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低温辐射计的吸收腔在测试过程中作为光陷阱,入射到腔中的辐射经过多次反射后被近似完全吸收,并经光热转换导致腔体温度的变化。通常吸收腔内壁涂黑材料吸收率越高、吸收腔内表面积与开口面积的比值越大,越有利于获得高吸收率。目前,国内外的低温辐射计多采用带斜底的圆柱腔,斜底角多为30°和60°。在吸收腔内壁涂黑材料性质相同的情况下,斜底角为30°相对于60°时具有略高的吸收率[5]。文中采用垂直排列碳纳米管作为发黑涂层,由于垂直排列阵列中的碳纳米管包含多种手性、多种壁厚,因此带隙分布展宽极大(0.1~4.0 eV),对全波段均能表现出吸收特性。此外,该类碳纳米管具有森林结构,引入了多重反射-吸收模式,极大提升了其光子束缚能力。其变波长镜面反射率如图1所示,当入射辐射波长延伸到6 μm以上,材料吸收率随入射角增大而急剧降低,当波长延伸至16 μm,纳米涂层的反射率可高达1.25%。该现象主要归因于长波光子较低的能量及较长的波长,难以通过激发吸收涂层本征电子禁带跃迁的方式实现光-电弛豫,只能在纳米森林结构中通过多次反射、缺陷激发等方式逐步降低能量。而随入射角的降低,纳米管阵列对光子的束缚能力大为提升,当入射角降低至30°,全波段反射率低至0.25%以下,满足低温辐射计设计需求,因此文中所讨论的低温黑体腔斜底角设计为60°。
图 1 不同入射角下碳纳米管吸收黑材料光谱镜面反射率测量曲线
Figure 1. Specular reflectance measurement curve of carbon nanotubes absorbing black materials at different incident angles
在斜底面倾角以及内壁涂黑材料确定时,增加腔长能有效地将光线限制在腔内,增加腔内反射次数,随着黑体腔长的增加,平均垂直有效吸收率单调上升。取腔体平均直径
$ \phi $ =10 mm、$ \theta $ =60°,在LightTools软件中,结合蒙特卡洛逆向光线追迹算法对不同腔长,不同内壁涂黑的黑体腔平均垂直有效吸收率进行计算,所得腔体有效吸收率如表1所示,ρ为内壁涂黑层的吸收率,L为腔体长度。对相同的内壁涂层吸收率,增加黑体腔内表面积与开口面积的比值,有利于获得高吸收率。但随腔长的延伸,腔体热容增加,将导致吸收腔响应时间的增加。基于积分球法测得碳纳米管吸收黑材料的光谱吸收率达到0.98,黑体腔腔长L选取为40 mm即可获得低于0.001%的吸收腔反射率。表 1 带斜底面圆柱腔平均垂直有效吸收率计算结果
Table 1. Calculation results of average vertical effective absorption rate of cylindrical cavity with inclined bottom
ρ=0.85 ρ=0.90 ρ=0.95 L=30 mm 0.99826 0.99964 0.99994 L=40 mm 0.99977 0.99991 0.99999 L=50 mm 0.99998 0.99999 0.99999 为了仿真低温辐射计吸收腔内的功率分布,最终确定吸收腔模型结构参数为:长度40 mm、内径10 mm、壁厚0.1 mm、斜底角60°。
Design of the absorption cavity in the cryogenic radiometer based on the ray-tracing method
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摘要: 当前,工作在液氦温度的低温辐射计可以有效规避电路系统中非自发加热带来的误差,是国际上精度最高的光功率计量设备。理想低温辐射计在工作过程中,其核心器件-吸收腔对相同的热功率与电功率应当表现出相同的温升。然而对于实际情况,由于吸收腔涂层中复杂的光-物质相互作用,系统的光-电加热路径难以重合,黑体腔热传导分布的梯度差异导致误差的产生。当前国际上对光电不等效性产生的影响仍缺乏直观清晰的认知。在此,利用蒙特卡洛光线追迹方法,文中对低温辐射计吸收腔辐照度的空间分布进行了仿真。计算表明:当吸收腔斜底角控制在60°,涂层吸收率达到0.95时,系统在激光进入的第一次与第二次反射中分别吸收了98%与1.9%的能量,比例约为51.2∶1。通过在吸收腔斜底板和下侧面同时布置加热器,可实现光加热、电加热路径的耦合。进一步地,通过分别计算单加热器与双加热器布置下系统温度随时间的变化,文中证明了加热路径的不同将引入约为0.005%的光电不等效性。Abstract: Based on the equivalent electrical and optical heating process, radiometers are employed for the metrology of irradiation powers. Working at the liquid helium temperature, the cryogenic radiometer is designed to reduce the nonspontaneous heating by the electric components in the system and is thus currently the most accurate irradiation power metrology measurement facility. During the calibration process of an ideal cryogenic radiometer, the core device-absorption cavity should demonstrate an equivalent temperature increase for the same optical and electrical heating power. However, practical heating routines lack equivalency due to the divergence in the temperature gradient from the complicated optical-matter interactions in black coatings. Herein, utilizing the ray-tracing method, we investigate the tilting angle-dependent spatial optical field distribution in the absorption cavity. With the inclined base angle of the absorption chamber controlled at 60° and the absorption rate of the coating reaching 0.95, the energy of the laser is absorbed in the first and second reflection processes of 98% and 1.9%, respectively, with a ratio of 51.2∶1. The coincidence of the optical and electrical heating paths could thus be realized by placing heaters simultaneously on the inclined bottom plate and the lower side of the absorption cavity. Furthermore, by calculating the time-dependent system temperature with a single inclined bottom heater and calculating the double heater arrangement, an optical-electrical nonequivalency induced by the different heating paths of approximately 0.005% is indicated. Our method constructs an equivalent heating routine for optical and electronic sources, indicating a nonequivalency of 0.005% induced by the different arrangements of heaters. Multiheaters applied with delicate power are recommended to optimize the temperature discrepancy.
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表 1 带斜底面圆柱腔平均垂直有效吸收率计算结果
Table 1. Calculation results of average vertical effective absorption rate of cylindrical cavity with inclined bottom
ρ=0.85 ρ=0.90 ρ=0.95 L=30 mm 0.99826 0.99964 0.99994 L=40 mm 0.99977 0.99991 0.99999 L=50 mm 0.99998 0.99999 0.99999 -
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