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NESR定标方法一般有电子学和光学两种。电子学方法[12-14]分析和测试红外遥感器的电子学噪声,计算设定入射光谱辐亮度下的NESR。光学方法利用红外遥感器观测设定光谱辐亮度的光源,由输出信号得到NESR。光学方法是一种直接测量法,需要高准确性的定标光源。文中采用光学方法,按照NESR的定义,其测量方程表述为:
$$ NESR(\lambda ) = \frac{{{L_1}(\lambda ) - {L_2}(\lambda )}}{{SNR(\lambda )}} $$ (1) 式中:L1(λ)和L2(λ)分别为规定测试条件下的定标光源高值和低值光谱辐亮度;λ为波长;SNR(λ)为红外遥感器观测定标光源时的信噪比。重复多次观测定标光源,取红外遥感器输出信号的平均值与标准偏差的比值作为信噪比[15]。
根据NESR的定义,NESR的定标技术流程[16-18]如图1所示。利用标准黑体校准定标光源,确定高值和低值光谱辐亮度L1(λ)和L2(λ)的量值。红外遥感器多次观测定标光源,由其输出信号的平均值和标准偏差,获得信噪比SNR(λ)。根据公式(1)计算红外遥感器的NESR(λ)。
红外遥感器的NESR定标系统主要由光源仓、工作仓、定标仓以及真空低温控制系统组成,如图2所示。光源仓内安装的级联镀金积分球是定标光源[10-11],由四个内置碳纤维灯的子球和一个内径600 mm、出光口直径250 mm的主积分球组成。子球发出的红外辐射通过可调光阑进入主积分球。调节子球的碳纤维灯点亮数量和可调光阑的通光孔径,主积分球可实现140~1600 μW·cm−2·sr−1·μm−1的宽动态范围光谱辐亮度输出。工作仓配置了电动三维平移台,用于调整待定标红外遥感器的位置,使其光轴对准主积分球出光口中心。
定标仓内部安装了低温(283~363 K)腔式黑体,作为光谱辐亮度的溯源标准。一台红外傅里叶变换光谱仪通过旋转反射镜交替观测黑体和主积分球的输出,实现光谱辐亮度的量值传递,确定主积分球的光谱辐亮度。
真空低温控制系统可实现光源仓、工作仓和定标仓的真空度和温度的独立控制,真空度可调范围为10−5 Pa~常压,温度可调范围为190~320 K,工作仓热沉温度稳定性优于1 K。为了降低主积分球背景辐射波动,主积分球的控温精度优于0.15 K。
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依据NESR的测量方程式(1)和不确定度评定规范[19],NESR测量不确定度可表示为:
$$ u[NESR(\lambda )] = \frac{{\sqrt {{u^2}[{L_1}(\lambda )] + {u^2}[{L_2}(\lambda )]} }}{{SNR(\lambda )}} $$ (2) 式中:u[NESR(λ)]为NESR的定标不确定度,是判断NESR定标系统是否满足使用要求的主要参数;u[L1(λ)]和u[L2(λ)]分别为主积分球高值和低值光谱辐亮度的不确定度。在规定的入射光谱辐亮度L1(λ)和L2(λ)下,信噪比SNR(λ)主要由红外遥感器自身的特性(例如读出电路噪声、热噪声以及1/f噪声)决定[2],可视为常量。这样u[NESR(λ)]取决于主积分球的光谱辐亮度不确定度u[L1(λ)]和u[L2(λ)]。
因L1(λ)和L2(λ)的测量过程完全相同,它们的不确定度可认为是相同的,则公式(2)可写为:
$$ u[NESR(\lambda )] = \frac{{\sqrt {2{u^2}[{L_1}(\lambda )]} }}{{SNR(\lambda )}} $$ (3) 对于信噪比SNR > 1000@10 μm的高性能红外遥感器,如果要求NESR的定标不确定度u[NESR(λ)] < 0.01 μW·cm−2·sr−1·μm−1@10 μm,则要求定标光源的光谱辐亮度不确定度u[L1(λ) ] < 7 μW·cm−2·sr−1·μm−1@10 μm。
根据图1,主积分球的光谱辐亮度不确定度来源于以下11种不确定性因素:
(1) 标准黑体的光谱辐亮度不确定度u1(λ);
(2) 旋转反射镜角度重复性引起的标准黑体和主积分球光谱辐亮度测量不确定度u2(λ)和u3(λ);
(3) 定标仓的温度波动引起的背景辐射测量不确定度u4(λ);
(4) 傅里叶变换光谱仪测量标准黑体和积分球的重复性u5(λ)和u6(λ);
(5) 傅里叶变换光谱仪的非线性u7(λ)和非稳定性u8(λ);
(6) 积分球的非稳定性u9(λ)、面非均匀性u10(λ)和角度非均匀性u11(λ)。
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实验评测了不确定度u1(λ)~u11(λ)所使用的仪器,结果如表1所示。设定光谱辐亮度范围为1040~1130 μW·cm−2·sr−1·μm−1,对应于303~308 K黑体在10 μm处的光谱辐亮度输出,这是红外成像光谱仪NESR定标的一种典型条件。
表 1 光谱辐亮度定标不确定度测量仪器
Table 1. Measuring instruments of spectral radiance calibration uncertainty
No. Instruments Parameters 1 Standard Fourier spectrometer (Bruker VERTEX 80 V) Spectral resolution: ≥ 0.06 cm−1;
Spectral range coverage: 3-14.5 μm2 Standard low temperature blackbody Temperature range: 283-363 K;
