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利用长焦距、大口径平行光管,基于调制函数法来完成相机焦平面组件的装调。为了保证集成测试精度,需要配备制冷设备和温度传感器,确保相机在每次测试过程中焦面组件、镜头及主框架温升区间的一致性。在保证相机状态及环境条件一致的条件下快速、多轮次测试,找到焦面组件空间位置的最优解。
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建立如图3所示的测试系统,利用测量手段将平行光管的视轴与相机的视轴调至平行状态。在进行焦面组件装调时,需建立相机安装基准与焦面组件之间的空间位置关系。平行光管焦面处安装MTF测试靶标,用相机对测试靶标进行成像,计算出相机在各视场、各谱段(全色谱段和多光谱谱段)的MTF,得到CCD在各视场、各谱段的离焦量。
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获取初步的光学测试数据后,建立焦面组件与相机镜头之间的三维模型,进一步将光学测试数据转换为机械加工数据,从而获得满足技术要求的垫片厚度的解。
利用三维设计软件建立焦面组件与焦面组件安装面的模型,如图4所示。以焦面组件中全色谱段的中心像元为基准点,以探测器的线阵水平度不变为约束条件,将上述MTF测试获得的各视场、各谱段的离焦量通过焦面组件在
${{O' - X'Y'Z'}}$ 坐标系中分别或同时绕X′轴和Y′轴旋转以及沿Z′轴平移来补偿,从而快速获取焦面组件调整后理想的空间位置。然后,在三维模型中计算调整前后两个状态下调整垫片在各安装孔位处的厚度差,最终确定焦面组件安装垫片的修配量。 -
经过多轮测试后,在三维模型的指导下确定了焦面组件的最佳空间位置,仅经过一轮垫片修配就完成了焦面组件的集成工作。测试结果表明,相机整机各视场及各谱段的MTF (详见表1)均可满足技术要求,各片CCD间的共焦性优于±0.04 mm,线阵水平优于±1′。
表 1 后视相机MTF
Table 1. MTF of the back camera
Test project P B1 B2 B3 B4 Average MTF 0.2 0.36 0.36 0.37 0.36 -
内方位元素与畸变的测试精度是影响测绘相机成图精度的重要因素,各级摄影测量数字化测图规范对测绘相机的内、外方位元素的测试误差均有明确的规定,测绘相机实验室测试结果作为摄影测量处理的初始值使用,其测试精度会影响初期的解算效率和精度。
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国内外通常采用光电精密测角法对长焦距航天测绘遥感相机的内方位元素与畸变进行测试,测试原理如图5所示。图中:
$N'$ 为被测相机镜头的后节点,O为像面中心,P为像面测量主点位置,角度$\Delta W$ 为测量主点和像面中心偏差所成的角度,f为被测相机主距,${H_i}$ 为测量点,${H'_i}$ 为被测点的理想位置,${L_i}$ 为${H_i}$ 距像面中心O点的距离,${W_i}$ 为对应${H_i}$ 点的偏角。图 5 一维内方位元素与畸变测试原理
Figure 5. Measuring principle of elements of interior orientation and distortion for one dimension
根据图中的几何关系,
${H_i}$ 点的畸变计算公式为:$${D_i} = {L_i} - f {\rm{tan}} {W_i} + p{{\rm{tan}} ^2}{W_i}$$ (1) 为了求解该方程,一般令畸变的平方和最小,从而得到该超定方程的解[6-7],求出主点和主距:
$$\left\{ \begin{array}{l} f = \frac{{\left(\displaystyle\sum\limits_{i = 1}^N {{L_i}{{\tan }^2}{W_i}} \cdot \displaystyle\sum\limits_{i = 1}^N {{{\tan }^3}{W_i}} \right) - \left(\displaystyle\sum\limits_{i = 1}^N {{L_i}\tan {W_i}} \cdot \displaystyle\sum\limits_{i = 1}^N {{{\tan }^4}{W_i}} \right)}}{{{{\left(\displaystyle\sum\limits_{i = 1}^N {{{\tan }^3}{W_i}} \right)}^2} - \left(\displaystyle\sum\limits_{i = 1}^N {{{\tan }^2}{W_i}} \cdot \displaystyle\sum\limits_{i = 1}^N {{{\tan }^4}{W_i}} \right)}} \\ p = \frac{{\left(\displaystyle\sum\limits_{i = 1}^N {{L_i}{{\tan }^2}{W_i}} \cdot \displaystyle\sum\limits_{i = 1}^N {{{\tan }^2}{W_i}} \right) - \left(\displaystyle\sum\limits_{i = 1}^N {{L_i}\tan {W_i}} \cdot \displaystyle\sum\limits_{i = 1}^N {{{\tan }^3}{W_i}} \right)}}{{{{\left(\displaystyle\sum\limits_{i = 1}^N {{{\tan }^3}{W_i}} \right)}^2} - \left(\displaystyle\sum\limits_{i = 1}^N {{{\tan }^2}{W_i}} \cdot \displaystyle\sum\limits_{i = 1}^N {{{\tan }^4}{W_i}} \right)}} \end{array} \right.\!\!\!\!$$ (2) 相机的主点与相面中心位置的差别一般在像元级,可以忽略不计,即p=0,可以得到:
$$f = \sum\limits_{i = 1}^N {{L_i} \cdot \tan {W_i}} \Big/\sum\limits_{i = 1}^N {{{\tan }^2}} {W_i}$$ (3) 假设被测相机的主距值f已知,可以得到:
$$ p = \left(\sum\limits_{i = 1}^N {f \cdot {{\tan }^3}{W_i} - } \sum\limits_{i = 1}^N {{L_i} \cdot {{\tan }^2}{W_i}} \right)\Big/\sum\limits_{i = 1}^N {{{\tan }^4}{W_i}} $$ (4) 将采集到的每个采样点的质心位移
${L_i}$ 以及对应的角量${W_i}$ 代入公式(2)中得到主点p和主距f,再将主点p和主距f代入公式(1)中求解每个采样点的畸变${D_i}$ 。畸变测量误差随着被测相机视场角的增大而变大,其中测角误差是畸变误差的主要来源,因而提高测角精度是关键。主距测试误差与被测相机设计的视场角有关,被测相机设计的视场角越小,主距的测试误差越大。在视场角一定的情况下,提高测试设备的测角精度也是提高主距测试精度的关键。在确保测角精度的提前下,适当增加采用点数量可以提高主距和畸变的测量精度[8]。但随着采样点数量的提高,相机开机测试的时间也会相应的延长,被测相机和测试系统的不稳定性会制约测试精度的提高。所以,测试系统测角精度的提高、采样点数量与测试时间的冲突是该相机内方位元素与畸变测试的难点。
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根据上节分析可知,在较短的测试时间内如何能确保测试系统具备较高的测角精度是高效、高精度完成内方位元素与畸变测试的关键。高精度转台分度误差的来源是多方面的,包括轴系误差、偏心误差、光栅分度误差、细分误差等,所有误差综合起来构成转台的分度示值误差。对于转台的综合误差,一般采用精度更高的仪器设备对其误差进行检定,然后采用插值的方式对其分段补偿,补偿后的分度视值误差可优于2″甚至更高,比较常见的检定方法是直接比较法和排列互比法[9-12]。对于大型高精度转台,由于其体积巨大,运行缓慢,一般采用直接比较法。考虑到高分七号双线阵相机进行内方位元素与畸变测试时,仅仅使用水平旋转5°以内的小区间,比较理想的检定方法是采用区域比较法测量出测试点的分度视值误差,然后利用非线性拟合方法对检定区域内的分度视值误差进行拟合与预测,从而可获得检定区域内较高精度的转台分度视值误差,为实现被测相机内方位元素与畸变的高精度测量提供了有力保障。
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(1)检定数据采集
建立如图6所示的测试系统,在温度(20±0.5) ℃、湿度50%±5%的条件下对高精度转台水平方向92°~112°之间的区域进行分度视值误差检定。在92°~112°范围内,每隔0.5°选取一个测量点,在该区域共采集41个点,重复采集10组有效数据,将分度视值误差绘制成图,如图7所示。
对测试数据进行统计分析,计算得到每个采样点视值误差10次测试数据的均方根最大值为0.081″。从图7中可以看出,转台视值误差具有一定的重复性,可作为系统误差叠加到测试结果中。采用肖维纳准则剔除较不可信的粗大误差后,视值误差平均值如图8所示,每个采样点视值误差RMS最大值为0.037″。
(2)分度误差拟合
常用的曲线拟合方法有分段线性拟合法、最小二乘拟合法、样条函数差值法以及神经网络算法等[13-15]。各种拟合方法各有优缺点,其中神经网络算法非常适合此类非线性拟合,它结构简单易于实现,最重要的是其拟合精度高。采用BP神经网络模型对高精度转台示值误差数据进行拟合,拟合值与实测值如图9所示。通过对拟合结果的分析可知,采用BP神经网络模型可以达到很高的非线性拟合精度,小区域内转台分度误差的RMS优于0.2″,可以满足遥感相机高精度畸变测量对转台分度精度的要求,同时可以降低测试时间50%以上。
(3)内方位元素与畸变测试
将获取的转台分度误差应用到高分七号某台相机的畸变测试中,被测相机全视场共选取55个采样点,进行了10次有效测试。分别使用转台的原始视值和补偿后的视值对被测相机的各个测试点的畸变进行了计算和统计。表3给出了两种数据处理结果对应的55个点的畸变测量值的均方根。
表 2 采样点畸变测量值的均方根
Table 2. RMS of measurement of distortion of sampling points
Test
pointRMS of
distortionRMS of
distortion after
compensationTest
pointRMS of
distortionRMS of
distortion after
compensation1 0.2 0.2 29 0.4 0.0 2 1.8 1.8 30 0.0 0.1 3 0.3 0.3 31 0.5 0.5 4 1.7 1.7 32 1.8 1.8 5 1.1 1.1 33 1.1 1.1 6 0.5 0.5 34 1.5 1.5 7 0.4 0.0 35 0.3 0.0 8 0.0 0.0 36 0.3 0.0 9 0.0 0.0 37 1.1 1.1 10 1.2 0.1 38 0.0 0.0 11 3.0 1.8 39 0.0 0.0 12 2.7 1.4 40 0.6 0.0 13 1.6 1.1 41 0.1 0.0 14 3.5 1.9 42 1.0 0.0 15 3.3 2.1 43 1.6 1.6 16 2.9 2.2 44 0.0 0.0 17 2.1 2.1 45 0.1 0.1 18 1.2 1.2 46 0.5 0.5 19 0.0 0.0 47 0.5 0.5 20 0.8 0.8 48 0.4 0.4 21 0.9 0.9 49 0.0 0.0 22 0.2 0.0 50 0.2 0.2 23 1.7 1.2 51 0.0 0.0 24 0.0 0.0 52 0.3 0.3 25 1.6 0.0 53 0.2 0.2 26 1.2 1.2 54 0.5 0.5 27 2.1 2.0 55 0.4 0.4 28 0.0 0.0 经过对比,使用补偿后的转台分度误差得到的畸变测量值的RMS降低35%。
