太阳模拟器用自由曲面聚光镜设计

刘石; 邹国星; 张国玉; 王刚; 张健; 段宗涛; 牛政杰; 任太阳

doi:doi:10.3788/AOS221913

光学学报, 2023, 43 (6): 0622001, 网络出版: 2023-03-20

太阳模拟器用自由曲面聚光镜设计下载： 602次

Design of Free-Form Surface Condenser for Solar Simulator

论文大纲

刘石 ^1,2邹国星 ^1,*张国玉 ^1,2王刚 ³张健 ^1,2段宗涛 ¹牛政杰 ¹任太阳 ¹

作者单位

¹ 长春理工大学光电工程学院，吉林长春 130022

² 吉林省光电测控仪器工程技术研究中心，吉林长春 130022

³ 连云港杰瑞电子有限公司，江苏连云港 222000

光学设计太阳模拟器自由曲面辐照不均匀度 optical design solar simulator free-form surface irradiation nonuniformity

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摘要

针对积分器入射面的辐照不均匀度高导致的太阳模拟器辐照均匀性较差的问题，设计了一种自由曲面聚光镜。基于点光源模型，根据能量守恒定律和非成像光学中的边光理论，建立光源出射角度与目标面对应点的映射关系；依据菲涅耳定律结合映射关系推导出微分方程，通过龙格-库塔法求解微分方程，计算出离散点数据；拟合离散点数据得到自由曲面聚光镜的母线，旋转母线获得自由曲面聚光镜的初始结构。使用贝塞尔曲线表征自由曲面母线，利用模拟退火算法对引入扩展光源的自由曲面进行反馈优化，从而得到连续的自由曲面面形。采用LightTools软件仿真太阳模拟器光学系统，结果表明：自由曲面聚光镜的辐照均匀性较椭球聚光镜的辐照均匀性显著提升，辐照面

?

50 mm内辐照不均匀度优于

\pm

0.32%，辐照面

?

100 mm内辐照不均匀度优于

\pm

0.53%；通过误差仿真分析，依据现有自由曲面加工与检测水平，验证了所设计自由曲面聚光镜加工、检测与装调的可行性。

Abstract

Results and Discussions According to the analysis results, the target surface of the developed free-form surface condenser displays a uniform irradiation distribution, which indicates an ideal improvement in the irradiation uniformity of the optical integrator's incident surface. In the design proposal, the generatrix is rotated to obtain the free-form surface condenser. After multiple parameters of the Bézier curve are optimized, the irradiation uniformity within ?60 mm of the target surface of the free-form surface condenser rises from 52% before optimization to 92% (Fig. 7). By contrast, the irradiation nonuniformity of the solar simulator using the free-form surface condenser is significantly lower than that of the solar simulator using the ellipsoidal condenser. In the case of the free-form surface condenser, the irradiation nonuniformity within ?50 mm of the irradiation surface is better than 0.32%, and the irradiation nonuniformity within ?100 mm of the irradiation surface is better than 0.53% (Table 1). When the surface accuracy of the free-form surface condenser is controlled within ±15 μm (Fig. 12), the axial position deviation is controlled within 0.3 mm (Fig. 13), the vertical-axis position deviation is controlled within 0.3 mm (Fig. 14), and the angle deviation is controlled within 0.4° (Fig. 15), the irradiance within ?100 mm of the irradiation surface of the solar simulator can be greater than S₀, and the irradiation nonuniformity is less than 1.5%.Objective

The solar simulator is a device that simulates solar irradiation characteristics indoors. In the design of the solar simulator, the irradiation uniformity is an important indicator, which directly determines the accuracy of the device. Hence, improving irradiation uniformity has become a key research direction. In a solar simulator, the concentrator system is one of the key components, which typically uses an ellipsoidal condenser. By the ellipsoidal condenser, the radiation flux from the light source placed on the first focal plane will be focused on the second focal plane. As a result, a convergent spot is formed on the incident surface of the optical integrator, which is dense at the center, sparse at the edge, and Gaussian in shape. This uneven illuminance distribution is detrimental to the irradiation uniformity of the entire system. To address the poor performance of the solar simulator due to the low irradiation uniformity of the optical integrator's incident surface, this paper proposes and designs a free-form surface condenser as the concentrator system of the solar simulator. On the premise that the focusing efficiency is ensured, the irradiation uniformity on the second focal plane is effectively improved as the irradiation uniformity of the solar simulator is improved through better irradiation distribution on the optical integrator's incident surface.

