温度场辐射测量及其标定研究
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摘要
自从1900年Planck定律创建以来,利用热辐射进行温度测量就成为人们研究的热点问题。辐射测温以Planek定律为基础通过测量物体表面的发射辐射来反演温度。目前,辐射测量传感器已经由单元传感器发展到传感器阵列,这也推动了辐射温度测量由传统的点温测量发展到了温度场测量。要实现温度场的辐射测量,除了传感器阵列技术外还需辅以光学成像技术,光学成像技术的引入使辐射场测量呈现出成像效应,成像效应会影响到温度场的测量及其定标。基于透镜成像的辐射测量在一定条件下属于有限立体角测量,此时具有非漫发射特征物体表面的温度该如何进行测量?本文主要围绕温度场的辐射测量及其定标进行了相关的研究。
首先,基于辐射测量的数学描述研究了小孔和透镜成像条件下的单色和波段测量,发现若以到达传感器的辐射能流为准,则可采用传感器的传统分析方法来分析；若以被测目标发射的辐射强度为准,则与传感器的传统分析方法相差一个常数因子,对于针孔成像辐射测量和透镜成像辐射测量而言,这个常数因子是不相同的。
其次,对辐射场测量中的成像效应进行了研究。由辐射测量的基本公式以及成像下目标微元与传感阵列像素的对应关系出发,分别建立了关于辐射的非成像和成像测量式。根据成像面的存在不会改变辐射传输的事实,比较非成像测量式和成像测量式后,得到了成像效应的数学表述。把成像效应与针孔和透镜两种成像技术结合后的分析指出：成像效应的主因是成像光轴角,辅因是测量天顶角；辅因作用的大小取决于测量天顶角与发射天顶角的差异度。
再次,对有限立体角条件下非漫发射体表面温度的多波长测量进行了研究。本文推导了有限立体角辐射测量条件下的单色测温方程,发现多光谱辐射测温能够实现温度和光谱发射率同时求解通常需满足特定的辐射测量条件：进行微元立体角辐射测量或仅针对漫发射体的有限立体角辐射测量。引入多项式发射率模型,经过数学转化,可以摆脱以上测量限制,得到具有测量普适性的单色测温方程,但却不一定能同时测量光谱发射率。
同时,对有限立体角条件下非漫发射体表面温度的谱色法测量进行了研究。本文结合线性发射率模型从辐射测温方程封闭求解的角度解释了谱色测温通常需采用微元立体角测量或针对漫发射体的有限立体角辐射测量的原因,并推导出了有限立体角辐射测量条件下非漫发射体表面温度测量方程,该方程具有测量普适性。以此方程为基础,推导了具有测量普适性的谱色测温方程组,发现不同的辐射测量条件下发射率标尺的取值范围相同,但物理意义发生了明显变化。
最后,提出了温度场测量时消除成像效应的方法。辐射测温的关键是如何解决发射率未知的问题,这可以通过发射率构建法来解决,从而产生了多通道辐射测温(多波长测温和多波段测温)方法。进行多通道测温时,采用测量信号的归一化处理后,可以消除成像效应对温度场测量的影响,仅需对仪器的光谱响应进行标定,无需进行绝对辐射定标。推导了基于标准传感器光谱响应替代法定标的数学描述,分析表明：发散光源照明条件下基于标准传感器的替代法不能用于数码相机绝对光谱响应定标,但可以进行相对光谱响定标。接着基于以上分析应用本实验室设计的ZLX-DR光谱响应定标系统对数码相机进行了光谱响应定标实验。同时本文还提出了一种不同于测量数据归一化的测温方法来消除成像效应的影响,该方法将包含成像效应的非光谱参数归入到有限项级数形式的光谱发射率中,这既不会影响多通道测温方程组的封闭性,又不会影响温度求解,此时的测量温方程也仅需标定仪器的光谱响应。
Since Planck's law was established in1900, radiation thermometry has always been the key research issue. Based on Planck's law, the surface temperature of an object can be determined by the measurement of emitted radiation. Radiation measurement sensor has been developed from a single sensor to a sensor array, and it also promotes the development of radiation thermometry from the traditional measurement at a point to the field measurement. Besides of the array sensor technology, the optical imaging technology which can result in the imaging effect is necessary for temperature field radiation measurement. And the imaging effect has influences on temperature field radiation measurement and its calibration. In some sense, the radiation measurement by lens imaging can be carried out within a finite solid-angle. Can the temperature of the object with non-diffuse emission be determined by radiation measurement within the finite solid-angle? In this paper, the problems of temperature field radiation measurement and its calibration have been investigated.
