The integrating sphere with sample inside (ISSI) method is useful for absorption spectroscopy of scattering samples, but the measured absorbance (Ameas) becomes nonlinear with dye concentration (c) because the sample is placed inside the sphere. This study modeled the Ameas−c relationship for ISSI using a cylindrical cell (CC) and a Brewster cell (BC) with simple analytical expressions based on the fraction of light not passing through the sample and the effective weights of light passing through it multiple times. Four aqueous dye solutions—Trypan Blue, Brilliant Blue FCF, Tartrazine, and New Coccine—were used as non-scattering samples. For CC, a single-pass model reproduced the measured relationship well for all dyes, and linearity was maintained in the low-absorbance region (up to approximately half of the saturation absorbance, Amax/2≈0.67 Abs). For BC, the same low-absorbance region (up to approximately Amax/2≈1.21 Abs) also exhibited practical linearity, but the full relationship including saturation required a multiple-pass model. Model selection based on adjusted RMSE and AICc identified the 3-pass model as the minimum sufficient model for BC. The saturation absorbance Amax was on average 1.81 times higher for BC than for CC (corresponding to an approximately 12-fold expansion in linear intensity ratio), and the upper concentration limit of the linear approximation was on average 1.85 times higher. These results demonstrate that BC extends the measurable concentration range while preserving practical low-absorbance linearity. In addition, the wavelength dependence of Amax observed at short wavelengths is attributed primarily to the reduced reflectance of the BaSO4 integrating-sphere wall rather than to the refractive-index dispersion of the quartz cell.
Yamashita et al. (Sun,) studied this question.