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图1为采用精密测角法测试平行光管焦距的基本原理图,将平行光管放置于整平的光学平台上,将星点目标板安装于平行光管焦面位置处并用卤钨灯光源照亮目标板,在平行光管正前方放置全站仪并调整全站仪3个脚螺使其垂直轴垂直于水平面,旋转水平轴使得全站仪视轴处于水平状态。转动全站仪垂直轴轴系使得星点像在方位方向处于全站仪的视场中心,若此时星点像在俯仰方向偏离视场中心,则调整平行光管调节旋钮最终使得星点像在方位方向和俯仰方向均处于全站仪视场中心。取下星点目标板将间距为L的双狭缝目标板安装于平行光管焦面位置处,调整目标板相位使得通过全站仪观察的狭缝像和全站仪竖丝平行,转动全站仪垂直轴轴系依次瞄准对称的两狭缝像,全站仪测得的双狭缝对平行光管的张角记为ω,按公式(1)计算平行光管焦距f,则:
图 1 基于精密测角法的焦距标定原理图
Figure 1. Schematic diagram of focal length calibration based on precision goniometry
$$ f = \frac{L}{{2 \times \tan \left( {\dfrac{\omega }{2}} \right)}} $$ (1) 式中:
$ f $ 为平行光管焦距,单位为mm;$ L $ 为狭缝间距,单位为mm;$ \omega $ 为双狭缝对平行光管的张角,单位为rad。 -
通常情况下在实验室采用图1的原理标定焦距即可,但为了避免重力因素对光管焦距产生影响以及准确评价光电经纬仪焦距,需要对平行光管进行原位检测。为了实现平行光管焦距的原位检测,根据光电经纬仪的实际工作角度范围,在检测架上安装不同倾斜角度的焦面带有狭缝目标板的平行光管,各光管光轴均相交于拱形检测架球心,在地基环上架设全站仪并调平,使用卤钨灯光源照亮待标定光管的双狭缝目标板,狭缝目标经平行光管和全站仪光学系统后用人眼接收并瞄准,标定示意图如图2所示,倾斜安装条件下全站仪测得的双狭缝对平行光管的张角记为
$ \omega ' $ 。图 2 倾斜安装条件下焦距标定示意图
Figure 2. Schematic diagram of focal length calibration under inclined installation
当全站仪视轴处于非水平状态,此时转动垂直轴轴系就会在方位方向产生投影误差,即倾斜状态下测得的张角
$ \omega ' $ 和水平状态下测得的张角$ \omega $ 不相等,倾斜角度越大两者相差越大,这是由全站仪自身的测角原理所决定的,属于系统性、原理性误差,因此需要对倾斜安装状态下测试的张角值进行修正,为此建立以下数学模型:设图3为平行光管狭缝目标板上的点与全站仪角度之间的映射关系,
$ MOQ $ 面为双狭缝所在的平面,$ O $ 点为焦平面的中心,$ {O_1} $ 点为平行光管主点,$ N $ 点为目标板十字横线与狭缝的交点,$ ON $ 为中心点到狭缝的距离,$ OQ $ 平行于水平面,$ OM $ 与$ OQ $ 垂直,以$ OQ $ 和$ OM $ 分别为横轴和纵轴建立直角坐标系$ OXY $ 。$ {N_1}Q\parallel MO $ ,$ M{N_1}\parallel OQ $ ,$ M' {O_1}Q' $ 为水平面,$ {O_1}P $ 为$ MP $ 在水平面内的投影,$ M $ 、$ {N_1} $ 、$ O $ 、$ Q $ 在水平面内的投影点为$ M' $ 、$ N' $ 、$ O' $ 、$ Q' $ ,令$ OQ = x $ ,$ OM = y $ ,$ O{O_1} = f $ ,$ \angle O{O_1}P = \angle {E_o} $ ,$ \angle P{O_1}N' = \angle A $ ,$ \angle N{O_1}N' = \angle E $ ,由空间几何关系,可推导出如下关系式:图 3 目标板上的点与全站仪角度之间的映射关系
Figure 3. Mapping between the point on the target board and the total station angle
$$ \begin{split} x = & f \times \sin\angle A \times \tan\angle A\Big/ ( \tan\angle E \times \sin\angle {E_o} \times \tan\angle A +\\ & \cos\angle {E_o} \times \sin\angle A ) \end{split} $$ (2) $$\begin{split} y=& f\times \left(\tan\angle A\times \tan\angle E\times \cos\angle {E}_{o}-\sin\angle {E}_{o} \times \sin\angle A\right)/\\ & \left(\tan\angle E\times \sin\angle {E}_{o} \times \tan\angle A+\cos\angle {E}_{o} \times \sin\angle A\right) \end{split} $$ (3) 点
$\left( {x,y} \right)$ 距离平行光管焦面中心的距离为:$$ O{N_1} = \sqrt {{x^2} + {y^2}} $$ (4) 则由公式(2)~(4)联立解得平行光管焦距:
$$ f = \frac{{O{N_1} \times \left( \tan \angle E \times \sin \angle {E_o} \times \tan \angle A + \cos \angle {E_o} \times \sin \angle A \right)}}{{\sqrt {{{\left( {\sin \angle A \times \tan \angle A} \right)}^2} + {{\left( \tan \angle A \times \tan \angle E \times \cos \angle {E_o} - \sin \angle {E_o} \times \sin \angle A \right)}^2}} }} $$ (5) -
