-
利用平行光管进行系统传函测试时,要求光管靶标夹具具备旋转调整能力,能够保证测试时条纹方向与相机探测器积分方向平行,避免由于条纹与积分方向不平行带来的传函值下降。
利用自准直原理测试传函的相机,需要在焦面位置预先设置靶标,该靶标需要位于相机有效视场内。为了设置和测试方便,通常需要在合适的边缘视场设置一块或两块矩形靶标(条纹靶标),通过拼接保证靶标与相机探测器光敏面共焦。
由于镜面反射的特性,当利用位于边缘视场的靶标测试相机中心视场系统传函时,靶标条纹会产生一定的偏转。当空间相机选用的探测器为TDI(时间延迟积分)型探测器时,反射后的靶标条纹将与探测器积分方向成一定角度。偏转角过大时会导致系统测试结果降低,进而影响对相机成像质量是否满足指标要求的判断。
下文对这一偏转角对自准直传函测试结果的影响进行分析。
-
某典型TDI线阵相机焦面靶标布局方案如图6所示。
空间相机入射光线为平行光,到焦面汇聚,因此从焦面打光,镜头出射光线也为平行光。位于镜头上方的平面镜对平行光进行反射。因此自准直传函测试系统搭建和分析时不需要限制平面镜与镜头的距离。为方便分析,自准直传函检测系统光路可以简化成图7。平面镜初始位置位于光学系统主面,探测器和靶标分别位于焦面不同位置(仅选取一处靶标,另一处与之对称)。
定义X为沿线阵方向,Y为垂直线阵方向,Z为光轴方向,相机线阵位于偏场位置。O为相机主面与光轴焦点,f为相机焦距。D0为靶标条纹中心位置,D为反射后靶标像的中心位置,D和D0均位于相机焦面上。欲将位于D0位置的靶标“反射”到位于线阵最小偏场中心的D位置,需要绕O旋转平面镜。已知相机线阵最小偏场角α(Y向),靶标中心沿线阵方向偏场角γ(X向),垂直于线阵方向偏场角β(Y向)。
已知靶标中心位置D0坐标为
$(-\mathrm{tan}\gamma \cdot f,\; -\mathrm{tan}\beta \cdot f,\; -f)$ ,靶标像中心位置D点坐标为$ (0,\;-\mathrm{tan}\alpha \cdot f,\;-f) $ 。定义从O点出发指向D0点的向量为${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over D}_{0}}$ ,从O点出发指向D点的向量为$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over D} $ ,将它们转化为列向量并单位化,则:$$ \displaystyle {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {{D}_{0}}}=\left[\begin{array}{c}-\dfrac{ \mathrm{tan}\gamma }{\sqrt{{( \mathrm{tan}\gamma )}^{ 2} \displaystyle +{( \mathrm{tan}\beta )}^{ 2} \displaystyle + \displaystyle 1}}\\ -\dfrac{ \mathrm{tan}\beta }{\sqrt{{( \mathrm{tan}\gamma )}^{ 2} \displaystyle +{( \mathrm{tan}\beta )}^{ 2} \displaystyle + \displaystyle 1}}\\ -\dfrac{ \displaystyle 1}{\sqrt{{( \mathrm{tan}\gamma )}^{ 2} \displaystyle +{( \mathrm{tan}\beta )}^{ 2} \displaystyle + \displaystyle 1}}\end{array}\right]=\left[\begin{array}{c}{D}_{0X}\\ {D}_{0Y}\\ {D}_{0Z}\end{array}\right]} $$ (1) $$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over D}=\left[\begin{array}{c} \displaystyle 0\\\\ -\dfrac{ \mathrm{tan}\alpha }{\sqrt{{( \mathrm{tan}\alpha )}^{ 2}+ \displaystyle 1}}\\\\ -\dfrac{ \displaystyle 1}{\sqrt{{(\displaystyle \mathrm{tan}\alpha )}^{ 2}+ \displaystyle 1}}\end{array}\right]=\left[\begin{array}{c}0\\\\ {D}_{Y}\\\\ {D}_{Z}\end{array}\right] $$ (2) 由镜面反射原理,可知单位化的
$\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n}= \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {{D}_{0}}}$ 与$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over D} $ 关于旋转后的镜面法向量$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} $ 对称,且$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n}=\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {{D}_{0}}}+\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over D} $ ,则:$$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over N}=\left[\begin{array}{c}{D}_{0X}\\\\ {D}_{0Y}+{D}_{Y}\\\\ {D}_{0Z}+{D}_{Z}\end{array}\right] $$ (3) 将