Methods

In this paper, the free-form surface condenser used in the solar simulation system is studied. First, the mapping relationship between the outgoing angle of the light source and the corresponding point on the target surface is determined. According to Fresnel's law and the mapping relationship, the differential equation is derived, which is solved by the Runge-Kutta method to calculate the discrete point data. After curve fitting of the discrete point data, the bus line of the free-form surface condenser is obtained. Second, the generatrix of the free-form surface is generated by the Bézier curve. A simulated annealing algorithm is employed to conduct feedback-oriented optimization on the free-form surface condenser with an extended light source. Third, the optical system of the solar simulator is modeled by the software LightTools, and the ellipsoidal condenser and the free-form surface condenser are configured in the same optical system of a solar simulator for comparative analysis. Fourth, the irradiance and the irradiation nonuniformity within ?100 mm of the irradiation surface are taken as the evaluation indexes, and error simulation analyses are performed to investigate the influence of surface accuracy, axial position offset, vertical-axis position offset, and angle offset of the free-form surface condenser on the irradiance and the irradiation nonuniformity.

Conclusions

In this paper, a free-form surface condenser is proposed and designed. The point light source model is used to construct a reasonable initial structure according to the law of conservation of energy, the edge light theory, and the mapping method. In the design proposal, the generatrix of the free-form surface condenser is represented by the Bézier curve. The parameters of the Bézier curve are selected as the optimization variables, and the irradiation uniformity on the target surface is selected as the evaluation function. In the meantime, a simulated annealing algorithm is used to optimize the free-form surface with an extended light source. The simulation results of LightTools show that the irradiation uniformity on the irradiation surface of the solar simulator is significantly improved when the free surface condenser is used. The irradiation nonuniformity within ?50 mm of the irradiation surface is better than 0.32%, and that within ?100 mm of the irradiation surface is better than 0.53%. When the surface and pose errors of the free-form surface condenser are taken into account according to the existing processing, assembly, and adjustment level, the irradiance greater than S₀ is considered feasible on the irradiation surface, and the irradiation nonuniformity is less than 1.5%. This verifies the feasibility of the processing, detection, assembly, and adjustment of the free-form surface condenser.

1　引言

太阳模拟器是一种模拟太阳光辐照特性的设备^［1］，可应用在航天器的热平衡和热控涂层特性实验、太阳能电池检测、遥感技术中室内模拟太阳光谱辐照、建筑行业中材料性能老化测试等方面^［2-4］。

辐照不均匀度是太阳模拟器设计的重要指标之一，直接决定太阳模拟器的精度。日本牛尾机电公司生产的USS-2000A太阳模拟器的辐照面直径为100 mm，辐照不均匀度为 $\pm$ 3%^［5］。美国Abet Technologies，Inc.公司研制的SUN2000太阳模拟器的辐照面积为100 mm $\times$ 100 mm，辐照不均匀度只能达到 $\pm$ 5%。中国科学院长春光学精密机械与物理研究所研制的TM-400A太阳模拟器在辐照面形成的光斑尺寸为100 mm $\times$ 100 mm，辐照不均匀度为 $\pm$ 3%^［6］。中科微能开发的CME-SOI8100-3A太阳模拟器的辐照面积为100 mm $\times$ 100 mm，辐照不均匀度达到 $\pm$ 2%。可见，太阳模拟器辐照面在 $ϕ$ 100 mm左右的辐照不均匀度仍有提升空间。