采用光刻工艺制做一块狭缝目标板,目标板形状为圆形,直径为30 mm,基底材料为K9玻璃,具体布局见图4,狭缝目标板中心制作有十字线,十字竖线一侧平行地刻划有三条狭缝,十字线和狭缝透光,其余部分均不透光,
$ {N_1} $ 、$ {N_2} $ 、$ {N_3} $ 分别为狭缝1、狭缝2、狭缝3与十字横线的交点,$ O $ 为十字线交点。三条狭缝距离十字竖线的距离分别用$ O{N_1} $ 、$ O{N_2} $ 、$ O{N_3} $ 表示,使用德国马尔公司制造的10106 HA型三坐标测量仪对狭缝到十字竖线的距离进行测量,测量结果由小到大依次为2.9245、6.5432、9.4979 mm。将制做好的目标板安装到检测架上平行光管的焦面位置处,在地基环上架设瑞士徕卡公司制造的TC2003型全站仪,如图5所示,使用全站仪首先瞄准目标板经平行光管出射的十字线交叉点
$ O $ ,记方位角为$ \angle {A_o} $ ,俯仰角为$ \angle {E_o} $ ,其次瞄准十字横线与狭缝的交点,记方位角为$ \angle A $ ,俯仰角为$ \angle E $ 。转动目标板并通过全站仪目镜进行观察,使得线段
$ {N_1}{N_3} $ 经平行光管出射后分别成像于全站仪分划板的第一象限、第二象限、第三象限、第四象限及与分划板的竖丝和横丝平行,按照上述测试流程依次瞄准交点$ O $ 、$ {N_1} $ 、$ {N_2} $ 、$ {N_3} $ 并采集对应的方位角和俯仰角,过程数据如表1所示。表 1 线段 N1、N3位于不同象限及与分划板横丝竖丝平行时的过程数据 (单位:弧度)
Table 1. Process data when the N1, N3 is located in different quadrants and parallel to the horizontal and vertical wire of the reticle (Unit: rad)
Points to be measured Imaging area of ${N_1},{N_3}$ First
quadrantSecond
quadrantThird
quadrantFourth
quadrantCoincidence with the
horizontal wireCoincidence with the
vertical wire$ {N_1} $ $ \angle {A_o} $ 0 0 0 0 0 0 $ \angle {E_o} $ 1.044524 1.044598 1.044626 1.044598 1.044621 1.044580 $ \angle A $ 0.000625 0.000568 0.002066 0.002547 0.002935 0 $ \angle E $ 1.045966 1.046047 1.043576 1.043868 1.044611 1.046057 $ {N_2} $ $ \angle {A_o} $ 0 0 0 0 0 0 $ \angle {E_o} $ 1.044524 1.044598 1.044626 1.044598 1.044621 1.044580 $ \angle A $ 0.001348 0.001277 0.004519 0.005625 0.006489 0 $ \angle E $ 1.047709 1.047788 1.042299 1.042988 1.044615 1.047836 $ {N_3} $ $ \angle {A_o} $ 0 0 0 0 0 0 $ \angle {E_o} $ 1.044524 1.044598 1.044626 1.044598 1.044621 1.044580 $ \angle A $ 0.002003 0.001749 0.006530 0.008002 0.009276 0 $ \angle E $ 1.049068 1.049175 1.041322 1.042263 1.044620 1.049236 -
将线段
${N_1}、{N_3}$ 分别位于不同象限及与分划板横丝平行时所采集的$ \angle {E_o} $ ,$ \angle A $ (另$ \angle {A_o} = 0 $ ,则$ \angle A - \angle {A_o} = \angle A $ ),$ \angle E $ 代入公式(5)可解得修正投影误差后的平行光管焦距,最终解算的焦距值如表2所示。由表2可知,经投影误差修正后由同名测试点解算的焦距最大差值为4.41 mm,测试点$ {N_1} $ 的焦距平均值为1982.19 mm,波动值为4.40 mm,测试点$ {N_2} $ 的焦距平均值为2009.94 mm,波动值为3.39 mm,测试点$ {N_3} $ 的焦距平均值为2039.15 mm,波动值为3.79 mm。各测试点焦距平均值出现较大差异是由畸变引入的原理性误差所致。平行光管半视场为15 mm,则$ {N_1} $ 点位于0.19视场位置处,$ {N_2} $ 点位于0.44视场位置处,$ {N_3} $ 点位于0.63视场位置处,由平行光管的光学设计结果可知0.19视场处系统畸变为0.02%,该值可忽略,0.44及0.63视场处系统畸变分别为−1.3%和−2.8%,根据畸变设计结果对$ O{N_2} $ 、$ O{N_3} $ 的长度进行修正重新代入公式(5)计算焦距,如表3所示,测试点$ {N_2} $ 的焦距平均值变为1983.81 mm、测试点$ {N_3} $ 的焦距平均值变为1982.06 mm,修正畸变后,测试点$ {N_2} $ 和$ {N_3} $ 的焦距平均值与测试点$ {N_1} $ 的焦距平均差值分别为1.62 mm和−0.13 mm。表 2 修正投影误差后线段 N1、N3位于不同象限及与分划板横丝平行时的焦距解算结果 (单位:毫米)