System integration and test of GF-7 bi-linear array stereo mapping sensing camera
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摘要: 2019年11月3日发射的高分七号立体测绘卫星搭载了前、后视两台高分辨率遥感相机,分别从前、后两个方向对地面同一景物进行不同角度的观测,从而形成立体测绘影像。在立体测绘相机的实验室研制阶段,需要确保双线阵相机的线阵水平、共焦一致性、内方位元素与畸变的高精度测试。为了满足高分七号双线阵相机上述技术指标的要求,采用了计算机辅助焦平面快速装调方法以及高精度内方位元素与畸变测试方法,所用方法提高了装调与测试效率,保证了测试精度,相机共焦性优于±0.04 mm,线阵水平优于±1′,畸变测试精度优于2.3 μm,可为其他大比例尺测绘遥感相机的研制提供参考。Abstract: GF-7 stereo mapping satellite launched on November 3, 2019 was equipped with two high-resolution remote sensing cameras “Front camera” and “Back camera”. By the two cameras, the same scene on the ground can be observed from different angles for forming a 3D mapping image. During the development of the stereo mapping camera in the lab, the horizontality of the linear array, field confocal, high-accuracy measurement for elements of interior orientation and distortion should be guaranteed. In order to meet the requirements of the above technical indicators of GF-7 bi-linear array cameras, computer-aided rapid fast adjustment for focal plane and high-precision test for elements of interior orientation and distortion was presented. These methods used in the GF-7 bi-linear array camera improve the efficiency of adjustment and test and guarantee the accuracy of the test results. Finally, confocal plane of each camera is better than ±0.04 mm, horizontality of each linear array is better than ±1′, the accuracy of distortion is better than 2.3 μm. It can provide reference for other large scale mapping camera.
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Key words:
- bi-linear array /
- mapping /
- system integration /
- elements of interior orientation /
- distortion
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表 1 后视相机MTF
Table 1. MTF of the back camera
Test project P B1 B2 B3 B4 Average MTF 0.2 0.36 0.36 0.37 0.36 表 2 采样点畸变测量值的均方根
Table 2. RMS of measurement of distortion of sampling points
Test
pointRMS of
distortionRMS of
distortion after
compensationTest
pointRMS of
distortionRMS of
distortion after
compensation1 0.2 0.2 29 0.4 0.0 2 1.8 1.8 30 0.0 0.1 3 0.3 0.3 31 0.5 0.5 4 1.7 1.7 32 1.8 1.8 5 1.1 1.1 33 1.1 1.1 6 0.5 0.5 34 1.5 1.5 7 0.4 0.0 35 0.3 0.0 8 0.0 0.0 36 0.3 0.0 9 0.0 0.0 37 1.1 1.1 10 1.2 0.1 38 0.0 0.0 11 3.0 1.8 39 0.0 0.0 12 2.7 1.4 40 0.6 0.0 13 1.6 1.1 41 0.1 0.0 14 3.5 1.9 42 1.0 0.0 15 3.3 2.1 43 1.6 1.6 16 2.9 2.2 44 0.0 0.0 17 2.1 2.1 45 0.1 0.1 18 1.2 1.2 46 0.5 0.5 19 0.0 0.0 47 0.5 0.5 20 0.8 0.8 48 0.4 0.4 21 0.9 0.9 49 0.0 0.0 22 0.2 0.0 50 0.2 0.2 23 1.7 1.2 51 0.0 0.0 24 0.0 0.0 52 0.3 0.3 25 1.6 0.0 53 0.2 0.2 26 1.2 1.2 54 0.5 0.5 27 2.1 2.0 55 0.4 0.4 28 0.0 0.0 -
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