-
透射式宽波段成像光学系统设计基本遵循复消色差理论,即对于理想透镜系统,需同时满足下述各条件:
$$ \left\{ \begin{aligned} & \varphi = \frac{1}{{{h_i}}}\sum {{h_i}{\varphi _i}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{(a)}}\\ & {L_{1ch}} = \frac{1}{{h_1^2{\varphi ^2}}}\sum {h_i^2{C_{1i}}{\varphi _{1i}}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{(b)}}\\ & {L_{2ch}} = \frac{1}{{h_1^2{\varphi ^2}}}\sum {h_i^2{C_{2i}}{\varphi _{2i}}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,{\rm{(c)}}\\ & {{L'}_p} = \frac{1}{{{{\left( {{h_1}\varphi } \right)}^2}}}\sum {h_i^2{P_i}{\varphi _i}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{(d)}}\\ & {\alpha _L}L = \frac{1}{{h_1^2{\varphi ^2}}}\sum {h_i^2{T_i}{\varphi _i}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{(e)}} \end{aligned} \right. $$ (1) 式中:φ为光焦度;h为光线高度;L为位置色差;C为波段内色差系数;P为部分相对色散,α为镜筒的线膨胀系数;L为镜筒长度;T为镜筒的温度。公式(1)中,(a)为光焦度;(b)为波段1内的色差;(c)为波段2内的色差;(d)为全波段的色差;(e)为热差。相对传统光学系统,公式(1)增加了消热差的条件,尤其在红外光学系统中,透镜材料的折射率温度系数dn/dT较大,且线膨胀系数也较大,导致光焦度随温度的变化较大,需在设计中予以考虑(即便是可调焦系统也应进行复核复算)。
复消色差理论的推导公式较为复杂,可参阅相关文献[1-2]。一个直观的结论是:单透镜无消色差能力;双胶合透镜具有一定的消色差能力,其位置色差曲线为二次曲线;而一般的,宽波段系统欲实现复消色差,至少需要三种光学材料,使位置色差曲线变为高次曲线,如图1所示。
对于公式(1),要满足色差为零的条件极为苛刻。但考虑光学系统的瑞利判据,即与位置色差相对应的波像差小于四分之一波长时,可认为光学系统在两个不同波段都成完善像,即光学系统焦深放宽了消色差难度。焦深的计算公式如下:
$$DOF = \pm \lambda /{(2NA)^2}$$ (2) 式中:DOF为焦深;λ为波长;NA为光学系统数值孔径。
从公式(1)和图1可知,复消色差光学系统通过细分中心波长,将位置色差导致的离焦量控制在焦深范围内,即可获得宽波段的消色差效果。
对于多波段共孔径光学系统,如短波+中波0.6~1.7 μm+3.7~4.8 μm双波段共孔径成像系统,受大气窗口和探测器对中间1.8~3.6 μm谱段限制,无需考虑该波段的色差校正,只需校正谱段间色差即可。此时,可对图1中曲线作如图2的改进,进一步给消色差条件减负:
不幸的是,光学材料折射率是波长的非线性函数,同一材料在不同波段具有不同的色散特性,即传统的阿贝数、规化色差系数等参量只能描述材料在单一波段内的色散特性,不能保证波段间色差的校正。一些常用红外材料在不同波段的色散情况如表1所示,其中最为异常的是 Ge材料,在3~5 μm的中波红外和8~12 μm的长波红外波段的色散系数与其他材料成反常变化,在中波红外波段可与Si搭配作为火石玻璃成为负透镜,但在长波红外波段Ge却可作为冕牌玻璃作为正透镜使用。因此,多波段共孔径(共光路)系统的光学设计需要从对材料在不同波段的色散特性了解开始,引入微分的思考方式,对材料的特征波段色散特性进行细化,通过镜组配对,既平衡波段内色差,又平衡波段间色差。从某种意义上,多波段系统减小波段间色差的方法可认为类似于光学系统中减小位置色差的方法:
(1)加入波段间相对离焦量为控制变量,约束该值小于两个波段焦深之和,可对系统优化进行控制;
(2)在材料配对上既要同时满足各个波段内的色差控制要求,也要满足波段间色差系数较小的要求,即:正光焦度元件在满足波段内色差系数较小的同时还需要同时满足波段间色差较小;负光焦度元件在满足波段内色差系数较大的同时尽量采用波段间色差系数较大的材料;
(3)同时尽可能地控制元件表面光线的入射高和入射角。
表 1 常用红外材料的色散特性对比
Table 1. Comparison of dispersion characteristics of common infrared material
Material Index of refraction Chromatic dispersive power Thermal dispersive power Interband chromatic dispersive power n4 μm n10 μm C3-5 μm C8-12 μm T(×10−5 K) P3-12 μm BaF2 1.456 7 1.414 4 2.22% 5.91% −5.51 9.26% Zns 2.250 1 2.198 3 0.91% 4.36% 3.02 4.32% Znse 2.433 1 2.406 7 0.50% 1.71% 3.77 1.88% IRG201 2.514 6 2.498 1 0.5% 0.91% 3.61 1.09% IRG202 2.510 1 2.494 4 0.51% 0.84% 1.98 1.03% IRG205 2.623 9 2.605 2 0.57% 0.92% 3.00 1.15% IRG206 2.794 5 2.777 7 0.06% 0.62% −0.25 0.95% CsBr 1.668 1 1.662 5 0.25% 0.76% −17.3 0.85% GaAs 3.307 0 3.278 1 0.68% 1.53% 5.58 1.27% Ge 4.022 4 4.003 6 0.99% 0.10% 12.61 0.63% 如此选择的材料组合代入初始结构进行优化,再据材料在各波段色散特性对比表进行材料的增减、替换、合成(短波红外及以下波段可胶合)等,以达到宽波段范围消色差的目的。