$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over N} $ 单位化,得到单位镜面法向量$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} $ ,即:$$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n}=\left[\begin{array}{c}\begin{array}{c}\dfrac{{D}_{0 X}}{\sqrt{{{(D}_{0 X})}^{2}+{\left({D}_{0 Y}+{D}_{Y}\right)}^{2}+{\left({D}_{0 Z}+{D}_{Z}\right)}^{2}}}\\ \dfrac{{D}_{0 Y}+{D}_{Y}}{\sqrt{{{(D}_{0 X})}^{2}+{\left({D}_{0 Y}+{D}_{Y}\right)}^{2}+{\left({D}_{0 Z}+{D}_{Z}\right)}^{2}}}\end{array}\\ \dfrac{{D}_{0 Z}+{D}_{Z}}{\sqrt{{{(D}_{0 X})}^{2}+{\left({D}_{0 Y}+{D}_{Y}\right)}^{2}+{\left({D}_{0 Z}+{D}_{Z}\right)}^{2}}}\end{array}\right]=\left[\begin{array}{c}{n}_{X}\\ {n}_{Y}\\ {n}_{Z}\end{array}\right]$$ (4) 已知靶标上刻蚀的条纹方向为
$ \mathop {DN}\limits^ \rightharpoonup $ ,与探测器积分方向平行,即$ \mathop {DN}\limits^ \rightharpoonup $ 位于焦平面内,且平行于Y轴。将其单位化,有:$$ \mathop {DN}\limits^ \rightharpoonup =\left[\begin{array}{c}0 \\ 1 \\ 0\end{array}\right] $$ (5) 靶标条纹经过单位镜面法向量为
$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} $ 的平面镜反射后的向量为$ {\mathop {DN}\limits^ \rightharpoonup }' $ ,由镜面反射原理有:$ \mathop {DN}\limits^ \rightharpoonup + {\mathop {DN}\limits^ \rightharpoonup} ' = 2 k\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} $ ,其中$ k $ 为$ \mathop {DN}\limits^ \rightharpoonup $ 在单位向量$ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} $ 上的投影长度,即:$${\mathop {DN}\limits^ \rightharpoonup} ' =2k\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n}-\mathop {DN}\limits^ \rightharpoonup =2\left(\mathop {DN}\limits^ \rightharpoonup \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n}\right)\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n}-\mathop {DN}\limits^ \rightharpoonup $$ (6) 将公式(4)、(5)代入,则有:
$${ \mathop {DN}\limits^ \rightharpoonup} '=\left[\begin{array}{c}2{n}_{Y}{n}_{X}\\\\ 2{n}_{Y}^{2}-1\\\\ 2{n}_{Y}{n}_{Z}\end{array}\right] $$ (7) 反射后,向量
$ {\mathop {DN}\limits^ \rightharpoonup} ' $ 在XY平面的投影与Y轴的夹角$ \eta $ 即为$ \mathrm{反}\mathrm{射}\mathrm{后}\mathrm{靶}\mathrm{标}\mathrm{条}\mathrm{纹}\mathrm{与}\mathrm{积}\mathrm{分}\mathrm{方}\mathrm{向}\mathrm{的}\mathrm{夹}\mathrm{角}, $ 则有:$$ \eta ={{{\rm{arcsin}}}}\left(\dfrac{2{n}_{Y}{n}_{X}}{\sqrt{1-{\left(2{n}_{Y}{n}_{Z}\right)}^{2}}}\right) $$ (8) -
靶标像条纹与积分方向的偏转对传函的影响可以简化成利用
${\rm{sinc}}$ 函数求解[9]。已知探测器像元尺寸为
$ d $ ,探测器积分级数为$ k $ ,反射后的靶标偏离原位置与像元尺寸的比为$ m $ ,则有:$$ m=\dfrac{{{\rm{tan}}}\eta \cdot kd}{d}={{\rm{tan}}}\eta \cdot k $$ (9) 计算其对传函的影响,则有:
$$ {{\rm{sinc}}}\left(m\right)=\dfrac{{{\rm{sin}}}\left(m\times \dfrac{\pi }{2}\right)}{m\times \dfrac{\pi }{2}} $$ (10) -
分析3.1节公式可以发现:靶标偏转角与系统焦距无关,仅与靶标和探测器在像面上的位置有关;Y向偏场α、β越大,偏转角
${\eta}$ 越大;靶标X向偏场γ越大,偏转角${\eta}$ 越大。分析3.2节公式可以发现:偏转角引起的传函值下降与探测器像元尺寸大小无关;靶标偏转角越大,对传函值影响越大;探测器积分级数越高,传函值下降越多。
将上述公式代入不同空间相机系统进行比较计算,得到如下结果:
代入某离轴TDI线阵相机,其α=5°、β=5.8°、γ=2.6°,依次代入公式(1)、(2)、(4) 、(8),得到
$ {\eta }_{离轴} $ =0.248°。代入某同轴TDI线阵相机,其α=0.5°、β=1.75°、γ=0.8°,得到$ {\eta }_{同轴} $ =0.011°。分别将上述偏转角度代入公式(9) 、(10),在不同积分级数下得到曲线,如图8所示。
