-
摘要:
鬼像是由于镜面间的残余反射所产生的一种杂散光。鬼像会降低光学系统的成像清晰度，湮灭目标，严重影响光学系统的性能。为了探究鬼像对成像系统性能的影响，构建了二次反射产生的鬼像影响下的调制传递函数(MTF)的计算模型。本文首先介绍了在近轴近似下的鬼像分析与描述的方法。接着，从调制传递函数的定义出发，考虑鬼像在像面处的照度对像面调制度的影响，构建了鬼像影响下的MTF计算模型。通过对一系统进行实例计算，并与仿真结果进行比对得到均方误差最大不超过0.049373，进而验证了该模型的准确性。同时针对误差较大的结果进行了详细分析，明确了该计算方法的适用范围。研究结果表明，利用近轴近似的方法计算鬼像影响下的MTF在大多数情况下是真实准确的，该研究为光学系统的鬼像分析方面做出了有益探索。
Abstract:Ghost images, as a type of stray light, are caused by residual reflected light between the optical surfaces. These images can degrade image clarity, annihilation targets, and severely affect the performance of optical systems. To investigate the impact of ghost images on optical system performance, we developed a Modulation Transfer Function (MTF) calculation model under the influence of ghost images generated by secondary reflection. This paper first introduces the method of analyzing and describing using the paraxial approximation. Then, starting from the definition of the MTF, and considering the influence of ghost image irradiance on the modulation of the image plane, a calculation model for calculating the MTF under the influence of ghost images is constructed. After performing calculations and comparing them to simulation results, it was found that the maximum mean square error was less than 0.049373, which verifies the accuracy of the model. Furthermore, a detailed analysis was conducted, examining cases that exhibited larger errors and clarifying the range in which this calculation method can be applied The research results indicate that the paraxial approximation method is both accurate and reliable when calculating the MTF under the influence of ghost images is accurate, and is applicable in most cases. This study serves as a valuable exploration in the ghost image analysis of optical systems.
-
Key words:
- paraxial approximation /
- stray light analysis /
- ghost analysis /
- modulation transfer function /
- MTF
-
图 3 (a) 2_1与4_2鬼像路径下两种计算方法下的MTF示意图；(b) 5_4与6_5鬼像路径下两种计算方法下的MTF示意图
Figure 3. (a) Schematic diagram of MTF curve of ghost image path 2_1 and 4_2; (b) Schematic diagram of MTF curve of ghost image path 5_4 and 6_5
图 4 3_2鬼像路径下的MTF曲线示意图
Figure 4. Schematic diagram of MTF curve of ghost image path 3_2
图 5 非序列光线追迹得到的鬼像光束在像面上的照度分布示意图
Figure 5. Schematic diagram of ghost image distribution on image plane calculated by non-sequential ray tracing
图 6 6_1鬼像路径下的MTF曲线示意图
Figure 6. Schematic diagram of MTF curve of 6_1 ghost image path
图 7 非序列光线追迹得到的鬼像光束在像面上的照度分布示意图
Figure 7. Schematic diagram of ghost image distribution on image plane calculated by non-sequential ray tracing
表 1 E0计算表达式，其中鬼像光束示意图中的蓝色光线代表鬼像光线，黑色代表成像光线
Table 1. Calculation expression for E0, where the blue lines in the ghost image beam schematic represent the ghost image rays and black ones represents the imaging rays.
