Integrating sphere-based relative methods for reflection measurements

We investigate the comparison method and the substitution method of integrating sphere-based relative methods for reflection measurements. Through an analytical description, we compare the two methods with a focus on the effects of a sphere: to determine reflectance without any correction on a sphere, the substitution method requires symmetry of a sphere in addition to the requirement of the comparison method, either uniformity of a sphere or equal reflectance distribution between a sample and a reference. We experimentally compare the two methods through reflection measurements of gray-scale diffuse samples with reflectance of 10%, 40%, and 99%, which results in agreement within their measurement uncertainties. Also, we observe a reflectance change depending on sample location on a sphere in the substitution type measurements, which is attributed to sphere's lack of symmetry. The experimental results are analyzed in terms of measurement uncertainty and reflection properties including bidirectional reflectance distribution function.