Table 2. Focal length when the N1, N3 is located in different quadrants and parallel to the horizontal wire of the reticle after correcting the projection error (Unit: mm)
Points to be measured Imaging area of ${N_1}, {N_3}$ First quadrant Second quadrant Third quadrant Fourth quadrant Coincidence with the horizontal wire $ {N_1} $ 1981.77 1980.37 1980.24 1984.65 1983.93 $ {N_2} $ 2009.70 2011.13 2011.01 2010.13 2007.73 $ {N_3} $ 2041.14 2038.21 2037.35 2040.33 2038.74 表 3 修正投影误差和畸变后各测试点的焦距解算结果 (单位:毫米)
Table 3. Focal length of different testing points after correcting the projection error and distortion (Unit: mm)
Points to be measured The imaging area of ${N_1}, {N_3}$ First quadrant Second quadrant Third quadrant Fourth quadrant Coincidence with the horizontal wire $ {N_1} $ 1981.77 1980.37 1980.24 1984.65 1983.93 $ {N_2} $ 1983.58 1984.98 1984.86 1984.00 1981.63 $ {N_3} $ 1983.99 1981.14 1980.31 1983.20 1981.66 为了解耦投影误差并获得焦距的真值,根据全站仪工作原理,转动水平轴轴系进行俯仰方向的角度测量时不存在投影误差,因此可以利用表1中线段
${N_1},{N_3}$ 与分划板竖丝平行时的过程数据解算焦距并作为真值来验证模型的正确性,需要注意的是,公式中的$ \omega $ 需以$ 2\left| {\angle {E_o} - \angle E} \right| $ 代替,最终解算的焦距值如表4所示。表 4 线段 N1、N3与分划板竖丝平行时的焦距解算结果 (单位:毫米)
Table 4. Focal length when the N1, N3 is parallel to the vertical wire of the reticle (Unit: mm)
Points to be measured Coincidence with the vertical wire $ {N_1} $ 1980.03 $ {N_2} $ 2009.58 $ {N_3} $ 2039.91 同样由于畸变的存在,各测试点解算的焦距值差异较大,测试点
$ {N_1} $ 、$ {N_2} $ 、$ {N_3} $ 的焦距值分别为1980.03、2009.58、2039.91 mm,进行畸变修正后对应的焦距值分别为1980.03、1983.45、1982.79 mm,波动值为3.43 mm,各测试点焦距平均值即真值为1982.09 mm。线段${N_1}、{N_3}$ 位于不同象限及与分划板横丝平行时的各测试点在修正投影误差和畸变后焦距平均值为1982.69 mm,此值与真值差值为0.6 mm,验证了模型的正确性及鲁棒性。修正畸变后将线段
${N_1}、{N_3}$ 与分划板横丝平行时所采集的$ \angle {A_o} $ 、$ \angle {E_o} $ 、$ \angle A $ 及$ \angle E $ 代入公式(2)中可解得传统意义下的焦距,需要注意的是公式中的$ \omega $ 需以$ 2\left| {\angle A - \angle {A_o}} \right| $ 代替,最终解算的焦距值如表5所示。表 5 修正畸变后线段 N1、N3与分划板横丝平行时的焦距解算结果(单位:毫米)
Table 5. Focal length when the N1, N3 is parallel to the horizontal wire of the reticle with correcting the distortion (Unit: mm)
Points to be measured Coincidence with the horizontal wire $ {N_1} $ 996.42 $ {N_2} $ 995.23 $ {N_3} $ 995.22 由表5可知,修正畸变但未修正投影误差的情况下由测试点
$ {N_1} $ 、$ {N_2} $ 、$ {N_3} $ 解算的焦距结果分别为996.42、995.23、995.22 mm,焦距平均值与真值之差为986.47 mm,相对误差为50.2%。 -
令公式(5)中的
$$O{N_1} \times \left( {\tan \angle E\sin \angle {E_o}\tan \angle A + \cos \angle {E_o}\sin \angle A} \right){\text{ = }}\alpha $$ $$ \begin{split} & {[ {{{\left( {\sin \angle A\tan \angle A} \right)}^2} + {{( \tan \angle A\tan \angle E\cos \angle {E_o} -}}}} \\ &{{{{ \sin \angle {E_o}\sin \angle A )}^2}} ]^{{{ - }}\tfrac{1}{2}}}{\text{ = }}\beta \end{split} $$ $$ \begin{split} &{\left( {\sin \angle A\tan \angle A} \right)^2} + {( \tan \angle A\tan \angle E\cos \angle {E_o} -} \\ & { \sin \angle {E_o}\sin \angle A)^2}{\text{ = }}\gamma \end{split}$$ $$ \tan \angle A\tan \angle E\cos \angle {E_o} - \sin \angle {E_o}\sin \angle A{\text{ = }}\xi $$ 则焦距f的表达式可变换为:
$$ f = \alpha \beta $$ (6) $\angle A$ 、$\angle E$ 、$\angle {E_\textit{o}}$ 及$O{N_1}$ 对焦距的灵敏度系数分别如下式所示:$$ \begin{split} \frac{{\partial f}}{{\partial \angle A}} =& \frac{{\partial f}}{{\partial \alpha }}\frac{{\partial \alpha }}{{\partial \angle A}} + \frac{{\partial f}}{{\partial \beta }}\frac{{\partial \beta }}{{\partial \angle A}} =\\ & \beta O{N_1}\left( \begin{gathered} \frac{{\tan\angle E\sin\angle {E_o}}}{{\cos{^2}\angle A + \cos\angle {E_o}\cos\angle A }} \\ \end{gathered} \right) - \\ & \alpha {\gamma ^{ - \tfrac{3}{2}}}\left[ \tan\angle A\left( {\sin{^2}\angle A + \tan{^2}\angle A} \right) +\right.\\ & \left. \xi \left( \frac{{\tan\angle E\cos\angle {E_o}}}{{\cos{^2}\angle A+ \sin\angle {E_o}\cos\angle A }} \right) \right] \\ \end{split} $$ (7) $$ \begin{split} \frac{{\partial f}}{{\partial \angle E}} =& \frac{{\partial f}}{{\partial \alpha }}\frac{{\partial \alpha }}{{\partial \angle E}} + \frac{{\partial f}}{{\partial \beta }}\frac{{\partial \beta }}{{\partial \angle E}} =\\ & \beta O{N_1}\left( \frac{{\sin\angle {E_o}\tan\angle A}}{{\cos{^2}\angle E + \cos\angle {E_o}\sin\angle A }} \right) - \\ & \alpha {\gamma ^{ - \tfrac{3}{2}}}\xi \frac{{\tan\angle A \cos\angle {E_o}}}{{\cos{^2}\angle E}} \\ \end{split} $$ (8) $$ \begin{split}& \frac{{\partial f}}{{\partial \angle {E_\textit{o}}}} = \frac{{\partial f}}{{\partial \alpha }}\frac{{\partial \alpha }}{{\partial \angle {E_\textit{o}}}} + \frac{{\partial f}}{{\partial \beta }}\frac{{\partial \beta }}{{\partial \angle {E_\textit{o}}}} =\\ & \beta O{N_1}\left( {\tan\angle A \tan\angle E \cos\angle {E_\textit{o}} - \sin\angle A \sin\angle {E_\textit{o}}} \right) +\\ & \alpha {\gamma ^{ - \tfrac{3}{2}}}\xi \left( {\tan\angle A \tan\angle E \sin\angle {E_\textit{o}} - \cos\angle {E_\textit{o}}\sin\angle A} \right) \end{split} $$ (9) $$ \begin{split} \frac{{\partial f}}{{\partial O{N_1}}} =& \frac{{\partial f}}{{\partial \alpha }}\frac{{\partial \alpha }}{{\partial O{N_1}}} = \beta( \tan\angle A \tan\angle E \sin\angle {E_\textit{o}} +\\ & \cos\angle {E_\textit{o}}\sin\angle A \end{split} $$ (10) 设