序号 鬼像光束示意图 E0表达式
1
$ {E_0} = \dfrac{{{n_k}[{h_k}{u_{kg}} - {h_{kg}}{u_k}]}}{H} $
2
$ {E_0} = \dfrac{{{n_k}[{h_k}{u_{kg}} + {h_{kg}}{u_k}]}}{H} $
3
$ {E_0} = \dfrac{{{n_k}[{h_{kg}}{u_k} - {h_k}{u_{kg}}]}}{H} $
下载: 导出CSV
表 2 所有表面的传输矩阵
Table 2. Transmission matrices for all surfaces
透射矩阵 反射矩阵 前表面 $ {{\rm{M}}_{{1}}}{{ = }}\left[ {\begin{array}{*{20}{c}} {{1}}&{{0}} \\ {{{ - }}\dfrac{{{{n' - 1}}}}{{{{n'}}{{{r}}_{{1}}}}}}&{\dfrac{{{1}}}{{{{n'}}}}} \end{array}} \right] $ $ {{\rm{M}}_{{{11}}}}{{ = }}\left[ {\begin{array}{*{20}{c}} {{1}}&{{0}} \\ {{{ - }}\dfrac{{{2}}}{{{{{r}}_{{1}}}}}}&{{{ - 1}}} \end{array}} \right] $ 后表面 $ {{\rm{M}}_{{2}}}{{ = }}\left[ {\begin{array}{*{20}{c}} {{1}}&{{0}} \\ {{{ - }}\dfrac{{{{1 - n'}}}}{{{{{r}}_{{2}}}}}}&{{{n'}}} \end{array}} \right] $ $ {{\rm{M}}_{{{22}}}}{{ = }}\left[ {\begin{array}{*{20}{c}} {{1}}&{{0}} \\ {{{ - }}\dfrac{{{2}}}{{{{{r}}_{{2}}}}}}&{{{ - 1}}} \end{array}} \right] $
下载: 导出CSV
表 3 三片式镜头参数数据(单位：mm)
Table 3. Triplet lens parameter data (in mm)
表面 曲率半径 厚度 材料 1 3.285 1 N-LASF31A 2 −30.01 0.142 3 −6.769 0.9 SF15 4 2.489 0.673 5 6.31 1 N-LAK21 6 −4.889 10.6713
下载: 导出CSV
表 4 所有路径下的杂光率与鬼像影响下的MTF值
Table 4. The veiling glare index and MTF value under the influence of all ghost images paths
路径 杂光率 $ \rm{M}\rm{T}\rm{F}' $与$ \rm{M}\rm{T}\rm{F} $之间的关系 2_1 0.058858 $ \rm{M}\rm{T}{\rm{F}}'=0.944413\rm{M}\rm{T}\rm{F} $ 3_2 0.877073 $ \rm{M}\rm{T}{\rm{F}}'=0.532744\rm{M}\rm{T}\rm{F} $ 3_1 0.029316 $ \rm{M}\rm{T}{\rm{F}}'=0.971518\rm{M}\rm{T}\rm{F} $ 4_3 0.008263 $ \rm{M}\rm{T}\rm{F}'=0.991804\rm{M}\rm{T}\rm{F} $ 4_2 0.005352 $ \rm{M}\rm{T}{\rm{F}}'=0.994676\rm{M}\rm{T}\rm{F} $ 4_1 0.061024 $ \rm{M}\rm{T}{\rm{F}}'=0.942485\rm{M}\rm{T}\rm{F} $ 5_4 0.119049 $ \rm{M}\rm{T}{\rm{F}}'=0.893615\rm{M}\rm{T}\rm{F} $ 5_3 0.006792 $ \rm{M}\rm{T}{\rm{F}}'=0.993252\rm{M}\rm{T}\rm{F} $ 5_2 0.004984 $ \rm{M}\rm{T}{\rm{F}}'=0.995040\rm{M}\rm{T}\rm{F} $ 5_1 0.019154 $ \rm{M}\rm{T}{\rm{F}}'=0.98120\rm{M}\rm{T}\rm{F} $ 6_5 0.067233 $ \rm{M}\rm{T}{\rm{F}}'=0.937001\rm{M}\rm{T}\rm{F} $ 6_4 0.064353 $ \rm{M}\rm{T}{\rm{F}}'=0.939534\rm{M}\rm{T}\rm{F} $ 6_3 0.037417 $ \rm{M}\rm{T}{\rm{F}}'=0.963936\rm{M}\rm{T}\rm{F} $ 6_2 0.018945 $ \rm{M}\rm{T}{\rm{F}}'=0.981406\rm{M}\rm{T}\rm{F} $ 6_1 0.044890 $ MT{F}'=0.957038\rm{M}\rm{T}\rm{F} $
下载: 导出CSV
表 5 所有鬼像路径下的MSE值
Table 5. MSE values of all ghost images paths
路径 MSE值 2_1 1.253505*10^-4 3_2 1.826590*10^-2 3_1 3.627304*10^-5 4_3 2.866007*10^-6 4_2 2.798693*10^-5 4_1 7.217275*10^-4 5_4 1.933488*10^-4 5_3 1.222153*10^-5 5_2 9.061267*10^-6 5_1 5.363379*10^-5 6_5 4.459207*10^-4 6_4 1.627363*10^-4 6_3 4.774974*10^-5 6_2 1.692015*10^-5 6_1 4.937398*10^-2
下载: 导出CSV
-
