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1.苏州科技大学 物理科学与技术学院, 苏州 215009
2.中国科学院苏州生物医学工程技术研究所医用光学室, 苏州 215163
3.江苏省先进诊疗技术与装备重点实验室, 苏州 215163
4.医学成像科学与技术系统全国重点实验室, 苏州 215163
5.苏州国科医工科技发展(集团)有限公司, 苏州 215163
Received:11 January 2026,
Revised:2026-04-02,
Accepted:17 April 2026,
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陈宝瑨,巩岩,吴泉英,等. 一种非轴对称热致折射率场建模方法[J].光子学报,2026,55(7):0722002
CHEN Baojin, GONG Yan, WU Quanying, et al. A Modeling Method for Non-Axisymmetric Thermally Induced Refractive Index Fields[J]. Acta Photonica Sinica, 2026, 55(7):0722002
陈宝瑨,巩岩,吴泉英,等. 一种非轴对称热致折射率场建模方法[J].光子学报,2026,55(7):0722002 DOI: 10.3788/gzxb20265507.0722002. CSTR: 32255.14.gzxb20265507.0722002.
CHEN Baojin, GONG Yan, WU Quanying, et al. A Modeling Method for Non-Axisymmetric Thermally Induced Refractive Index Fields[J]. Acta Photonica Sinica, 2026, 55(7):0722002 DOI: 10.3788/gzxb20265507.0722002. CSTR: 32255.14.gzxb20265507.0722002.
针对高功率激光照射下透镜内部形成的非轴对称温度场,现有折射率模型难以兼顾表达精度与光线追迹稳定性。本文提出一种非轴对称热致折射率场建模方法。沿光轴方向将透镜温度场分层,并在各层内采用二维高斯函数对垂直光轴方向温度分布进行拟合,结合材料温度-折射率关系实现温度场到折射率场的映射。进一步将模型封装成动态链接库接口,实现光学设计软件对折射率及其梯度的实时查询与追迹计算。以隐形切割激光头为例,分析了分层数对温度拟合误差与光学评价结果的影响规律,并完成了非轴对称温度场下的波前畸变与焦面漂移评估,验证了该方法的可行性与工程适用性。
This paper aims to develop a stable and accurate modeling method for thermally induced refractive-index fields in lenses under non-axisymmetric heating conditions. The target problem is the transformation of discrete three-dimensional temperature data from finite element analysis into a refractive-index model that can be directly loaded into optical design software for ray tracing and image-quality evaluation. To address the contradiction between field representation accuracy and numerical robustness in ray tracing, a segmented analytical strategy is established for complex off-axis thermal conditions. The method is further verified on a stealth dicing laser head so that the influence of thermally induced refractive-index variation on wavefront quality and focus position can be quantitatively predicted within an optothermal integrated analysis framework.A layered Gaussian regression scheme was proposed to represent the non-axisymmetric internal temperature field of a lens. Along the optical axis, the effective axial interval of the lens was divided into K non-overlapping layers. Within each layer, the transverse temperature distribution on the plane perpendicular to the optical axis was fitted by a two-dimensional Gaussian function with offset center, amplitude, spread parameters, and background term. Based on the material thermo-optic relation, the fitted temperature rise in each layer was converted into the corresponding refractive-index increment, and a piecewise refractive-index field was constructed. To improve tracing stability, the axial variation was represented by parameter switching between adjacent layers, while the axial refractive-index gradient inside each layer was approximated as zero. A user-defined dynamic link library was then developed to return the refractive index and its spatial derivatives at arbitrary coordinates during optical tracing. For validation, an optothermal integrated simulation was carried out for a stealth dicing laser head with focal length 9 mm, wavelength 1099 nm, numerical aperture 0.83, and maximum half field angle about 1°. Under a 20 W Gaussian beam with 1° tilted off-axis incidence, the absorbed power obtained from non-sequential ray tracing was imported into the finite element model as a volumetric heat source, and the resulting temperature data of lenses L1 to L8 were used for fitting, model loading, and optical evaluation.The proposed method reproduced the three-dimensional temperature