语句含有高斯滤波器参数标准差, 低阈值和高阈值之比, 高阈值占图像像素总数之比,几个参数不仅无法唯一确定,而且还存在一定人为因素。 2) The call statement of the Canny operator contains the standard deviation of the Gaussian filter parameters, the ratio of the low threshold to the high threshold, and the ratio of the high threshold to the total number of image pixels. Not only can several parameters not be uniquely determined, but there are also certain human factors.

3)分辨图像中不仅存在加性噪声, 还存在着乘性噪声,Canny 算子无法解决乘性噪声。 3) There is not only additive noise in the resolution image, but also multiplicative noise, and the Canny operator cannot solve the multiplicative noise.

发明内容 Contents of the invention

为了解决现有技术中存在的上述技术问题,本发明提供了一种基于暗影剔除的光纤面板极限分辨率测试仪器,包括:标准光源及其稳流源,聚光镜,积分球及其移动机构,分辨率靶,和CCD数据采集和微机处理系统,所述分辨率靶设置在所述积分球的均匀漫射出口上。 In order to solve the above-mentioned technical problems existing in the prior art, the present invention provides an optical fiber panel limit resolution test instrument based on shadow removal, including: a standard light source and its steady current source, a condenser, an integrating sphere and its moving mechanism, a resolution Rate target, and CCD data acquisition and microcomputer processing system, the resolution target is set on the uniform diffuse outlet of the integrating sphere.

进一步的,所述的标准光源为溴钨灯,稳流源为精度很高直流电源。 Further, the standard light source is a bromine tungsten lamp, and the steady current source is a DC power supply with high precision.

进一步的,所述聚光镜为石英聚光镜。 Further, the condenser is a quartz condenser.

进一步的,所述标准光源距离所述聚光镜的距离小于聚光镜的焦距。 Further, the distance between the standard light source and the condenser lens is shorter than the focal length of the condenser lens.

进一步的,所述积分球是内部涂有无波长选择性的漫反射性的白色涂料的空心球体。 Further, the integrating sphere is a hollow sphere coated with non-wavelength-selective diffuse reflective white paint inside.

进一步的,所述移动机构是和所述积分球连在一起的金属滑台,其周边标有刻度。 Further, the moving mechanism is a metal sliding table connected with the integrating sphere, and the periphery thereof is marked with scales.

进一步的,待测光纤面板设置所述分辨率靶和所述积分球的均匀漫射出口之间。 Further, the optical fiber panel to be tested is arranged between the resolution target and the uniform diffusion outlet of the integrating sphere.

进一步的,还包括显微镜观察系统,该显微镜观察系统带有CCD接口,其物镜对准所述待测光纤面板。 Further, it also includes a microscope observation system, the microscope observation system has a CCD interface, and its objective lens is aligned with the optical fiber panel to be tested.

进一步的,还包括Z轴移动机构,用来调整显微镜物镜Z轴位置。 Further, it also includes a Z-axis moving mechanism, which is used to adjust the Z-axis position of the microscope objective lens.

本发明还提供了一种基于暗影剔除的光纤面板极限分辨率测试方法,包括如下步骤: The present invention also provides a method for testing the limit resolution of an optical fiber panel based on shadow removal, comprising the following steps:

将待测光纤面板设置分辨率靶和积分球的均匀漫射出口之间; Set the optical fiber panel to be tested between the resolution target and the uniform diffuse outlet of the integrating sphere;

标准光源发出单色光经过聚光镜,然后射入所述积分球的一个补偿口; The monochromatic light emitted by the standard light source passes through the condenser, and then enters a compensation port of the integrating sphere;

之后,入射光在所述积分球内发生漫反射再从积分球的另一补偿口射出; Afterwards, the incident light is diffusely reflected in the integrating sphere and then emitted from another compensation port of the integrating sphere;

再透射过所述待测光纤面板和分辨率靶到显微物镜。 Then transmit through the optical fiber panel to be tested and the resolution target to the microscope objective lens.