[1] 王虎, 陈钦芳, 马占鹏, 等. 杂散光抑制与评估技术发展与展望(特邀)[J]. 光子学报,2022,51(7):0751406. doi: 10.3788/gzxb20225107.0751406WANG H, CHEN Q F, MA ZH P, et al. Development and prospect of stray light suppression and evaluation technology (Invited)[J]. Acta Photonica Sinica, 2022, 51(7): 0751406. (in Chinese). doi: 10.3788/gzxb20225107.0751406 [2] 陆强. 地球同步轨道空间相机杂散光分析与应用技术的研究[D]. 上海: 中国科学院上海技术物理研究所, 2016.LU Q. Study on stray light analysis and application technology of the earth synchronous orbit space camera[D]. Shanghai: Shanghai Institute of Technical Physics of the Chinese Academy of Sciences, 2016. (in Chinese). [3] 梁斌, 朱海龙, 张涛, 等. 星敏感器技术研究现状及发展趋势[J]. 中国光学,2016,9(1):16-29. doi: 10.3788/CO.20160901.0016LIANG B, ZHU H L, ZHANG T, et al. Research status and development tendency of star tracker technique[J]. Chinese Optics, 2016, 9(1): 16-29. doi: 10.3788/CO.20160901.0016 [4] 吕博, 冯睿, 寇伟, 等. 折反射式空间相机光学系统设计与杂散光抑制[J]. 中国光学,2020,13(4):822-831. doi: 10.37188/CO.2019-0036LÜ B, FENG R, KOU W, et al. Optical system design and stray light suppression of catadioptric space camera[J]. Chinese Optics, 2020, 13(4): 822-831. doi: 10.37188/CO.2019-0036 [5] 姚雪峰, 高毅, 龙兵, 等. 数字微镜器件(DMD)杂散光特性测试方法及装置[J]. 中国光学,2022,15(2):339-347. doi: 10.37188/CO.2021-0132YAO X F, GAO Y, LONG B, et al. Method and device for testing stray light characteristics of Digital Micro-mirror Device (DMD)[J]. Chinese Optics, 2022, 15(2): 339-347. doi: 10.37188/CO.2021-0132 [6] 冷荣宽, 王上, 王智, 等. 空间引力波探测前向杂散光测量和抑制[J]. 中国光学(中英文),2023,16(5):1081-1088. doi: 10.37188/CO.2022-0251LENG R K, WANG SH, WANG ZH, et al. Measurement and suppression of forward stray light for spaceborne gravitational wave detection[J]. Chinese Optics, 2023, 16(5): 1081-1088. doi: 10.37188/CO.2022-0251 [7] 耿安兵. 光学系统的鬼像分析及快速计算方法[J]. 舰船光学,2004,40(4):34-36.GENG A B. Ghost image anlysis and rapid calculation for optical system[J]. Ship Optical, 2004, 40(4): 34-36. (in Chinese). [8] ABD EL-MAKSOUD R H, SASIAN J. Modeling and analyzing ghost images for incoherent optical systems[J]. Applied Optics, 2011, 50(15): 2305-2315. doi: 10.1364/AO.50.002305 [9] 颜昌翔, 许杰, 彭岩. 离轴三反空间光学望远系统杂散光分析[J]. 光学 精密工程,2010,18(2):289-293.YAN CH X, XU J, PENG Y. Stray light suppression of three-mirror off-axis space optical telescope[J]. Optics and Precision Engineering, 2010, 18(2): 289-293. (in Chinese). [10] NAYLOR A G. Veiling glare due to multiple reflections between surfaces[J]. Canadian Journal of Physics, 1970, 48(22): 2720-2724. doi: 10.1139/p70-337 [11] ABD EL-MAKSOUD R H, SASIAN J M. Paraxial ghost image analysis[J]. Proceedings of SPIE, 2009, 7428: 742807. doi: 10.1117/12.828564 [12] CLERMONT L, MICHEL C, STOCKMAN Y. Stray light correction algorithm for high performance optical instruments: the case of metop-3MI[J]. Remote Sensing, 2022, 14(6): 1354. doi: 10.3390/rs14061354 [13] 陈志勇. 透镜系统的镜面反射杂光的计算——鬼像的模拟与分析[J]. 