To determine this instrument parameter $\kappa (\lambda )$, a reference sample with known BRDF needs to be measured by our instrument. In our work, we choose a piece of flat polytetrafluoroethylene (or PTFE) panel as the reference sample. The diffuse reflectance $\rho PTFE(\lambda ,10\u2009\u2009deg)$ of this reference sample is measured at 10 deg incidence by the National Institute of Metrology, China. With less than 1.0% uncertainty, the measured diffuse reflectance $\rho PTFE(\lambda ,10\u2009\u2009deg)$ has $\u223c5%$ variations (0.93 to 0.98) over the wavelength range of 250 to 370 nm, as shown in Fig. 3(a). Unfortunately, we are unable to obtain BRDF data at $<12\u2009\u2009deg$ incidence due to the occlusion of the detector and the light source. As the scattering characteristic of the reference sample is determined mainly by its strong subsurface scattering, slight variations of the incidence angles (5 deg) have little influence on its BRDF and diffuse reflectance, as long as the incidence angle is $\u226420\u2009\u2009deg$.^{22} Thus, the BRDF at 15 deg incidence is measured. Assuming $\rho PTFE(\lambda ,10\u2009\u2009deg)\u2248\rho PTFE(\lambda ,15\u2009\u2009deg)$ and the reference sample has a Lambertian surface Display Formula
$\rho PTFE(\lambda ,10\u2009\u2009deg)\u2248\rho PTFE(\lambda ,15\u2009\u2009deg)\u2248\pi fr,PTFE(\lambda ;0\u2009\u2009deg,15\u2009\u2009deg;0\u2009\u2009deg,0\u2009\u2009deg)=\pi \kappa (\lambda )VPTFE(\lambda ;15\u2009\u2009deg,0\u2009\u2009deg;0\u2009\u2009deg,0\u2009\u2009deg)cos\u200915\u2009\u2009deg,$(3)
where $\rho PTFE(\lambda ,15\u2009\u2009deg)$ is the diffuse reflectance of the PTFE sample at 15 deg incidence, $fr,PTFE(\lambda ;0\u2009\u2009deg,15\u2009\u2009deg;0\u2009\u2009deg,0\u2009\u2009deg)$ is the measured BRDF at (15 deg, 0 deg; 0 deg, 0 deg), and $VPTFE(\lambda ;0\u2009\u2009deg,15\u2009\u2009deg;0\u2009\u2009deg,0\u2009\u2009deg)$ is the spectral signal obtained by measuring the PTFE sample by the imaging spectrometer. Thus, we have Display Formula$\rho PTFE(\lambda ,10\u2009\u2009deg)\u2248\pi \kappa (\lambda )VPTFE(\lambda ;15\u2009\u2009deg,0\u2009\u2009deg;0\u2009\u2009deg,0\u2009\u2009deg)cos\u200915\u2009deg.$(4)
With Eq. (4), we then calculate $\kappa (\lambda )$ at various sampling wavelengths. $\rho PTFE(\lambda ,10\u2009\u2009deg)$ at these sampling wavelengths are obtained by interpolation. The obtained $\kappa (\lambda )$ is shown as the black dots in Fig. 3(b). Figure 3(b) shows small variations except at both sides of the spectra, where the bandpass film of the oscillating mirror in the imaging spectrometer filters out the spectral signal $VPTFE$ at these wavelengths.