Blackbody cavity emissivity: ≥ 0.9993 Infrared radiometer (KT15.99 IIP) Spectral range: 9.6-11.5 μm;
Instability: <0.01%/month4 Rotation reflector Rotation angle range: 0°-270°;
Rotation angle repeatability: 0.003°;
Adjustment precision: 0.2° -
根据普朗克定律,标准黑体的光谱辐亮度由其温度和发射率决定。标准黑体材质和腔形结构在不改变的前提下,其发射率可视为不变量。标准黑体的控温精度为50 mK[20],在此控温精度下,标准黑体的光谱辐亮度相对不确定度为:
$$ {u_1}(\lambda ) = \frac{{L(T + \Delta T,\lambda ) - L(T,\lambda )}}{{L(T,\lambda )}} $$ (4) 式中:L为标准黑体的光谱辐亮度;T = 302~310 K为设定温度;ΔT = 50 mK为控温精度。标准黑体的光谱辐亮度由普朗克公式计算[1]:
$$ L(T,\lambda ) = \frac{{{c_1}}}{{\pi {\lambda ^5}[\exp \left( { \dfrac{{{c_2}}}{{\lambda T}} } \right) - 1]}} $$ (5) 式中:c1 = 3.7418×10−16 W·m2;c2 = 1.4388×10−2 m·K;T为标准黑体的设定温度,K;λ为波长,μm。如图3所示,在设定的温区和温控精度下,标准黑体的光谱辐亮度不确定度u1(λ) < 0.08%,考察波长λ=10 μm。
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傅里叶变换光谱仪通过旋转反射镜,交替观测标准黑体和红外主积分球,实现绝对光谱辐亮度的量值传递,如图4所示。通过傅里叶变换光谱仪的实测数据,可以获得交替观测引入的不确定度u2(λ)和u3(λ),它们实际上取决于旋转反射镜的角度重复性。
以傅里叶光谱仪对准标准黑体中心时的角度为0°,改变旋转反射镜的角度,傅里叶光谱仪的输出信号变化如图5(a)所示。旋转反射镜对准黑体的最大角度允差为0.2°,引入的标准黑体观测不确定度为:
$$ \begin{split} {u_2}(\lambda ) = \frac{{S({T_B},0.2^\circ ,\lambda ){\text{ + }}S({T_B},{{ - }}0.2^\circ ,\lambda ) - 2S({T_B},0^\circ ,\lambda )}}{{2S({T_B},0^\circ ,\lambda )}} \end{split}$$ (6) 式中:S为傅里叶光谱仪的输出信号。实验测量结果见图5(b),可知6~15 μm波段范围内,u2(λ) < 0.025%。
图 5 (a)傅里叶变换光谱仪观测标准黑体的输出信号随反射镜旋转角度的变化,T=303 K,λ=10 μm;(b)旋转反射镜角度重复性引入的不确定度u2(λ)
Figure 5. (a) Fourier transform spectrometer output changing with the rotation angle of reflector when observing standard blackbody @T=303 K, λ=10 μm; (b) Uncertainty u2(λ) due to angle repeatability of rotating mirror
利用同样的方法,可以得到傅里叶光谱仪观测主积分球的不确定度,如图6所示。因主积分球距傅里叶光谱仪的光程更长,为保证主积分球出光口充满傅里叶光谱仪的视场,旋转反射镜对准主积分球的最大角度允差为0.1°。
$$\begin{split} \\ {u}_{3}(\lambda )=\frac{S({T}_{I},0.1°,\lambda )\text+S({T}_{I},-0.1°, \lambda )-2S({T}_{I},0°, \lambda )}{2S({T}_{I},0°, \lambda )}\times 100 {\text{%}} \end{split} $$ (7) 其中,主积分球的温度设定为TI =153 K,由制冷系统控制[8],红外积分球的输出信号随反射镜旋转角度变化如图6(a)所示,u3(λ)的测试结果如图6(b)所示。
图 6 (a)傅里叶变换光谱仪观测红外积分球的输出信号随反射镜旋转角度的变化,T=153 K,λ = 10 μm;(b)旋转反射镜角度重复性引入的不确定度u3(λ)
Figure 6. (a) Fourier transform spectrometer observation of output signal of infrared integrating sphere changing with the rotation angle of reflector, T=153 K, λ=10 μm; (b) The uncertainty u3(λ) affected by angle repeatability of rotating mirror
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u4(λ)是定标仓的温度波动引起的背景辐射不确定度。改变定标仓的设置温度,利用傅里叶光谱仪输出信号的相对变化评估u4(λ),即