比对两条曲线可以发现:(1) 对于某典型离轴系统,α、β、γ均较大,导致偏转角较大。随着探测器积分级数增大,偏转角对系统传函的影响急剧增加。当积分级数为128级时,测试传函将为系统实际传函值的87.9%。(2) 对于某典型同轴系统,α、β、γ均较大小,导致偏转角小。系统传函对积分级数高低不敏感,偏转角对系统传函的影响不明显,测试传函与系统实际传函接近。
-
由于自准直传函测试靶标为预先拼接在相机焦面组件内,为了保证严格的共焦,通常粘接(或其他固连)安装,无法方便地调整靶标角度。
为避免自准直传函测试时靶标经反射后的偏转角对系统传函值造成影响,应首先利用3.1节、3.2节公式进行计算预估,判断系统传函下降情况。当传函下降量不能接受时,可以采用在一块靶标上刻划多组不同角度条纹靶标的方法。即:首先计算偏转角
$ \eta $ ,然后在靶标光刻面设计两组条纹靶标,一组为正常方向靶标,一组为偏转$ \eta $ 角的预置倾斜靶标。测试时,根据不同被测视场选择不同靶标。同样,当视场偏场过大,两组靶标无法满足需求时,可以设计多组不同偏转角靶标,多组靶标条纹互为补充,满足全视场传函测试需求。 -
自准直传函测试方案要求靶标与探测器严格共焦。自准直传函检测系统实际焦面拼接时,可以利用拼接仪实现靶标刻画面与探测器光敏面“共焦面”[10-12]。同时利用拼接仪也可以实现靶标条纹与探测器积分方向的精确配准。
探测器表面常设有滤光片,用来控制探测器接收到的光谱范围。该滤光片可以看做光学平行平板。由Snell定律可知,插入平板不会改变光学系统的焦距和像的大小,但是会将光程拉长,从而影响焦点的物理位置,即造成像的纵向位移[4-5],如图9所示。可以得到纵向位移量
$\Delta $ 的精确计算公式:$$ \Delta =d\left(1-\dfrac{{\rm{tan}}{U}^{\text{'}}}{{\rm{tan}}U}\right)=\dfrac{d}{n}(n-\dfrac{{\rm{cos}}U}{{\rm{cos}}{U}^{\text{'}}}) $$ (11) 因此,对于利用自准直原理进行传函测试的相机,结构设计时应区分直通焦面位置和加入滤光片后的焦面位置,按照两个位置分别布放靶标和探测器,不能简单地将其放置在同一平面。
对于普通同种探测器的焦面拼接,它们在拼接仪上共焦且等光程。即在给定一片基准探测器的理论位置时,利用等光程原理,将其余探测器拼接到同一焦深方向位置即可实现共焦。
但是对于这种探测器与靶标混合拼接的系统,“共焦”并不意味着“等光程”。这是由于在拼接仪上拼靶标时,拼接光路中没有滤光片,可以称作“直通光路”,如图10所示的左侧光路。当拼接仪镜头“平移”(保证共焦)到有滤光片的探测器上时,由于滤光片的影响,光程会伸长,焦点位置将后移,如图10所示的右侧光路。
综合上述分析可以发现,对于自准直法传函测试靶标的共焦面拼接,首先应在三维结构设计软件中得到没有滤光片的直通焦面到结构基准的距离。然后利用拼接仪按照此距离将靶标放置在设计位置。最后通过平移拼接仪镜头进行探测器拼接,保证探测器与靶标“共焦面”。
Self-collimating MTF test method and application of space camera
-
摘要: 调制传递函数(传函)测试是空间相机研制过程的重要环节,常规传函测试需要用到平行光管。自准直传函测试方法是一种不依赖于平行光管的系统传函测试方案。首先介绍了自准直传函测试系统的原理和搭建方案。其次对比了平行光管测试的过焦曲线和自准直传函测试的过焦曲线,发现该系统对焦面离焦敏感程度不亚于平行光管,得到该系统可以用于判定焦面位置正确性的结论。再次分析了自准直靶标条纹经过平面镜反射后偏转的现象,该现象将引入测试误差。给出了偏转角的数值计算公式和条纹偏转对传函值影响的计算公式。针对离轴系统对偏转角敏感的问题,给出自准直靶标的设计方法。利用该方法可以将靶标条纹偏转造成的传函测试误差降至可以忽略的量级。然后讨论了采用自准直传函测试方案时相机探测器与测试靶标的拼接,分析了探测器滤光片对焦面位置的影响,提出了探测器与靶标共焦面的设计及拼接方案。最后总结了该测试方法在某型号相机的实际应用,为自准直传函测试方法在后续系统的应用打下基础。Abstract: MTF test is an important part of the camera manufacture process. General practice of MTF test needs to use the parallel light tube. Self-collimating MTF test method does not rely on the parallel light tube. Firstly, the principle and construction plan of the self-collimating MTF test system were introduced. Secondly, the curve measured by parallel light tube and self-collimating MTF test were compared. It is obtained that the self-collimating MTF test system has high sensitivity to the off-focus, this method can be used to determine the focal plane position. Thirdly, the phenomenon of the deflection of the self-collimating target fringe were analyzed, which will affect the MTF test result. The formula of the deflection angle of target fringe and the formula of the influence of fringe deflection on MTF test result were given. Design method of the self-collimating target of off-axis system were given. With this method, the deviation of MTF caused by the deflection of