$\angle A$ 、$\angle E$ 、$\angle {E_o}$ 及$O{N_1}$ 的测量标准不确定度分别为$ {\mu _A} $ 、${\;\mu _E}$ 、$ {\;\mu _{{E_o}}} $ 、$ {\;\mu _{O{N_1}}} $ 且相互独立。则线段${N_1}、{N_3}$ 位于不同象限及与分划板横丝平行时焦距测量结果的不确定度应是所有不确定度分量的合成,用合成标准不确定度${\;\mu _{{c}}}$ 来表示,如下式所示:$$ \;{\mu _{{c}}}{{ = }}\sqrt {{\left( {\frac{{{\partial} f}}{{{\partial} \angle A}}{\mu _A}} \right)^2}{{ + }}{\left( {\frac{{{\partial} f}}{{{\partial} \angle E}}{\mu _E}} \right)^2} + {\left( {\frac{{{\partial} f}}{{{\partial} \angle {E_o}}}{\mu _{{E_o}}}} \right)^2} + {\left( {\frac{{{\partial} f}}{{{\partial} O{N_1}}}{\mu _{O{N_1}}}} \right)^2} } $$ (11) 线段
${N_1}、{N_3}$ 与分划板竖丝平行时焦距的解算公式可表示为:$$ f = \frac{{O{N_1}}}{{\tan \left( {\left| {\angle {E_o} - \angle E} \right|} \right)}} $$ (12) 合成标准不确定度用
${\;\mu _{{c}}}^\prime$ 来表示,如下式所示:$$ {\mu _{{c}}}^\prime {\text{ = }}\sqrt {{{\left( {\frac{1}{{\tan\left( {\left| {\angle {E_o} - \angle E} \right|} \right)}}{\mu _{O{N_1}}}} \right)}^2}{\text{ + }}{{\left( {\frac{{O{N_1}}}{{\sin\left( {\left| {\angle {E_o} - \angle E} \right|} \right)}}{\mu _E}} \right)}^2}} $$ (13) 通过查验全站仪和三坐标测量仪计量证书可知
$ \;{\mu }_{A}\text{=0}\text{.3}″ $ ,$ \;{\mu }_{E}\text{=}{\mu }_{{E}_{o}}\text{=}0.4″ $ ,$\; {\mu _{O{N_1}}}{\text{ = }}1.0\;{\text{μ}} {\rm{m}}$ 。修正畸变后将采集的过程数据及相应的测量标准不确定度代入公式(11)和公式(13)中,可得各测试点对应焦距的合成标准不确定度,取包含因子k=2,则展伸不确定度U=2${\;\mu _{{c}}}$ (2$\;{\mu _{{c}}}'$ ),如表6所示。表 6 焦距测量结果的展伸不确定度 (单位:毫米)
Table 6. Extended uncertainty of focal length (Unit: mm)
Points to be measured Extended uncertainty First quadrant Second quadrant Third quadrant Fourth quadrant Coincidence with the
horizontal wireCoincidence with the
vertical wire$ {N_1} $ 7.33 7.35 5.58 4.26 2.39 1.36 $ {N_2} $ 3.33 3.34 2.55 1.93 1.08 0.60 $ {N_3} $ 2.33 2.33 1.76 1.36 0.76 0.42 由表6可知:线段
${N_1}、{N_3}$ 位于不同象限及与分划板横丝平行时,各测试点的焦距测量结果展伸不确定度均大于与竖丝平行时的焦距测量结果展伸不确定度,测量结果的展伸不确定度与焦距真值的最大相对误差为0.36%,该值远小于GB/T 9917.1—2002 照相镜头中实测焦距对名义焦距的相对误差不超过±5%的规定。
Research on focal length calibration method of oblique installation collimator
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摘要:
平行光管水平放置和倾斜安装时由于受力状态不同其光学参数会有较大差异,为了精准评价平行光管的焦距,根据平行光管焦面上的点与全站仪角度之间的映射关系,建立了倾斜安装条件下光管焦距与全站仪角度关系的精确数学模型,修正了全站仪垂直轴轴系转动时产生的原理性投影误差。使用全站仪采集了多组数据并进行了实验验证:修正畸变后由焦面目标与竖丝平行时的各测试点解算的焦距值分别为1980.03、1983.45、1982.79 mm,焦距平均值即真值为1982.09 mm。修正畸变但未修正投影误差的情况下由焦面目标与分划板横丝平行时的各测试点解算的焦距值分别为996.42、995.23、995.22 mm,焦距平均值相对误差为50.2%。修正投影误差和畸变后由焦面目标位于不同象限及与分划板横丝平行时的各测试点 解算的焦距值极差为4.74 mm,焦距平均值为1982.69 mm,与真值差值为0.6 mm。测量结果的展伸不确定度与焦距真值的最大相对误差为0.36%,该值远小于GB/T 9917.1—2002 照相镜头中实测焦距对名义焦距的相对误差不超过±5%的规定。实验结果表明:该模型具有较高的解算精度,目标狭缝在分划板中的相位可以是随机值,对于倾斜安装条件下平行光管焦距的原位检测具有极大的工程应用价值。 