在任意时刻,所述分辨率靶内任意一点的电位                                                由二维拉普拉斯方程及相应的边界条件决定: At any moment, the potential of any point in the resolution target Determined by the two-dimensional Laplace equation and the corresponding boundary conditions:

 ; ;

;

;

其中为分辨率靶的厚度,为分辨率靶表面电位分布,为靶压; in is the thickness of the resolution target, is the resolution target surface potential distribution, is the target pressure;

由于分别满足一个带有齐次边界条件的二维拉普拉斯方线性叠加可以导出其最终表达式为: because have Respectively satisfying a linear superposition of two-dimensional Laplace squares with homogeneous boundary conditions can lead to the final expression as:

,

其中分别为的导出系数,是双曲正弦函数,另外,C为靶的对比度,I为当前光电流,为靶的基准电流; in respectively The derived coefficient of is a hyperbolic sine function, and , C is the contrast of the target, I is the current photocurrent, is the reference current of the target;

当某处存在暗影点时该处电势为零,可以唯一确定x、y的坐标。 When there is a shadow point somewhere, the electric potential is zero, and the coordinates of x and y can be uniquely determined.

本发明的基于暗影剔除的光纤面板极限分辨率测试方法及仪器补充当前对光纤面板极限分辨率测试技术的空白,利用一种分辨率靶剔除暗影点来精确的系统测量光纤面板各个部分的极限分辨率,可以给出不同光纤面板各个部分的分辨率分布,还能定位出光纤面板存在的暗影坐标。 The optical fiber panel limit resolution test method and instrument based on shadow elimination of the present invention supplement the current blank of the optical fiber panel limit resolution test technology, and use a resolution target to eliminate shadow points to accurately and systematically measure the limit resolution of each part of the optical fiber panel The ratio can give the resolution distribution of each part of different fiber optic panels, and can also locate the shadow coordinates of the fiber optic panels.

与现有技术相比,本发明的有益效果如下: Compared with the prior art, the beneficial effects of the present invention are as follows:

1)通过显微目视观察系统直接判断光纤面板不同区域的极限分辨力,比传统的方法更加直观,操作也相对简单; 1) Directly judge the limit resolution of different areas of the fiber optic panel through the microscopic visual observation system, which is more intuitive than the traditional method, and the operation is relatively simple;

2)分辨率靶剔除暗影,解决了光纤面板分辨率测不准的问题; 2) The resolution target eliminates shadows, which solves the problem of inaccurate measurement of the resolution of the fiber optic panel;

3)给出了光纤面板不同部分的极限分辨率的测量,可以精确的给出面板的暗影位置。 3) The measurement of the limit resolution of different parts of the fiber optic panel is given, and the shadow position of the panel can be accurately given.

附图说明 Description of drawings

图1是本发明的基于暗影剔除的光纤面板极限分辨率测试仪器的结构示意图; Fig. 1 is the structural representation of the optical fiber panel limit resolution testing instrument based on shadow elimination of the present invention;

图2为分辨率靶的截面图。 Fig. 2 is a cross-sectional view of a resolution target.

具体实施方式 Detailed ways

下面结合附图对本发明作进一步说明。 The present invention will be further described below in conjunction with accompanying drawing.

如图1所示,本发明的基于暗影剔除的光纤面板极限分辨率测试仪器包括标准光源1及其稳流源2,聚光镜3,积分球4及其移动机构,分辨率靶5,显微镜观察系统6和Z轴移动机构7,CCD数据采集和微机处理系统8组成。 As shown in Figure 1, the optical fiber panel limit resolution test instrument based on shadow removal of the present invention includes a standard light source 1 and its steady flow source 2, a condenser lens 3, an integrating sphere 4 and its moving mechanism, a resolution target 5, and a microscope observation system 6 and Z-axis moving mechanism 7, CCD data acquisition and microcomputer processing system 8.

    所述的标准光源1及其稳流源2部分为一种溴钨灯和精度很高直流电源的光源系统,使光源输出光的强度与色温稳定。该标准光源1一定要与外界光源隔绝,因此必须在一定温度下的暗箱中进行。 The standard light source 1 and its steady current source 2 are a light source system with a bromine tungsten lamp and a high-precision DC power supply, which stabilizes the intensity and color temperature of the output light of the light source. The standard light source 1 must be isolated from external light sources, so it must be carried out in a dark box at a certain temperature.