fields of all lenses with high fidelity. As the number of layers increased, the fitting root mean square error decreased significantly and became stable after K≥7, indicating convergence of the layered approximation. Considering both computational efficiency and fitting accuracy, K=10 was selected for subsequent analysis. For lenses L1 to L8, the coefficient of determination ranged from 0.9939 to 0.9999, the RMSE remained below 0.02 °C, and the normalized RMSE was within 0.0033 to 0.0225, confirming that the method can accurately characterize complex non-axisymmetric temperature distributions. After the fitted parameters were loaded into the DLL, the refractive-index field of the lens could be reconstructed in optical software in real time. Numerical stability analysis using lens L7 showed that when K≥9, the system wavefront RMS and P-V no longer changed noticeably with increasing layer number. Under the representative 20 W and 1° off-axis incidence condition, the RMS of the thermally induced wavefront difference was 0.0212λ. Although the heating condition was non-axisymmetric, the induced aberration was still dominated by defocus. The focus-shift analysis based on RMS spot radius versus defocus further showed that, after the system reached steady state, the best image plane shifted by about 0.16 μm along the negative optical-axis direction. These results verify that the proposed method can complete the prediction chain from finite element temperature field to refractive-index field and then to optical-performance metrics.The layered refractive-index modeling method provides a practical interface between non-axisymmetric thermal analysis and optical performance evaluation. It can transform discrete thermal results into a queryable analytical refractive-index model with sufficient fitting accuracy and reliable tracing stability. The method is suitable for optothermal integrated analysis of high-power laser systems under asymmetric thermal loads. Because the in-layer basis function is replaceable, the framework also has good extensibility for other temperature-field morphologies and more complicated engineering conditions.
LI Ben , ZHOU Jingfeng , WANG Yi , et al . Finite Element Thermal Analysis of Optical Lenses in 10 kW Rectangular Spot Laser Space Combiner [J]. Acta Photonica Sinica , 2022 , 51 ( 2 ): 135 - 146 .
李奔 , 周井锋 , 王艺 , 等 . 10 kW 矩形光斑激光空间合束器光学透镜的有限元热分析 [J]. 光子学报 , 2022 , 51 ( 2 ): 135 - 146 . DOI: 10.3788/gzxb20225102.0251213 http://dx.doi.org/10.3788/gzxb20225102.0251213
CHEN Chi , DONG Tingting , PAN Haijun . Optothermal-mechanical integrated analysis method for optothermal effects [J]. Optics & Optoelectronic Technology , 2015 , 13 ( 3 ): 64 - 70 .
陈驰 , 董亭亭 , 潘海俊 . 光致热效应的光机热集成分析方法 [J]. 光学与光电技术 , 2015 , 13 ( 03 ): 64 - 70 .
PAN Yue , XU Xiping , QIAO Yang . Optical-structural-thermal analysis of zoom infrared dual-band projection lens [J]. Acta Optica Sinica , 2018 , 38 ( 5 ): 242 - 249 .
潘越 , 徐熙平 , 乔杨 . 变焦红外双波段投影镜头的光机热分析 [J]. 光学学报 , 2018 , 38 ( 5 ): 242 - 249 .
DU Weifeng , LIU Yongzhi , GAO Wenjie , et al . Analysis of passive athermalization structure design and integrated optomechanical-thermal of zoom lens of photoelectric countermeasure platform [J]. Laser & Optoelectronics Progress , 2020 , 57 ( 13 ): 166 - 176 .
杜伟峰 , 刘永志 , 高文杰 , 等 . 光电对抗平台变焦镜头被动消热差结构设计与光机热集成分析 [J]. 激光与光电子学进展 , 2020 , 57 ( 13 ): 166 - 176 . DOI: 10.3788/lop57.131204 http://dx.doi.org/10.3788/lop57.131204
WU Yao , XU Mingming , CHEN Sujuan , et al . Application of thermal/structural/optical integrated analysis to ultraviolet lens of hyperspectral imaging spectrometer [J]. Journal of Applied Optics , 2016 , 37 ( 2 ): 262 - 266 .