At first, based on the mathematical descriptions of radiation measurements with a pinhole or a lens, radiation measurements for spectrum or spectrum band have been studied and it can been seen that if the radiation energy flux is used as the input quantity of sensors, the traditional analysis method for sensors can be employed, while if the spectrum radiation intensity emitted from the measurement target is used, a constant factor will be introduced, compared with the traditional analysis method for sensors. In addition, the factor for pinhole imaging is different from that for lens imaging.
Secondly, the imaging effect in temperature field radiation measurement has been studied.In this paper, the mathematical descriptions of the imaging and non-imaging radiation measurement are deduced based on the basic equations of radiation measurement and the correspondence between the infinitesimal planes of the target and the pixels of the sensor array. Because the imaging plane will not change the radiation transfer from the target to the sensor, the mathematical descriptions of the imaging effect can be obtained by comparing the two mathematical descriptions. A concrete analysis of the imaging effect based on pinhole imaging and lens imaging has been carried out. The results show that the primary cause of the imaging effect is the imaging optical axis angle while the subsidiary cause is the imaging zenith angle, and the influence of the subsidiary cause is determined by the difference between the imaging optical axis angle and the imaging zenith angle.
Thirdly, multi-spectral thermometry for a non-diffuser based on radiation measurement within a finite solid-angle has been investigated. The equation for monochromatic radiation thermometry within a finite solid-angle is deduced, and it is found that if the surface temperature and spectral emissivity can be solved at the same time, the specific radiation measurement conditions for multi-spectral thermometry should be generally met that radiation measurement should be implemented within an infinitesimal solid-angle or within a finite solid-angle only for a perfect diffuser. When the directional spectral emissivity modeled by finite polynomial series is employed and proper mathematical transformation is used, a universal equation for monochromatic radiation thermometry is obtained. So the above restrictions in radiation measurement can be got rid of, but spectral emissivity may not be solved simultaneously.
Meanwhile, the primary spectrum pyrometry for a non-diffuser based on radiation measurement within a finite solid-angle has been studied. Primary spectrum pyrometry should be generally carried out by radiation measurement within an infinitesimal solid-angle or within a finite solid angle in case of diffuse emission, so that the radiation thermometry equations become a closed system for temperature and other undetermined parameters. The radiation thermometry equation which can be used for temperature measurement of non-diffusive objects within a finite solid-angle has been deduced based on the linear emissivity model and a proper mathematical transformation. This equation is universal in radiation measurement, based on which equations for primary spectrum pyrometry are deduced. These equations are also universal in radiation measurement. The emissivity scaleplates under different measurement conditions are limited to the same range, but have different physical meanings.
Finally, one method for getting rid of the influence of the imaging effect in temperature field radiation measurement has been proposed in this paper. The key problem in radiation thermometry is that the emissivity of an object is unknown, so multi-channel radiation thermometry including multi-spectral thermometry and multi-band thermometry has been proposed by emissivity constructing. If normalization of measurement data is used in multi-band thermometry, the influence of the imaging effect can be got rid of, and the calibration of spectral responsivity is needed in stead of the absolute radiation calibration. The mathematical descriptions of the calibration by substitution method based on reference sensor have been deduced and it can be seen that when divergent light is used to illuminate, absolute spectral responsivity calibration for the digital camera can not be conducted derectly while the relative spectral responsivity calibration can do by substitution method. Calibration experiments have been completed using the ZLX-DR calibration system based on the above analisis. In stead of normalization of measurement data, a new method has been proposed at the same time that the non-spectral parameter including the influence of the imaging effect is immigrated into the undetermined coefficients of emissivity modeled by finite series, which will not affect the solution of the true surface temperature. And by using this method the calibration of spectral responsivity is needed in stead of the absolute radiation calibration.