the target fringe can be reduced to a negligible level. Splicing relationship between the detector and the test target of self-collimating MTF test system were discussed, influence of detector's filter on focal plane position was analyzed, and design and splicing program of the detector and the target were proposed. Finally, the application of self-collimating MTF test on a camera were summarized. The result obtained by this study can be used to other camera in the future.
-
Key words:
- space camera /
- self-collimating /
- MTF test /
- focal plane position /
- plane mirror /
- target
-
[1] 张孝弘, 王宇. 面阵CCD相机的MTF测试技术 [C]//中国空间科学学会空间探测专业委员会第十九次学术会议论文集(上册), 2006: 359-366. [2] Yue Tao. The achievements and future prospects of chinese space optical remote sensing technology [J]. Spacecraft Recovery & Remote Sensing, 2008, 29(3): 10-19. (in Chinese) doi: 10.3969/j.issn.1009-8518.2008.03.004 [3] Wang Xiaoyong. Development and prospect of space optical technology [J]. Spacecraft Recovery & Remote Sensing, 2018, 39(4): 79-86. (in Chinese) doi: 10.3969/j.issn.1009-8518.2018.04.010 [4] Li Shengyang, Liu Zhiwen, Liu Kang, et al. Advances in application of space hyperspectral remote sensing (Invited) [J]. Infrared and Laser Engineering, 2019, 48(3): 0303001. (in Chinese) [5] Yoder P R Jr. 光机系统设计[M]. 北京: 机械工业出版社. 2008.1. Yoder P R Jr. Opto-Mechanical Systems Design [M]. 3rd ed. Zhou Haixian, Cheng Yunfang, translated. Beijing: China Machine Press, 2008. (in Chinese) [6] 沃伦J. 史密斯. 现代光学工程[M]. 北京: 化学工业出版社. 2017.1. Smith W J. Modern Optical Engineering [M]. 4th ed. Zhou Haixian, Cheng Yunfang, translated. Beijing: Chemical Industry Press, 2011. (in Chinese) [7] Shi Lei, Jin Guang, Tian Haiying, et al. Autofocusing method with automatic calibration for aerial camera [J]. Optics and Precision Engineering, 2008, 16(12): 2460-2464. (in Chinese) doi: 10.3321/j.issn:1004-924X.2008.12.023 [8] Zhu He, Liang Wei, Gao Xiaodong. Autofocusing system with opto-electronic auto-collimation method for aerial camera [J]. Opto-Electronic Engineering, 2011, 38(3): 35-39. (in Chinese) [9] Xiao Zhanquan, Zhai Linpei, Ding Yalin, et al. Research of optical assembly errors effects on TDI-CCD camera [J]. Semiconductor Optoelectronics, 2008, 29(5): 795-798. (in Chinese) [10] Yong Chaoliang, Lin Jianchun, Zhao Ming, et al. Mosaic of spatial large scale CMOS focal plane array [J]. Infrared and Laser Engineering, 2012, 41(10): 2562-2566. (in Chinese) [11] Zhou Huaide, Liu Jinguo, Zhang Liping, et al. Development of focal plane module for three-line LMCCD mapping cameras [J]. Optics and Precision Engineering, 2012, 20(7): 1492-1499. (in Chinese) doi: 10.3788/OPE.20122007.1492 [12] Meng Qinghua. Structure design of stitching instrument for area CCD [J]. OME Information, 2010, 27(11): 32-35. (in Chinese)