聚光系统是太阳模拟器的关键系统之一，通常采用椭球聚光镜。它将放置在第一焦点附近的光源发出的辐射通量会聚到其第二焦面上，即在积分器入射端面形成一定范围的辐照分布，该辐照分布先被积分器场镜组对称分割，经过积分器投影镜组叠加成像后，再经准直系统，最终在辐照面上形成一个辐照均匀的光斑^［7］，而聚光镜第二焦面上的辐照均匀性直接影响整个太阳模拟器系统辐照面上的辐照均匀性。为了提高第二焦面的辐照均匀性，Wang等^［8］采用抛物面反射镜结合菲涅耳透镜作为光学聚光器，但其聚光后的通量仍服从高斯分布。Li等^［9］设计了一种三维复合抛物线聚光器（CPC），该聚光器虽然提高了聚光效率，但是第二焦面能量分布分散的情况并未得到改善。为此，任兰旭等^［10］提出一种非共轴椭球聚光镜，该椭球聚光镜是在子午面内以第一焦点为中心，将椭圆曲线的长轴相对于光轴旋转一定角度，再绕原轴线旋转一周后形成的，可有效提高第二焦面的辐照均匀性，但加工过程过于复杂。吕涛等^［11］从椭球面方程泰勒展开后得到的高阶方程中演变得到一个变形的椭球面，并通过几个变形系数控制面型，但该方法只能通过试凑确定系数数值，操作性较差。

本文设计了一种自由曲面聚光镜作为太阳模拟器的聚光系统，该系统在保证聚光效率的前提下，有效提高了第二焦面上的辐照均匀性，即改善了积分器入射面的辐照分布情况，最终显著提高了太阳模拟系统辐照面的辐照均匀性。所设计系统的辐照度不小于一个太阳常数S₀（1353 W/m²），辐照面 $ϕ$ 100 mm内的辐照不均匀度优于 $\pm$ 1.5%，高于国家太阳模拟器A级标准^［12］。

2　自由曲面聚光镜的设计

2.1　自由曲面聚光镜的生成

针对传统椭球聚光镜第二焦面的能量分布中心高、边缘低，呈高斯分布的问题^［13］，以提高第二焦面上的辐照均匀性为目标，提出一种自由曲面聚光镜的设计方法。根据能量守恒定律、边光原理和映射法对自由曲面聚光镜进行设计，建立光源出射角度与自由曲面目标面对应点的映射关系，并依据菲涅耳定律结合映射关系推导出微分方程，通过龙格-库塔法求解微分方程，计算出自由曲面母线上的离散点^［14］。

首先基于点光源模型，计算出光源选定发光区域出射光的光通量 $Φ$ ^［15］，即

Φ = \int_{θ_{m i n}}^{θ_{m a x}} I (θ) d Ω = 2 π \int_{θ_{m i n}}^{θ_{m a x}} I (θ) s i n θ d θ

，（1）

式中： $I (θ)$ 为光源各角度的发光强度； $θ$ 表示天顶角，为光源有效发光角度； $Ω$ 为立体角； $θ_{m a x}$ 和 $θ_{m i n}$ 分别为光源最大和最小有效发光角度。

选取短弧氙灯作为光源，短弧氙灯的配光曲线呈轴对称分布，发光角度为20°~125°，短弧氙灯的配光曲线如图1所示。取氙灯的配光曲线数据作为光源有效发光角度对应的发光强度，对式（1）作数值积分，计算出离散区间 $Δ θ = θ_{i + 1} - θ_{i}$ 内的光通量^［16］，即

Φ_{i} = 2 π \int_{θ_{i}}^{θ_{i + 1}} I (θ) s i n θ d θ \approx π \times [I (θ_{i}) + I (θ_{i + 1})] \times (c o s θ_{i} - c o s θ_{i + 1})