首先,基于辐射测量的数学描述研究了小孔和透镜成像条件下的单色和波段测量,发现若以到达传感器的辐射能流为准,则可采用传感器的传统分析方法来分析；若以被测目标发射的辐射强度为准,则与传感器的传统分析方法相差一个常数因子,对于针孔成像辐射测量和透镜成像辐射测量而言,这个常数因子是不相同的。
其次,对辐射场测量中的成像效应进行了研究。由辐射测量的基本公式以及成像下目标微元与传感阵列像素的对应关系出发,分别建立了关于辐射的非成像和成像测量式。根据成像面的存在不会改变辐射传输的事实,比较非成像测量式和成像测量式后,得到了成像效应的数学表述。把成像效应与针孔和透镜两种成像技术结合后的分析指出：成像效应的主因是成像光轴角,辅因是测量天顶角；辅因作用的大小取决于测量天顶角与发射天顶角的差异度。
再次,对有限立体角条件下非漫发射体表面温度的多波长测量进行了研究。本文推导了有限立体角辐射测量条件下的单色测温方程,发现多光谱辐射测温能够实现温度和光谱发射率同时求解通常需满足特定的辐射测量条件：进行微元立体角辐射测量或仅针对漫发射体的有限立体角辐射测量。引入多项式发射率模型,经过数学转化,可以摆脱以上测量限制,得到具有测量普适性的单色测温方程,但却不一定能同时测量光谱发射率。
同时,对有限立体角条件下非漫发射体表面温度的谱色法测量进行了研究。本文结合线性发射率模型从辐射测温方程封闭求解的角度解释了谱色测温通常需采用微元立体角测量或针对漫发射体的有限立体角辐射测量的原因,并推导出了有限立体角辐射测量条件下非漫发射体表面温度测量方程,该方程具有测量普适性。以此方程为基础,推导了具有测量普适性的谱色测温方程组,发现不同的辐射测量条件下发射率标尺的取值范围相同,但物理意义发生了明显变化。
最后,提出了温度场测量时消除成像效应的方法。辐射测温的关键是如何解决发射率未知的问题,这可以通过发射率构建法来解决,从而产生了多通道辐射测温(多波长测温和多波段测温)方法。进行多通道测温时,采用测量信号的归一化处理后,可以消除成像效应对温度场测量的影响,仅需对仪器的光谱响应进行标定,无需进行绝对辐射定标。推导了基于标准传感器光谱响应替代法定标的数学描述,分析表明：发散光源照明条件下基于标准传感器的替代法不能用于数码相机绝对光谱响应定标,但可以进行相对光谱响定标。接着基于以上分析应用本实验室设计的ZLX-DR光谱响应定标系统对数码相机进行了光谱响应定标实验。同时本文还提出了一种不同于测量数据归一化的测温方法来消除成像效应的影响,该方法将包含成像效应的非光谱参数归入到有限项级数形式的光谱发射率中,这既不会影响多通道测温方程组的封闭性,又不会影响温度求解,此时的测量温方程也仅需标定仪器的光谱响应。
Since Planck's law was established in1900, radiation thermometry has always been the key research issue. Based on Planck's law, the surface temperature of an object can be determined by the measurement of emitted radiation. Radiation measurement sensor has been developed from a single sensor to a sensor array, and it also promotes the development of radiation thermometry from the traditional measurement at a point to the field measurement. Besides of the array sensor technology, the optical imaging technology which can result in the imaging effect is necessary for temperature field radiation measurement. And the imaging effect has influences on temperature field radiation measurement and its calibration. In some sense, the radiation measurement by lens imaging can be carried out within a finite solid-angle. Can the temperature of the object with non-diffuse emission be determined by radiation measurement within the finite solid-angle? In this paper, the problems of temperature field radiation measurement and its calibration have been investigated.