$$ {u_4}(\lambda ) = \frac{{S({T_{C1}},\lambda ) - S({T_{C2}}{\text{,}}\lambda )}}{{S({T_{C1}}{\text{,}}\lambda )}} \times \frac{{\Delta T}}{{{T_{C1}} - {T_{C2}}}} \times 100 {\text{%}} $$ (8) 式中:TC1 = 173 K,TC2 = 153 K为定标仓的设置温度区间,在该区间内的任意温度,控温精度ΔT=0.15 K。图7(a)为设置温度为153 K时定标仓的温度波动情况。S(TC1, λ)和S(TC2, λ)为傅里叶变换光谱仪连续测量36次的输出信号的平均值。图7(b)为定标仓温度波动引入的背景辐射不确定度,可知u4(λ) < 0.036%。
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傅里叶变换光谱仪测量标准黑体的重复性u5(λ)见公式(9),真空低温定标仓的工作温度设置为153 K,傅里叶变换光谱仪测量标准黑体36次,第i次(i从1~36)测量响应值为S(TB, λ, i)。u5(λ)的测量结果如图8所示。
图 8 (a)傅里叶变换光谱仪测量标准低温黑体(300 K)响应值曲线;(b)重复性测量结果u5(λ)
Figure 8. (a) Response curve of standard low temperature blackbody (300 K) measured by Fourier transform spectrometer; (b) Repeatability measurement results u5(λ)
$$ \begin{split} \\& {u_5}(\lambda ) = \\& \frac{1}{{\left\langle {S({T_B},\lambda ,i)} \right\rangle }} \sqrt {\frac{{\displaystyle \sum\limits_{t = 1}^M {{{[S({T_B},\lambda ,i) - \left\langle {S({T_B},\lambda ,i)} \right\rangle ]}^2}} }}{{M - 1}}} \times 100 {\text{%}} \end{split}$$ (9) 傅里叶变换光谱仪测量主积分球的重复性u6(λ)的数据处理方法与u5(λ)相同。u6(λ)的测量结果如图9所示,其中标准光源的四个内置碳纤维灯子积分球同时点亮输出[7]。
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根据NESR的测量要求,主积分球和标准黑体的温度范围均设置为303~308 K@10 μm。在此狭窄的温度范围内,傅里叶变换光谱仪的非线性u7(λ)可忽略,即u7(λ)≈0。
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傅里叶变换光谱仪输出信号随时间的波动用非稳定性u8(λ)表征,见公式(10):
$$ \begin{split} {u_8}(\lambda ) = \frac{1}{{\left\langle {S({T_B},\lambda )} \right\rangle }}\sqrt {\frac{{ \displaystyle \sum\limits_{i = 1}^M {{{[S({T_B},\lambda ,i) - \left\langle {S({T_B},\lambda )} \right\rangle ]}^2}} }}{{M - 1}}} \times 100 {\text{%}} \end{split} $$ (10) 式中:u8(λ)为规定时间段内的非稳定性;S(TB, λ, i)为第i次测量的输出信号;< S(TB, λ)>为时间段内多次测量的输出信号平均值;M为总的测量次数。u8(λ)的测量结果如图10所示。
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u9(λ)表示主积分球的光谱辐亮度随时间的变化,评测方法见参考文献[6],计算公式同公式(10)。图11所示为红外辐射计观测主积分球30 min的辐亮度相对变化,计算可得非稳定性为0.052%@10 μm。
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u10(λ)表示主积分球的面非均匀性,评测方法见参考文献[6]。将红外辐射计放置于测试平台,分别沿水平和竖直方向进行网格测量,各采样点测量四次并取均值,同时开启四个子积分球。测量结果如图12所示,可知面非均匀性为0.25%@10 μm。
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u11(λ)表示主积分球的角度非均匀性,评测方法见参考文献[8]。将红外辐射计放置于测试平台,以1°为间隔旋转,测量角度范围为−20° ~ 20°,每个角度测量四次并取均值作为该角度下测量值。图13所示为主积分球角度非均匀性测量结果,可知u11(λ)=0.15%@10 μm。
图 13 主积分球随测量角度变化的相对光谱辐亮度
Figure 13. Relative spectral radiance of primary integrating sphere changed with measurement angle
根据上述不确定度影响因素u1(λ) ~ u11(λ)的测量分析和测量结果,取10 μm处的不确定度贡献数值进行汇总,见表2,计算得到红外积分球的光谱辐亮度输出合成不确定度为0.34%。
作为NESR定标的示例,以傅里叶变换光谱仪作为待定标的仪器,观测主积分球光谱辐亮度值L1(λ)和L2(λ),相当于观测308 K和303 K的黑体辐射,测量结果如图14(a)所示。信噪比SNR的结果如图14(b)所示,其中10 μm处的信噪比为1473。
表 2 NESR@10 μm定标不确定度因素表