对于轴外像差,可通过透镜曲率、厚度、空气间隔、非球面系数等变量进行优化。为控制光线的入射高,可采用折反式光学系统,让无色差和热差的反射镜承担主要光焦度,再通过透射元件扩大视场。
热差也是现代光学设计中不可忽视的像差,尤其是对某些大相对孔径红外镜头,热差可能会成为主要像差。相关研究文献较多[3-4],此处不再赘述。但值得注意的是,材料的温度折射率系数dn/dT是温度和波长的函数,不同温度和不同波长下的实测值差异较大,尤其是长波红外光学材料往往理化性能不理想,或易潮解,或易解理,或有毒,或内应力大,而且波长跨度越大的红外材料越稀少,这都导致光学被动消热差难以同时兼顾多波段共孔径系统的所有波段,往往需要温度调焦来补偿。近年来国产硫系玻璃材料研究进步显著[5-7],包括宁波大学、中国建材研究院、湖北新华光信息材料有限公司、成都光明光电股份有限公司等厂家相继推出了系列可工程使用的硫系玻璃,尤其是湖北新华光,以平均两年一种新材料的速度推出新型硫系玻璃,并制定了多项国际验收标准。
硫系玻璃的理化性能尚可,但光学性能尤其是色散和热性能优良(如表1中的IRG201、IRG202、IRG205和IRG206),且能覆盖很宽的波长范围而价格适中,具有广阔的应用前景。
Several ways to realize multi-band common aperture optical imaging system(Invited)
-
摘要: 借助微分方法,提出光学系统内的消波段间色差和波段内色差条件,建立了扩展的复消色差理论,通过对比各自波段和全波段的折射率-色差系数,进行材料配对,并迭代优化校正各类像差。由此介绍了几种多波段共孔径光学系统的实现途径和具体设计实例,包括:透射式结构的宽波段及多波段成像物镜光学系统;透射式结构的中波/近红外二次成像变焦系统;透射式结构的中/长波红外二次成像变焦系统;通过反求工程(Reverse Engineering)设计了AN/AAQ-33“狙击手XR”吊舱采用的中波/近红外共孔径透射式前置望远系统主光路;AN/ASQ-228 ATFLIR吊舱采用的共孔径离轴三反射式消像散前置望远系统主光路;AN/AAS-52 MTS-B吊舱采用的同轴偏视场三反前置望远系统主光路;EKV采用的同轴四反二次成像系统;拓展介绍了采用同轴折反式前置望远+后置成像结构的光路结构,包括同轴折反式中波/短波/近红外和长/中/短波红外望远系统+后置分光成像系统的设计;以及一些典型弹载光学系统共孔径或共光路的设计。Abstract: By using differential method, the inter-band chromatic aberration and intra-band chromatic aberration conditions in optical system were introduced, and the extended complex chromatic aberration theory was established. By comparing the refractive vs chromatic coefficients of each band and the whole band, the material was matched and iteratively optimized to correct all kinds of aberrations. Several ways of realizing the multi-band common aperture (MCA) optical system were discussed, including the medium-wave (MW)/near-infrared (NIR) secondary imaging system with transmission structure, which was introduced into the respective detectors by the dichroic beam splitter in convergent optical path; the MW/long-wave (LW) infrared secondary imaging system with transmission structure, which adopted the co-focal surface design of the co-optical road; and the AN/AAQ-33 “Sniper XR” pod’s main optical system, which adopted MW/NIR co-aperture transmission fore telescope system; the AN/ASQ-228 ATFLIR pod’s main optical system, which adopted the MCA off-axis three-mirror anastigmatic (TMA) fore telescope system; the AN/AAS-52 MTS-B pod’s main optical system, which adopted the MCA coaxial bias field of view (FOV) TMA fore telescope system; the EKV’s main optical system, which adopted the MCA coaxial four mirror secondary imaging system. And correspondingly, some coaxial mirror-lens fore telescope systems were introduced, and the last, some typical missile borne MCA imaging optical structures were introduced.