武耀 , 徐明明 , 陈素绢 , 等 . 光机热集成分析在高光谱成像仪紫外镜头中的应用 [J]. 应用光学 , 2016 , 37 ( 02 ): 262 - 266 .
HAN Xu , ZHANG Jian , GAO Tianyuan , et al . Research on thermal integration analysis method of transmissive infrared optical system [J]. Infrared Technology , 2018 , 40 ( 12 ): 1136 - 1141 .
韩旭 , 张健 , 高天元 , 等 . 透射式红外光学系统光机热集成分析方法的研究 [J]. 红外技术 , 2018 , 40 ( 12 ): 1136 - 1141 .
WU Wei , BAI Yu , CHEN Chi . Infrared system application of optomechanical heat integration [J]. Infrared and Laser Engineering , 2019 , 48 ( 6 ): 414 - 419 .
吴卫 , 白瑜 , 陈驰 . 光机热集成方法的红外系统应用 [J]. 红外与激光工程 , 2019 , 48 ( 06 ): 414 - 419 .
MA Hongchuan , FAN Hanbo , LIN Yu , et al . Overview of thermal integration analysis of thermal imager [J]. Infrared Technology , 2019 , 41 ( 2 ): 134 - 141 .
马宏川 , 范宏波 , 林宇 , 等 . 热像仪光机热集成分析综述 [J]. 红外技术 , 2019 , 41 ( 02 ): 134 - 141 .
JIANG Dongxu , SUN Baoyu , LI Yingchun , et al . Effect of Thermally Induced Gradient Index on Imaging Quality of Aspherical Optical System [J]. Acta Photonica Sinica , 2020 , 49 ( 01 ): 60 - 67 .
姜东旭 , 孙宝玉 , 李迎春 , 等 . 热致梯度折射率对非球面光学系统成像质量的影响 [J]. 光子学报 , 2020 , 49 ( 01 ): 60 - 67 .
ZHANG Q P , TAN Y , REN G , et al . Ray tracing method of gradient refractive index medium based on refractive index step [J]. Applied Sciences , 2021 , 11 ( 3 ): 912 .
ANSYS , Inc . Ansys Zemax OpticStudio 2025 R2 User Guide [EB/OL]. ( 2025-07 )[ 2026-03-25 ]. https://ansyshelp.ansys.com/public/Views/Secured/Zemax/v252/zh-Hans/OpticStudio_User_Guide/index.html https://ansyshelp.ansys.com/public/Views/Secured/Zemax/v252/zh-Hans/OpticStudio_User_Guide/index.html .
KANG Shouwan , CAI Tianfang . Relationship Between Layer Number and Computational Error in a Multilayer “Staircase” Approximation Method [J]. Acta Photonica Sinica , 1996 , ( 08 ): 724 - 731 .
康寿万 , 蔡天芳 . 多层“台阶”近似方法中层数与计算误差的关系 [J]. 光子学报 , 1996 , ( 08 ): 724 - 731 .
YAO Changcheng , GONG Yan . Research on temperature distribution of deep ultraviolet lithographic projection objective [J]. Chinese Journal of Lasers , 2016 , 43 ( 5 ): 276 - 285 .
姚长呈 , 巩岩 . 深紫外光刻投影物镜温度特性研究 [J]. 中国激光 , 2016 , 43 ( 05 ): 276 - 285 .
SONG X F , LI L , HUANG Y . Method of determining effects of heat-induced irregular refractive index on an optical system [J]. Applied Optics , 2015 , 54 ( 25 ): 7701 - 7707 .
ZHOU Chao . Thermal Analysis of Large Telescope Structure [J]. Acta Photonica Sinica , 2014 , 43 ( 04 ): 118 - 122 .
周超 . 大口径望远镜结构热分析 [J]. 光子学报 , 2014 , 43 ( 04 ): 118 - 122 .
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