    所述的聚光镜3为石英聚光镜,其石英纯度较高,不易影响光的折射角。其离标准光源1一固定距离设置,此距离小于聚光镜3的焦距,且光源沿光轴方向的投影恰在聚光镜3的中心上。 The condenser lens 3 is a quartz condenser lens, the purity of which is relatively high, and the refraction angle of light is not easily affected. It is set at a fixed distance from the standard light source 1 , this distance is less than the focal length of the condenser 3 , and the projection of the light source along the optical axis is just on the center of the condenser 3 .

所述的积分球4是内部涂有无波长选择性的(均匀)漫反射性的白色涂料的空心球体,积分球共有两个补偿口,其中一个为聚光镜3输出光入口,另一个为均匀漫射出口。积分球4设置在移动机构上,移动机构是和积分球紧紧连在一起的金属滑台,其周边均标有刻度,使积分球4可以顺利在X-Y平面内前后左右移动。 The integrating sphere 4 is a hollow sphere coated with non-wavelength selective (uniform) diffuse reflective white paint inside, and the integrating sphere has two compensation ports, one of which is the output light entrance of the condenser lens 3, and the other is a uniform diffuse ejection port. Integrating sphere 4 is arranged on the moving mechanism, and moving mechanism is the metal sliding platform that is closely connected together with integrating sphere, and its periphery is all marked with scale, makes integrating sphere 4 can move back and forth, left and right in X-Y plane smoothly.

    待测光纤面板9和分辨率靶5紧贴在一起,其中分辨率靶5是标准分辨率靶,其分辨率条带宽度均匀,且明暗对比度在90%以上。 The optical fiber panel 9 to be tested is closely attached to the resolution target 5, wherein the resolution target 5 is a standard resolution target with a uniform resolution strip width and a light-dark contrast of over 90%.

    所述的显微镜观察系统6为一种光学显微镜,该显微镜中带有CCD接口,可以通过微机处理。显微镜的物镜对准待测光纤面板9。所述的Z轴移动机构7为一种调整显微镜焦距的外围辅助装置。 The microscope observation system 6 is an optical microscope with a CCD interface, which can be processed by a microcomputer. The objective lens of the microscope is aimed at the optical fiber panel 9 to be tested. The Z-axis moving mechanism 7 is a peripheral auxiliary device for adjusting the focal length of the microscope.

所述的CCD数据采集和微机处理系统8包括CCD图像采集卡和微机平台,CCD图像采集卡位于显微镜的接口连接处,可将所观察到的像的模拟量转为数字量。微机可以对传送的数据进行综合处理,如暗影定位、参数设置、绘制图像、打印报表等操作。 The CCD data acquisition and microcomputer processing system 8 includes a CCD image acquisition card and a microcomputer platform. The CCD image acquisition card is located at the interface connection of the microscope, and can convert the analog quantity of the observed image into a digital quantity. The microcomputer can comprehensively process the transmitted data, such as shadow positioning, parameter setting, drawing images, printing reports and other operations.

本发明的光路为标准光源1发出单色光经过聚光镜3,然后射入积分球4的一个补偿口,之后入射光在积分球内发生漫反射再从积分球的另一补偿口射出,再透射过待测光纤面板9,再从分辨率靶5到显微物镜,由显微物镜发射到目镜,最后再进入人的眼球。 The optical path of the present invention is that the standard light source 1 emits monochromatic light through the condenser lens 3, and then enters a compensation port of the integrating sphere 4, and then the incident light is diffusely reflected in the integrating sphere and then emitted from another compensation port of the integrating sphere, and then transmitted Pass through the optical fiber panel 9 to be tested, then from the resolution target 5 to the microscopic objective lens, and then from the microscopic objective lens to the eyepiece, and finally enter the human eyeball.

标准光源1和稳流源2提供2856K光具有强度与色温稳定的标准光,经过聚光镜3,由于聚光镜3的聚光作用,此时光源已被汇聚,再调节积分球4下移动机构的金属面板的XY坐标,使汇聚的光经过积分球的一个补偿口,进入积分球内部,积分球将光束均匀漫射后照明均匀漫射出口处的分辨率靶5。 The standard light source 1 and the steady flow source 2 provide 2856K standard light with stable intensity and color temperature. After passing through the condenser lens 3, the light source has been converged due to the light-gathering effect of the condenser lens 3. Then adjust the metal panel of the moving mechanism of the integrating sphere 4 XY coordinates, so that the converged light enters the interior of the integrating sphere through a compensation port of the integrating sphere, and the integrating sphere uniformly diffuses the light beam and illuminates the resolution target 5 at the uniformly diffused exit.