At first, based on the mathematical descriptions of radiation measurements with a pinhole or a lens, radiation measurements for spectrum or spectrum band have been studied and it can been seen that if the radiation energy flux is used as the input quantity of sensors, the traditional analysis method for sensors can be employed, while if the spectrum radiation intensity emitted from the measurement target is used, a constant factor will be introduced, compared with the traditional analysis method for sensors. In addition, the factor for pinhole imaging is different from that for lens imaging.
Secondly, the imaging effect in temperature field radiation measurement has been studied.In this paper, the mathematical descriptions of the imaging and non-imaging radiation measurement are deduced based on the basic equations of radiation measurement and the correspondence between the infinitesimal planes of the target and the pixels of the sensor array. Because the imaging plane will not change the radiation transfer from the target to the sensor, the mathematical descriptions of the imaging effect can be obtained by comparing the two mathematical descriptions. A concrete analysis of the imaging effect based on pinhole imaging and lens imaging has been carried out. The results show that the primary cause of the imaging effect is the imaging optical axis angle while the subsidiary cause is the imaging zenith angle, and the influence of the subsidiary cause is determined by the difference between the imaging optical axis angle and the imaging zenith angle.
Thirdly, multi-spectral thermometry for a non-diffuser based on radiation measurement within a finite solid-angle has been investigated. The equation for monochromatic radiation thermometry within a finite solid-angle is deduced, and it is found that if the surface temperature and spectral emissivity can be solved at the same time, the specific radiation measurement conditions for multi-spectral thermometry should be generally met that radiation measurement should be implemented within an infinitesimal solid-angle or within a finite solid-angle only for a perfect diffuser. When the directional spectral emissivity modeled by finite polynomial series is employed and proper mathematical transformation is used, a universal equation for monochromatic radiation thermometry is obtained. So the above restrictions in radiation measurement can be got rid of, but spectral emissivity may not be solved simultaneously.
Meanwhile, the primary spectrum pyrometry for a non-diffuser based on radiation measurement within a finite solid-angle has been studied. Primary spectrum pyrometry should be generally carried out by radiation measurement within an infinitesimal solid-angle or within a finite solid angle in case of diffuse emission, so that the radiation thermometry equations become a closed system for temperature and other undetermined parameters. The radiation thermometry equation which can be used for temperature measurement of non-diffusive objects within a finite solid-angle has been deduced based on the linear emissivity model and a proper mathematical transformation. This equation is universal in radiation measurement, based on which equations for primary spectrum pyrometry are deduced. These equations are also universal in radiation measurement. The emissivity scaleplates under different measurement conditions are limited to the same range, but have different physical meanings.
Finally, one method for getting rid of the influence of the imaging effect in temperature field radiation measurement has been proposed in this paper. The key problem in radiation thermometry is that the emissivity of an object is unknown, so multi-channel radiation thermometry including multi-spectral thermometry and multi-band thermometry has been proposed by emissivity constructing. If normalization of measurement data is used in multi-band thermometry, the influence of the imaging effect can be got rid of, and the calibration of spectral responsivity is needed in stead of the absolute radiation calibration. The mathematical descriptions of the calibration by substitution method based on reference sensor have been deduced and it can be seen that when divergent light is used to illuminate, absolute spectral responsivity calibration for the digital camera can not be conducted derectly while the relative spectral responsivity calibration can do by substitution method. Calibration experiments have been completed using the ZLX-DR calibration system based on the above analisis. In stead of normalization of measurement data, a new method has been proposed at the same time that the non-spectral parameter including the influence of the imaging effect is immigrated into the undetermined coefficients of emissivity modeled by finite series, which will not affect the solution of the true surface temperature. And by using this method the calibration of spectral responsivity is needed in stead of the absolute radiation calibration.
引文
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