Abstract: When the collimator is placed horizontally and installed obliquely, its optical parameters will be greatly different due to different stress states. In order to accurately evaluate the focal length of collimator, according to the mapping relationship between the point on the focal plane of the collimator and the angle of the total station, an accurate mathematical model of the relationship between the focal length and the angle of the total station under the condition of oblique installation is established, the principle projection error caused by the rotation of the vertical axis of the total station is corrected. Several groups of data are collected by total station and experimental verification is carried out. After correcting the distortion, the focal length calculated by each testing point when the line segment is parallel to the vertical wire are 1 980.03 mm, 1 983.45 mm, 1 982.79 mm, the average focal length, i.e. the true value, is 1 982.09 mm. When the distortion is corrected but the projection error is not corrected, the focal length calculated from each testing point when the line segment is parallel to the horizontal wire of the reticle is 996.42 mm, 995.23 mm, 995.22 mm, the relative error of the average focal length is 50.2%. The range of focal length calculated by each testing point when the line segment is located in different quadrants and parallel to the horizontal wire of the reticle is 4.74 mm after correcting the projection error and distortion, the average focal length of all testing points is 1982.69 mm, the difference between the average value and the true value is 0.6 mm. The maximum relative error between the extended uncertainty of the focal length calculated by different testing point and the true value of the focal length is 0.36%. This value is far less than the stipulation in GB/T 9917.1-2002 that the relative error between the measured focal length and the nominal focal length in the photographic lens does not exceed ±5%. The experimental results show that the model has universality and high accuracy, the phase of the target slit in the reticle is allowed to be a random value, there is no need to adjust the slit to be strictly parallel to the vertical wire of the total station, the model has great engineering application value for the in-situ detection of the focal length of the collimator under the condition of oblique installation.-
Key words:
- focal length /
- distortion /
- projection error /
- in-situ calibration /
- random phase
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表 1 线段 N1、N3位于不同象限及与分划板横丝竖丝平行时的过程数据 (单位:弧度)
Table 1. Process data when the N1, N3 is located in different quadrants and parallel to the horizontal and vertical wire of the reticle (Unit: rad)
Points to be measured Imaging area of ${N_1},{N_3}$ First
quadrantSecond
quadrantThird
quadrantFourth
quadrantCoincidence with the
horizontal wireCoincidence with the