如图2所示,在任意时刻,分辨率靶5的电势与Z轴无关,可以化为二维问题来计算,因此靶内任意一点的电位必由二维拉普拉斯方程及相应的边界条件决定: As shown in Figure 2, at any moment, the potential of the resolution target 5 has nothing to do with the Z axis, and can be calculated as a two-dimensional problem, so the potential of any point in the target must be determined by the two-dimensional Laplace equation and the corresponding boundary conditions:

 ; ;

;

;

其中为分辨率靶5的厚度,为靶表面电位分布,为靶压。由于可以有分别满足一个带有齐次边界条件的二维拉普拉斯方线性叠加可以导出其最终表达式为: in is the thickness of the resolution target 5, is the target surface potential distribution, is the target pressure. because You may have Respectively satisfying a linear superposition of two-dimensional Laplace squares with homogeneous boundary conditions can lead to the final expression as:

,

其中分别为的导出系数,是双曲正弦函数,另外,C为靶的对比度,I为当前光电流,为靶的基准电流,为了维持较高的精度,采用对比度大于90%的分辨率靶,此时可以忽略其电荷泄露造成的影响。当该处存在暗影点时该处电势为零,因此该方法可以唯一确定x、y的坐标。用手动或自动调整显微物镜的Z坐标,直至通过显微镜目镜能够观察到清晰的像,显微物镜将局部面板图案放大,显微目镜供人眼直接观察。同时,显微镜观察系统中带有CCD接口,配备CCD采集卡采集图像的模拟数据,经微机处理计算输出所需的结果。 in respectively The derived coefficient of is a hyperbolic sine function, and , C is the contrast of the target, I is the current photocurrent, is the reference current of the target, in order to maintain a high precision, a resolution target with a contrast ratio greater than 90% is used, and the influence caused by the charge leakage can be ignored at this time. When there is a shadow point there, the electric potential is zero, so this method can uniquely determine the coordinates of x and y. Adjust the Z coordinate of the microscopic objective lens manually or automatically until a clear image can be observed through the microscope eyepiece, the microscopic objective lens will enlarge the partial panel pattern, and the microscopic eyepiece can be directly observed by the human eye. At the same time, the microscope observation system has a CCD interface, and is equipped with a CCD acquisition card to collect the analog data of the image, which is processed and calculated by a microcomputer to output the required results.

实际情况可以根据光线面板分辨率的参数要求,有两种做法: The actual situation can be based on the parameter requirements of the resolution of the light panel, and there are two methods:

   1)更换显微放大倍数目镜(10X、16X等)和消色差目镜(5X、10X、40X等),通过显微目镜观察,直接判断光纤面板不同区域的分辨力; 1) Replace the microscopic magnification eyepieces (10X, 16X, etc.) and achromatic eyepieces (5X, 10X, 40X, etc.), and observe through the microscopic eyepieces to directly judge the resolution of different areas of the fiber optic panel;

   2)如要给出定量的数据图像,可将CCD接口与外围微机设备连接。通过CCD数据采集、计算处理输出数据综合参数的报表。 2) To give quantitative data images, the CCD interface can be connected with peripheral microcomputer equipment. Through CCD data acquisition, calculation and processing, the output data comprehensive parameter report.

Claims (6)