-
Key words:
- optical design /
- multi-band /
- common aperture /
- mirror-lens optical system /
- fore telescope
-
表 1 常用红外材料的色散特性对比
Table 1. Comparison of dispersion characteristics of common infrared material
Material Index of refraction Chromatic dispersive power Thermal dispersive power Interband chromatic dispersive power n4 μm n10 μm C3-5 μm C8-12 μm T(×10−5 K) P3-12 μm BaF2 1.456 7 1.414 4 2.22% 5.91% −5.51 9.26% Zns 2.250 1 2.198 3 0.91% 4.36% 3.02 4.32% Znse 2.433 1 2.406 7 0.50% 1.71% 3.77 1.88% IRG201 2.514 6 2.498 1 0.5% 0.91% 3.61 1.09% IRG202 2.510 1 2.494 4 0.51% 0.84% 1.98 1.03% IRG205 2.623 9 2.605 2 0.57% 0.92% 3.00 1.15% IRG206 2.794 5 2.777 7 0.06% 0.62% −0.25 0.95% CsBr 1.668 1 1.662 5 0.25% 0.76% −17.3 0.85% GaAs 3.307 0 3.278 1 0.68% 1.53% 5.58 1.27% Ge 4.022 4 4.003 6 0.99% 0.10% 12.61 0.63% -
[1] 曲锐, 邓键. 红外双波段双视场消热差光学系统设计中消波段间色差条件(方法)的研究[J]. 光学学报, 2015, 35(1): 0122006. doi: 10.3788/AOS201535.0122006 Qu Rui, Deng Jian. Methods of correcting between-band chromatic aberration in infrared dual-band dual-field of view athermalized optical design [J]. Acta Optica Sinica, 2015, 35(1): 0122006. (in Chinese) doi: 10.3788/AOS201535.0122006 [2] Thomas H. Jamieson. Decade wide waveband optics[C]// SPIE, 1998, 3482: 306-320. [3] Tamagawa Y, Tajime T. Dual-band optical systems with a projective athermal chart: design [J]. Appl Opt, 1997, 36(1): 297−301. doi: 10.1364/AO.36.000297 [4] 张春艳, 沈为民. 中波和长波红外双波段消热差光学系统设计[J]. 红外与激光工程, 2012, 41(5): 1323−1328. doi: 10.3969/j.issn.1007-2276.2012.05.037 Zhang Chunyan, Shen Weimin. Design of an athermalized MWIR and LWIR dual band optical system [J]. Infrared and Laser Engineering, 2012, 41(5): 1323−1328. (in Chinese) doi: 10.3969/j.issn.1007-2276.2012.05.037 [5] 戴世勋, 陈惠广, 李茂忠, 等. 硫系玻璃及其在红外光学系统中的应用[J]. 红外与激光工程, 2012, 41(4): 847−852. doi: 10.3969/j.issn.1007-2276.2012.04.004 Dai Shixun, Chen Huiguang, Li Maozhong, et al. Chalcogenide glasses and their infrared optical applications [J]. Infrared and Laser Engineering, 2012, 41(4): 847−852. (in Chinese) doi: 10.3969/j.issn.1007-2276.2012.04.004 [6] 孙杰, 聂秋华, 王训四, 等. 新型远红外Ge-Te-Se-Sn硫系玻璃的热学与光学性质研究[J]. 光学学报, 2011, 31(11): 1116003. doi: 10.3788/AOS201131.1116003 Sun Jie, Nie Qiuhua, Wang Xunsi, et al. Reaserch on thermal and optical properties of novel Ge-Te-Se-Sn far infrared transmitting chalcogenide glasses [J]. Acta Optica Sinica, 2011, 31(11): 1116003. (in Chinese) doi: 10.3788/AOS201131.1116003 [7] 姜波, 吴越豪, 戴世勋, 等. 