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肖鹏益; 刘铭鑫; 闫磊; 胡铭钰; 张新

doi:10.37188/CO.2023-0121

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doi: 10.37188/CO.2023-0121

肖鹏益 ^{1, 2,},
刘铭鑫 ^1,,,
闫磊 ¹,
胡铭钰 ¹,
张新 ¹

1.
中国科学院长春光学精密机械与物理研究所, 吉林长春 130033
2.
中国科学院大学, 北京100049

基金项目:国家自然科学基金项目（No. 62005217）

详细信息

作者简介:
肖鹏益（1999—）,男，辽宁抚顺人，硕士研究生，主要从事光学设计、杂散辐射分析方面的研究。E-mail：[email protected]

刘铭鑫（1991—），男，吉林辽源人，博士，中国科学院长春光学精密机械与物理研究所助理研究员，主要从事光学设计分析软件研发、杂散辐射分析方面的研究工作。E-mail：[email protected]

中图分类号:O439
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- 网络出版日期: 2023-11-08

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XIAO Peng-yi ^{1, 2
,},
LIU Ming-xin ^{1
,,},
YAN Lei ¹,
HU Ming-yu ¹,
ZHANG Xin ¹

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Funds:Supported by the National Natural Science Foundation of China（No. 62005217）

More Information

Corresponding author: [email protected]

摘要

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。
- 近轴近似 /
- 杂散光分析 /
- 鬼像 /
- 调制传递函数 /
- MTF
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.
- paraxial approximation /
- stray light analysis /
- ghost analysis /
- modulation transfer function /
- MTF

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图 1 单透镜鬼像路径示意图

Figure 1. Schematic diagram of ghost path of a single lens

下载: 全尺寸图片幻灯片

图 2 MTF计算流程图

Figure 2. MTF Calculation flowchart

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

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