Error and Uncertainty Analyses of Reference and Sample Reflectances Measured with Substitution Integrating Spheres

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.