大口径硫系玻璃内部缺陷检测物镜设计及实验验证[J]. 红外与激光工程, 2016, 45(7): 0718002. doi: 10.3788/irla201645.0718002 Jiang Bo, Wu Yuehao, Dai Shixun, et al. Optical design of inspection lens for internal defect of large-diameter chalcogenide glasses and experimental verification [J]. Infrared and Laser Engineering, 2016, 45(7): 0718002. (in Chinese) doi: 10.3788/irla201645.0718002 [8] 曲锐, 邓键, 彭晓乐, 等. 0.4~1.7μm宽波段大相对孔径光学系统设计[J]. 光学学报, 2015, 35(8): 0822007. doi: 10.3788/AOS201535.0822007 Qu Rui, Deng Jian, Peng Xiaole,et al. 0.4-1.7 μm wideband fast F-number optical system design [J]. Acta Optica Sinica, 2015, 35(8): 0822007. (in Chinese) doi: 10.3788/AOS201535.0822007 [9] 邓键, 吴辉,钟小兵. 共光路红外双波段共焦面变焦光学系统: 中国, CN103197407A[P]. 2013-07-10. Deng Jian, Wu Hui, Zhong Xiaobing. Common optical path common focal plane infrared dual- band zoom optical system: China, CN103197407A[P]. 2013-07-10. [10] Housand Brien J, Tener Gens D, Jesse Susan J - EP. Combined laser/FLIR optics system[P]. US6359681 B1. 2002-03-19. [11] Ken Riehl. Raptor (DB-110) reconnaissance system: in operation[C]//SPIE, 2002: 4824:1-12. [12] 许世文, 付苓, 徐波, 等. 小轻型CCD遥感相机全反射光学系统设计[J]. 光学学报, 2000, 20(9): 1268−1271. doi: 10.3321/j.issn:0253-2239.2000.09.021 Xu Shiwen, Fu Ling, Xu Bo, et al. Design of a compact all-reflective optical system for a CCD remote sensing camera [J]. Acta Optica Sinica, 2000, 20(9): 1268−1271. (in Chinese) doi: 10.3321/j.issn:0253-2239.2000.09.021 [13] 常军, 翁志成, 姜会林, 等. 长焦空间三反光学系统的设计[J]. 光学 精密工程, 2001, 9(4): 315−318. doi: 10.3321/j.issn:1004-924X.2001.04.004 Chang Jun, Weng Zhicheng, Jiang Huilin, et al. Design of long focal length space optical system with three reflective mirrors [J]. Opt Precision Eng, 2001, 9(4): 315−318. (in Chinese) doi: 10.3321/j.issn:1004-924X.2001.04.004 [14] 陈哲, 张星祥, 陈长征, 等. 高分辨率共孔径同轴三反光学系统[J]. 中国激光, 2015, 42(11): 1116002. doi: 10.3788/CJL201542.1116002 Chen Zhe, Zhang Xingxiang, Chen Changzheng, et al. A common aperture coaxial three-mirror optical system with high resolution [J]. Chinese Journal of Lasers, 2015, 42(11): 1116002. (in Chinese) doi: 10.3788/CJL201542.1116002 [15] Gerald Uyeno. Raytheon advanced forward looking infrared (ATFLIR) pod[C]//SPIE, 2006, 6209: 62090H. [16] 伍和云, 王培纲. 离轴反射式光学系统设计[J]. 光电工程, 2006, 33(1): 34−37. doi: 10.3969/j.issn.1003-501X.2006.01.009 Wu Heyun, Wang Peigang. Designs of reflective off-axis system [J]. Opto-Electronic Engineering, 2006, 33(1): 34−37. (in Chinese) doi: 10.3969/j.issn.1003-501X.2006.01.009