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

Diffuse reflectance spectra (DRS) of biological samples are commonly measured using an integrating sphere (IS), in which spectrally broad illumination light is multiply scattered and homogenized. The measurement begins by placing a highly reflective white standard against the IS sample opening and collecting the reflected light at the signal output port to account for illumination field. After replacing the white standard with test sample of interest, DRS of the latter is determined as the ratio of the two values at each involved wavelength. However, because test samples are invariably less reflective than the white standard, such a substitution modifies the illumination field inside the IS. This leads to underestimation of the sample’s reflectivity and distortion of measured DRS, which is known as single-beam substitution error (SBSE). Barring the use of much more complex dual-beam experimental setups, involving dedicated IS, literature states that only approximate corrections of SBSE are possible, e.g., by using look-up tables generated with calibrated low-reflectivity standards. We present a practical way to eliminate the SBSE using IS equipped with an additional “reference” output port. Two additional measurements performed at this port (of the white standard and sample, respectively) namely enable an accurate compensation for above described alteration of the illumination field. In addition, we analyze the dependency of SBSE on sample reflectivity and illustrate its impact on measurements of DRS in human skin with a typical IS.