Table 2. The uncertainty scale of NESR@10 μm calibration
Uncertainty factors Symbol Relative uncertainty
@10 μmUncertainty of spectral radiance output of standard blackbody u1(λ) 0.081% Uncertainty of standard blackbody spectral radiance
(by Fourier spectrometer)u2(λ) 0.025% Uncertainty of integrating sphere spectral radiance (by Fourier spectrometer) u3(λ) 0.020% Background radiation testing uncertainty in optical source chamber and calibration chamber u4(λ) 0.036% Repeatability of standard blackbody (by Fourier spectrometer) u5(λ) 0.13% Repeatability of infrared integrating sphere (by Fourier spectrometer) u6(λ) 0.017% The nonlinearity of Fourier spectrometer u7(λ) 0 The instability of Fourier spectrometer u8(λ) 0.051% The instability of infrared integrating sphere u9(λ) 0.052% The plane inhomogeneity of infrared integrating sphere u10(λ) 0.25% The angular nonuniformity of infrared integrating sphere u11(λ) 0.15% Uncertainty of spectral radiance calibration U(λ) 0.34% 根据图14的测量数据和公式(1),计算得到傅里叶变换光谱仪的NESR,如图15(a)所示。依据公式(3),NESR的测量不确定度可写为:
$$ u[NESR(\lambda )] = \frac{{\sqrt {2{u^2}[{L_1}(\lambda )]} }}{{SNR(\lambda )}} = \frac{{\sqrt {2{{[{L_1}(\lambda )U(\lambda )]}^2}} }}{{SNR(\lambda )}} $$ (11) 其中,相对不确定度U(λ) = 0.34%,由表2的最后一行给出。根据公式(11)测评傅里叶变换光谱仪的NESR定标不确定度,如图15(b)所示。可以看出,10 μm处的NESR不确定度为3.7×10−3 μW·cm−2·sr−1·μm−1。
Performance evaluation of noise equivalent spectral radiance calibration system
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摘要: 噪声等效光谱辐亮度(NESR)是代表红外遥感器极限探测能力的关键性指标。高灵敏红外遥感器的NESR定标需要高稳定、高均匀和充满视场的红外辐射光源,其光谱辐亮度的不确定度应当显著低于红外遥感器的NESR。针对一种新型的级联积分球型大孔径NESR定标系统,开展了NESR定标不确定度的实验测试研究,评定了绝对光谱辐亮度的量值溯源、积分球输出的均匀性和稳定性等11种不确定性因素的影响。测试结果表明,在规定的303~308 K亮温范围内,主积分球光谱辐亮度的相对不确定度优于0.34%,6~15 μm波段的NESR定标不确定度优于0.1~0.0037 μW·cm−2·sr−1·μm−1,验证了新型定标系统应用于高性能红外遥感器NESR定标的可行性。Abstract: Noise equivalent spectral radiance (NESR) is a significant index representing the ultimate detection capability of infrared remote sensors. NESR calibration of highly sensitive infrared remote sensor requires an infrared radiation source with high stability, high uniformity and full field of view, and the uncertainty of its spectral radiance should be significantly lower than that of NESR of infrared remote sensor. Aiming at a new large aperture cascade integrating sphere NESR calibration system, this paper carried out experimental testing and research on the calibration uncertainty of NESR, and evaluated the influence of 11 uncertainty factors, such as the magnitude traceability of absolute spectral