Elimination of single-beam substitution error in diffuse reflectance measurements using an integrating sphere revisited

In measurements of diffuse reflectance spectra (DRS) using an integrating sphere (IS), a highly reflective "white standard" (WS) is used to compensate for spectral properties of the incident light and detection setup. The DRS of the investigated sample is then obtained as the ratio between the values obtained with the sample and the white standard, calculated at each included wavelength. However, because the substitution of the WS with the sample may alter light fluence inside the IS, measured DRS are prone to a systematic distortion called single-beam substitution error (SBSE). An earlier report from our group(1) has demonstrated a method for rigorous elimination of the SBSE based on additional measurements performed at the IS reference port. In addition, a more practical solution was presented, involving analytical correction of the measured DRS based on advance characterization of the specific IS. However, we have recently observed that such analytical correction can sometimes deviate from the rigorous experimental elimination of SBSE, depending on reflectance spectrum of the sample. In present study, we attribute this discrepancy to the spectral variation of diffuse reflectance of the IS inner wall, which was disregarded in the original derivation of the analytical correction. We describe experimental characterization of this spectral dependence, which improves the accuracy of analytical removal of SBSE for any object, regardless of its spectral properties.