vertical wire$ {N_1} $ $ \angle {A_o} $ 0 0 0 0 0 0 $ \angle {E_o} $ 1.044524 1.044598 1.044626 1.044598 1.044621 1.044580 $ \angle A $ 0.000625 0.000568 0.002066 0.002547 0.002935 0 $ \angle E $ 1.045966 1.046047 1.043576 1.043868 1.044611 1.046057 $ {N_2} $ $ \angle {A_o} $ 0 0 0 0 0 0 $ \angle {E_o} $ 1.044524 1.044598 1.044626 1.044598 1.044621 1.044580 $ \angle A $ 0.001348 0.001277 0.004519 0.005625 0.006489 0 $ \angle E $ 1.047709 1.047788 1.042299 1.042988 1.044615 1.047836 $ {N_3} $ $ \angle {A_o} $ 0 0 0 0 0 0 $ \angle {E_o} $ 1.044524 1.044598 1.044626 1.044598 1.044621 1.044580 $ \angle A $ 0.002003 0.001749 0.006530 0.008002 0.009276 0 $ \angle E $ 1.049068 1.049175 1.041322 1.042263 1.044620 1.049236 表 2 修正投影误差后线段 N1、N3位于不同象限及与分划板横丝平行时的焦距解算结果 (单位:毫米)
Table 2. Focal length when the N1, N3 is located in different quadrants and parallel to the horizontal wire of the reticle after correcting the projection error (Unit: mm)
Points to be measured Imaging area of ${N_1}, {N_3}$ First quadrant Second quadrant Third quadrant Fourth quadrant Coincidence with the horizontal wire $ {N_1} $ 1981.77 1980.37 1980.24 1984.65 1983.93 $ {N_2} $ 2009.70 2011.13 2011.01 2010.13 2007.73 $ {N_3} $ 2041.14 2038.21 2037.35 2040.33 2038.74 表 3 修正投影误差和畸变后各测试点的焦距解算结果 (单位:毫米)
Table 3. Focal length of different testing points after correcting the projection error and distortion (Unit: mm)
Points to be measured The imaging area of ${N_1}, {N_3}$ First quadrant Second quadrant Third quadrant Fourth quadrant Coincidence with the horizontal wire $ {N_1} $ 1981.77 1980.37 1980.24 1984.65 1983.93 $ {N_2} $ 1983.58 1984.98 1984.86 1984.00 1981.63 $ {N_3} $ 1983.99 1981.14 1980.31 1983.20 1981.66 表 4 线段 N1、N3与分划板竖丝平行时的焦距解算结果 (单位:毫米)
Table 4. Focal length when the N1, N3 is parallel to the vertical wire of the reticle (Unit: mm)
Points to be measured Coincidence with the vertical wire $ {N_1} $ 1980.03 $ {N_2} $ 2009.58 $ {N_3} $ 2039.91 表 5 修正畸变后线段 N1、N3与分划板横丝平行时的焦距解算结果(单位:毫米)
Table 5. Focal length when the N1, N3 is parallel to the horizontal wire of the reticle with correcting the distortion (Unit: mm)
Points to be measured Coincidence with the horizontal wire $ {N_1} $ 996.42 $ {N_2} $ 995.23 $ {N_3} $ 995.22 表 6 焦距测量结果的展伸不确定度 (单位:毫米)
Table 6. Extended uncertainty of focal length (Unit: mm)
Points to be measured Extended uncertainty First quadrant Second quadrant Third quadrant Fourth quadrant Coincidence with the
horizontal wireCoincidence with the
vertical wire$ {N_1} $ 7.33 7.35 5.58 4.26 2.39 1.36 $ {N_2} $ 3.33 3.34 2.55 1.93 1.08 0.60 $ {N_3} $ 2.33 2.33 1.76 1.36 0.76 0.42 -
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