radiance, the uniformity and stability of integrating sphere output. The test results show that the relative uncertainty of the spectral radiance of the primary integrating sphere is better than 0.34% within the specified brightness temperature range of 303-308 K; the NESR calibration uncertainty is better than 0.1-0.0037 μW·cm−2·sr−1·μm−1 within the wavelength range of 6-15 μm, which verifies the feasibility of applying the new calibration system to the NESR calibration of high-performance infrared remote sensor.
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图 6 (a)傅里叶变换光谱仪观测红外积分球的输出信号随反射镜旋转角度的变化,T=153 K,λ = 10 μm;(b)旋转反射镜角度重复性引入的不确定度u3(λ)
Figure 6. (a) Fourier transform spectrometer observation of output signal of infrared integrating sphere changing with the rotation angle of reflector, T=153 K, λ=10 μm; (b) The uncertainty u3(λ) affected by angle repeatability of rotating mirror
表 1 光谱辐亮度定标不确定度测量仪器
Table 1. Measuring instruments of spectral radiance calibration uncertainty
No. Instruments Parameters 1 Standard Fourier spectrometer (Bruker VERTEX 80 V) Spectral resolution: ≥ 0.06 cm−1;
Spectral range coverage: 3-14.5 μm2 Standard low temperature blackbody Temperature range: 283-363 K;
Blackbody cavity emissivity: ≥ 0.9993 Infrared radiometer (KT15.99 IIP) Spectral range: 9.6-11.5 μm;
Instability: <0.01%/month4 Rotation reflector Rotation angle range: 0°-270°;
Rotation angle repeatability: 0.003°;
Adjustment precision: 0.2°表 2 NESR@10 μm定标不确定度因素表
Table 2. The uncertainty scale of NESR@10 μm calibration
Uncertainty factors Symbol Relative uncertainty
@10 μmUncertainty of spectral radiance output of standard blackbody u1(λ) 0.081% Uncertainty of standard blackbody spectral radiance
(by Fourier spectrometer)u2(λ) 0.025% Uncertainty of integrating sphere spectral radiance (by Fourier spectrometer) u3(λ) 0.020% Background radiation testing uncertainty in optical source chamber and calibration chamber u4(λ) 0.036% Repeatability of standard blackbody (by Fourier spectrometer) u5(λ) 0.13% Repeatability of infrared integrating sphere (by Fourier spectrometer) u6(λ) 0.017% The nonlinearity of Fourier spectrometer u7(λ) 0 The instability of Fourier spectrometer u8(λ) 0.051% The instability of infrared integrating sphere u9(λ) 0.052% The plane inhomogeneity of infrared integrating sphere u10(λ) 0.25% The angular nonuniformity of infrared integrating sphere u11(λ) 0.15% Uncertainty of spectral radiance calibration U(λ) 0.34% -
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