Development of primary reference facilities and measurement comparison of standard artifacts for the bidirectional transmittance distribution function

To determine the bidirectional transmittance distribution function (BTDF) of diffusely transmitting materials, two new primary facilities have been developed at the Physikalisch-Technische Bundesanstalt (PTB) and Aalto University (Aalto). A detailed description of both facilities and the different approaches used are presented in this paper. The performance of both facilities is compared by determining the BTDF of two different diffuser types in both in-plane and out-of-plane bidirectional geometries at four different wavelengths in the visible spectral range. Due to delayed completion of PTB's primary facility, the measured BTDF values are compared between Aalto's primary facility and another PTB setup, whose measurement scales are successfully transferred to PTB's primary facility by an internal comparison. A thorough analysis of the measurement uncertainty is presented, leading to a combined k = 1 standard uncertainty of 0.8%-1.2% for PTB's primary facility and 1.3%-1.7% for Aalto's primary facility. The BTDF results obtained agree well within their expanded k = 2 uncertainty. This indirect bilateral comparison shows that Aalto's and PTB's new facilities are suited as primary reference setups for the determination of the BTDF. These studies also reveal action points to improved measurement capabilities and for a reduction of the measurement uncertainty, depending on the type of diffuser under test.