，（2）

式中： $I (θ) = \frac{I (θ_{i + 1}) + I (θ_{i})}{2}$ ，为 $Δ θ$ 内发光强度的平均值。

太阳模拟器用自由曲面聚光镜设计 下载： 602次

1 引言

2 自由曲面聚光镜的设计

2.1 自由曲面聚光镜的生成

图 1. 短弧氙灯的配光曲线

Fig. 1. Light distribution curves of short arc xenon lamp

图 2. 光源与目标面能量映射示意图

Fig. 2. Schematic of energy mapping between light source and target surface

图 3. 光源和自由曲面以及目标面分布示意图

Fig. 3. Distribution diagram of light source, free-form surface, and target surface

2.2 基于贝塞尔曲线多参数优化自由曲面聚光镜的方法

图 4. 利用贝塞尔曲线构建自由曲面聚光镜轮廓线示意图

Fig. 4. Sketch map of contour line of free-form surface condenser constructed by Bézier curve

图 5. 自由曲面聚光镜的三维离散点云模型。（a）优化前的模型；（b）优化后的模型

Fig. 5. 3D discrete point cloud models of free-form surface condenser. (a) Model before optimization; (b) optimized model

图 6. 初始结构和优化结构轮廓线对比

Fig. 6. Comparison of contour lines between initial structure and optimized structure

图 7. 自由曲面聚光镜的目标面辐照度分布。（a）优化前的辐照度分布；（b）优化后的辐照度分布

Fig. 7. Irradiance distribution of target surface of free-form surface condenser. (a) Irradiance distribution before optimization; (b) optimized irradiance distribution

3 仿真分析

图 8. 太阳模拟器光学系统仿真图

Fig. 8. Optical system simulation diagram of solar simulator

图 9. 使用椭球聚光镜的太阳模拟器辐照面的辐照度分布

Fig. 9. Irradiance distribution of solar simulator on irradiation surface using ellipsoidal condenser

表 1. 使用椭球聚光镜和自由曲面聚光镜的太阳模拟器辐照不均匀度比较

Table 1. Comparison of irradiation nonuniformity of solar simulator using ellipsoidal condenser and free-form surface condenser

图 10. 使用自由曲面聚光镜的太阳模拟器辐照面的辐照度分布

Fig. 10. Irradiance distribution of solar simulator on irradiation surface using free-form surface condenser

图 11. 椭球聚光镜和自由曲面聚光镜的辐照不均匀度对比

Fig. 11. Comparison of irradiation nonuniformity between ellipsoidal condenser and free-form surface condenser

图 12. 自由曲面聚光镜的面形精度对辐照度和辐照不均匀度的影响。（a）辐照度；（b）辐照不均匀度

Fig. 12. Influence of surface accuracy of free-form surface condenser on irradiance and irradiation nonuniformity. (a) Irradiance; (b) irradiation nonuniformity

图 13. 自由曲面聚光镜的沿轴位置偏移对辐照度和辐照不均匀度的影响。（a）辐照度；（b）辐照不均匀度

Fig. 13. Influence of the axial position offset of the free-form surface condenser on irradiance and irradiation nonuniformity. (a) Irradiance; (b) irradiation nonuniformity

图 14. 自由曲面聚光镜的垂轴位置偏移对辐照度和辐照不均匀度的影响。（a）辐照度；（b）辐照不均匀度

Fig. 14. Influence of vertical axis position offset of free-form surface condenser on irradiance and irradiation nonuniformity. (a) Irradiance; (b) irradiation nonuniformity

图 15. 自由曲面聚光镜的角度偏移对辐照度和辐照不均匀度的影响。（a）辐照度；（b）辐照不均匀度

Fig. 15. Influence of angle offset of free-form surface condenser on irradiation and irradiation nonuniformity.

4 结论

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太阳模拟器用自由曲面聚光镜设计下载： 602次

1　引言

2　自由曲面聚光镜的设计

2.1　自由曲面聚光镜的生成

2.2　基于贝塞尔曲线多参数优化自由曲面聚光镜的方法

3　仿真分析

4　结论