ABSTRACT

The use of integrating sphere has been known as a method to measure hemispherical reflectance of a material sample. Mathematical expressions of such reflectance are available in literature, but most of them are not explicit in describing the relation between reflectance and the relevant input variables. This study aims to derive closed-form expressions for determining reference and sample reflectances, provided the irradiance values when the sample and the reference are measured using substitution integrating sphere. Moreover, this study also aims to determine the relative error in reflectance measurement when the fractional area of the ports is neglected, and to derive uncertainty expressions of reflectances due to uncertain irradiance values. The derived expressions have been verified with theoretical calculation tests comprising 10,000 random combinations of input variables. The proposed expressions, together with the error and uncertainty analyses, are expected to be applicable for low-cost, self-assembled integrating spheres.

摘要

作为测量材料样品的半球反射率的方法，已知积分球的使用。这种反射率的数学表达式在文献中是可用的，但它们中的大多数在描述反射率与相关输入变量之间的关系时并不明确。本研究旨在推导出用于确定参考和样品反射率的封闭式表达式，前提是使用替代积分球测量样品和参考时的辐照度值。此外，本研究还旨在确定忽略端口小数面积时反射率测量的相对误差，并推导出因辐照度值不确定而导致的反射率不确定性表达式。导出的表达式已通过理论计算测试验证，包括 10，000 个输入变量的随机组合。所提出的表达式，连同误差和不确定性分析，预计适用于低成本、自组装积分球。