光学机械,1989(2):23-27.CHEN ZH Y. Calculation of veiling glare due to reflections between surfaces-ghost image simulation and analysis[J]. Optics and Precision Engineering, 1989(2): 23-27. (in Chinese). [14] 岑兆丰, 何志平, 李晓彤, 等. 一种基于光线光学的杂光分析模型[J]. 计算机工程与应用,2003,39(23):188-190.CEN ZH F, HE ZH P, LI X T, et al. A computer modeling for stray light analysis based on geometrical optics[J]. Computer Engineering and Applications, 2003, 39(23): 188-190. (in Chinese). [15] 胡福生, 金光, 张楠. 复杂光学系统鬼像分析的单向链表实现算法[J]. 红外与激光工程,2007,36(3):322-325.HU F SH, JIN G, ZHANG N. Algorithm of list structure of ghost images analyzing in complicated optical systems[J]. Infrared and Laser Engineering, 2007, 36(3): 322-325. (in Chinese). [16] 李洋, 鲍书龙, 穆生博, 等. 透射式光学系统焦平面鬼像特性及验证[J]. 光学 精密工程,2021,29(11):2567-2573. doi: 10.37188/OPE.20212911.2567LI Y, BAO SH L, MU SH B, et al. Ghost image characteristic and experimental verification of focal plane in refractive optical systems[J]. Optics and Precision Engineering, 2021, 29(11): 2567-2573. doi: 10.37188/OPE.20212911.2567 [17] GREIVENKAMP J E. Field Guide to Geometrical Optics[M]. Bellingham: SPIE, 2004. [18] 张国玉, 曹维国, 高玉军, 等. 光学系统杂散光的计算与分析方法[J]. 长春光学精密机械学院学报,1995,18(4):21-24.ZHANG G Y, CAO W G, GAO Y J, et al. The methods of analyses and calculation for stray light in optical system[J]. Journal of Changchun Institute of Optics and Fine Mechanics, 1995, 18(4): 21-24. (in Chinese). [19] 卜和阳, 卢振武, 张红鑫, 等. 内掩式透射地基日冕仪中杂光鬼像的消除[J]. 中国光学,2013,6(2):231-236.BU H Y, LU ZH W, ZHANG H X, et al. Suppresion of stray light ghost image in internally occulting refractive ground-based coronagraph[J]. Chinese Optics, 2013, 6(2): 231-236. (in Chinese). [20] 王子余, 钟伯亮, 史云飞. 用近轴近似方法计算二次反射杂散光[J]. 光学仪器,1982,4(2):6-15.WANG Z Y, ZHONG B L, SHI Y F. Calculation of secondary reflection stray light by Paraxial approximation[J]. Optical Instruments, 1982, 4(2): 6-15. (in Chinese)(查阅网上资料, 未找到本条文献英文翻译, 请确认). [21] 石荣宝, 季轶群, 赵知诚, 等. 适于逆光条件的消鬼像镜头光学设计与实验验证[J]. 光学学报,2014,34(9):0922002. doi: 10.3788/AOS201434.0922002SHI R B, JI Y Q, ZHAO ZH CH, et al. Optical design and experimental verification of a reduced ghost image lens for backlight condition[J]. Acta Optica Sinica, 2014, 34(9): 0922002. (in Chinese). doi: 10.3788/AOS201434.0922002 [22] 马卫红. 基于图像分析的光学传递函数测试技术研究[D]. 西安: 中国科学院西安光学精密机械研究所, 2005.MA W H. Study of MTF measurement technique based on image analysis[D]. Xi’an: Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, 2005. (in Chinese). [23] 郑克哲. 光学计量[M]. 北京: 原子能出版社, 2002.ZHENG K ZH. Optical Metrology[M]. Beijing: Atomic Energy Publishing House, 2002. (in Chinese) (查阅网上资料, 未找到本条文献英文翻译, 请确认) . [24] Photon Engineering. FRED Reference Manual[J/OL]. 2012. (查阅网上资料, 未找到本条文献信息, 请确认) .Photon Engineering. FRED Reference Manual[J/OL]. 2012. (查阅网上资料, 未找到本条文献信息, 请确认). -
下载:
点击查看大图
计量
- 文章访问数: 95
- HTML全文浏览量: 49
- PDF下载量: 13
- 被引次数: 0