1.一种基于暗影剔除的光纤面板极限分辨率测试仪器,包括:标准光源(1)及其稳流源(2),聚光镜(3),积分球(4)及其移动机构,分辨率靶(5),和CCD数据采集和微机处理系统(8),其特征在于:所述分辨率靶(5)设置在所述积分球(4)的均匀漫射出口上;待测光纤面板(9)设置所述分辨率靶(5)和所述积分球(4)的均匀漫射出口之间;所述聚光镜(3)为石英聚光镜。 1. An optical fiber panel limit resolution test instrument based on shadow removal, including: standard light source (1) and its steady current source (2), condenser lens (3), integrating sphere (4) and its moving mechanism, resolution target (5), and CCD data acquisition and microcomputer processing system (8), characterized in that: the resolution target (5) is set on the uniform diffuse outlet of the integrating sphere (4); the optical fiber panel to be tested (9 ) between the resolution target (5) and the uniform diffusion outlet of the integrating sphere (4); the condenser lens (3) is a quartz condenser lens. 2.如权利要求1所述的基于暗影剔除的光纤面板极限分辨率测试仪器,其特征在于:所述标准光源(1)距离所述聚光镜(3)的距离小于聚光镜(3)的焦距。 2 . The optical fiber panel limit resolution testing instrument based on shadow removal according to claim 1 , wherein the distance between the standard light source ( 1 ) and the condenser lens ( 3 ) is smaller than the focal length of the condenser lens ( 3 ). 3 . 3.如权利要求1所述的基于暗影剔除的光纤面板极限分辨率测试仪器,其特征在于:所述积分球(4)是内部涂有无波长选择性的漫反射性的白色涂料的空心球体。 3. The optical fiber panel limit resolution test instrument based on shadow elimination according to claim 1, characterized in that: the integrating sphere (4) is a hollow sphere coated with non-wavelength-selective diffuse reflective white paint inside . 4.如权利要求1所述的基于暗影剔除的光纤面板极限分辨率测试仪器,其特征在于:所述移动机构是和所述积分球(4)连在一起的金属滑台,其周边标有刻度。 4. The optical fiber panel limit resolution test instrument based on shadow removal according to claim 1, characterized in that: the moving mechanism is a metal sliding table connected with the integrating sphere (4), and its periphery is marked with scale. 5.如权利要求4所述的基于暗影剔除的光纤面板极限分辨率测试仪器,其特征在于:还包括显微镜观察系统(6),该显微镜观察系统(6)带有CCD接口,其物镜对准所述待测光纤面板(9)。 5. The optical fiber panel limit resolution test instrument based on shadow removal as claimed in claim 4, characterized in that: it also includes a microscope observation system (6), the microscope observation system (6) has a CCD interface, and its objective lens is aligned with The optical fiber panel to be tested (9). 6.一种基于暗影剔除的光纤面板极限分辨率测试方法,包括如下步骤: 6. A method for testing the limit resolution of an optical fiber panel based on shadow removal, comprising the steps of: 将待测光纤面板(9)设置分辨率靶(5)和积分球(4)的均匀漫射出口之间; Set the optical fiber panel (9) to be tested between the resolution target (5) and the uniform diffuse outlet of the integrating sphere (4); 标准光源(1)发出单色光经过聚光镜(3),然后射入所述积分球(4)的一个补偿口; The monochromatic light emitted by the standard light source (1) passes through the condenser lens (3), and then enters a compensation port of the integrating sphere (4); 之后,入射光在所述积分球(4)内发生漫反射再从积分球(4)的另一补偿口射出; Afterwards, the incident light is diffusely reflected in the integrating sphere (4) and then emitted from another compensation port of the integrating sphere (4); 再透射过所述待测光纤面板(9)和分辨率靶(5)到显微物镜, Then transmit through the optical fiber panel to be tested (9) and the resolution target (5) to the microscope objective lens, 在任意时刻,所述分辨率靶(5)内任意一点的电位                                                由二维拉普拉斯方程及相应的边界条件决定: At any moment, the potential of any point within the resolution target (5) Determined by the two-dimensional Laplace equation and the corresponding boundary conditions:  ; ; ; ; 其中为分辨率靶(5)的厚度,为分辨率靶(5)表面电位分布,为靶压; in is the thickness of the resolution target (5), is the surface potential distribution of the resolution target (5), is the target pressure; 由于分别满足一个带有齐次边界条件的二维拉普拉斯方线性叠加可以导出其最终表达式为: because have Respectively satisfying a linear superposition of two-dimensional Laplace squares with homogeneous boundary conditions can lead to the final expression as: , 其中分别为的导出系数,是双曲正弦函数; in respectively The derived coefficient of is the hyperbolic sine function; 当某处存在暗影点时该处电势为零,可以唯一确定x、y的坐标。 When there is a shadow point somewhere, the electric potential is zero, and the coordinates of x and y can be uniquely determined.
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