For a nonisothermal blackbody cavity, different reference temperatures have influence on the calculation of effective emissivity. Previous studies proposed a weighted average method which can be indicated by a priori to calculate the reference temperature. However, these studies did not mention how to define the weight function but used some arbitrary temperature or the temperature of a fixed position like the central bottom of the cavity as the reference temperature. In this study, a quantitative analysis and calculation method, which is implemented in the Monte Carlo method based optical simulation software Tracepro, is proposed to define the weight coefficients and optimize the reference temperature. To do so, in the Tracepro software, a surface source is placed in front of the cavity opening and emits radiation to the blackbody cavity. The radiation from this surface source can be absorbed or reflected many times in the cavity, and finally the incident radiation distribution in the cavity can be obtained. According to the principle of light path reversibility, the normalized incident radiation can be considered as the contribution of its position to the effective emissivity. In the experiment, the actual temperatures of two different-shaped blackbody cavities are measured with the non-contact method in 873 K temperature. By dividing the inner surface of each blackbody cavity into several regions based on the positions of the actually measured temperature points, the incident radiation from the surface source to each segmented region is calculated and normalized to the total incident radiation across all regions as its weight coefficient; the reference temperature is the sum of the weighted temperature (by multiplying each weight coefficient with its measured temperature) in each region. Different from previous studies, this study optimizes the reference temperature by considering the contribution of the whole cavity to the effective emissivity, which should be more consistent with the actual situation. Moreover, the influences of different shapes of the blackbody cavities, different radiation characteristics of the inner surface materials and different viewing conditions of the effective emissivity on the reference temperature are discussed and compared. The results suggest that the optimization of reference temperature has close link with above factors and thus should be calculated individually.

中文翻译：

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非等温黑体腔有效发射率计算中优化参考温度的方法

对于非等温黑体腔，不同的参考温度会影响有效发射率的计算。先前的研究提出了一种加权平均方法，该方法可以通过先验表示来计算参考温度。但是，这些研究没有提及如何定义重量函数，而是使用了任意温度或固定位置的温度（例如腔体中央底部）作为参考温度。在这项研究中，提出了一种定量分析和计算方法，该方法在基于蒙特卡洛方法的光学仿真软件Tracepro中实现，以定义重量系数并优化参考温度。为此，在Tracepro软件中，将表面源放置在腔体开口的前面，并向黑体腔体发出辐射。来自该表面源的辐射可以在空腔中被吸收或反射多次，最终可以得到入射辐射在空腔中的分布。根据光路可逆性原理，归一化入射辐射可被视为其位置对有效发射率的贡献。在实验中，使用非接触法在873 K温度下测量了两个不同形状的黑体腔的实际温度。通过根据实际测量的温度点的位置将每个黑体腔的内表面划分为几个区域，可以计算出从表面源到每个分段区域的入射辐射，并将其归一化为所有区域的总入射辐射作为权重系数; 参考温度是每个区域中加权温度的总和（将每个权重系数乘以其测得的温度）。与以前的研究不同，本研究通过考虑整个腔体对有效发射率的影响来优化参考温度，这应该与实际情况更加一致。此外，讨论并比较了黑体腔的不同形状，内表面材料的不同辐射特性以及有效发射率的不同观察条件对参考温度的影响。结果表明，参考温度的优化与上述因素密切相关，因此应单独计算。