Measuring absorption coefficient of scattering liquids using a tube inside an integrating sphere

A method for measuring the absorption coefficient μ_a of absorbing and scattering liquid samples is presented. The sample is injected into a small transparent tube mounted through an integrating sphere. Two models for determining the absorption coefficient using the relative optical output signal are described and validated using aqueous ink absorbers of 0.5 vol.% (0.3  mm^-1<μ_a<1.55  mm^-1) and 1.0 vol.% (1.0  mm^-1<μ_a<4.0  mm^-1) concentrations with 1 vol.% (μs'≈1.4  mm^-1) and 10 vol.% (μs'≈14  mm^-1) Intralipid dilutions. The low concentrations give μ_a and μ_s values, which are comparable with those of biological tissues. One model assumes a uniform light distribution within the sample, which is valid for low absorption. Another model considers light attenuation that obeys Lambert-Beer's law, which may be used for relatively high absorption. Measurements with low and high scattering samples are done for the wavelength range of 400-900 nm. Measured spectra of purely absorbing samples are within 15% agreement with measurements using standard transmission spectrophotometry. For 0.5 vol.% ink absorbers and at wavelengths below 700 nm, measured μ_a values are higher for samples with low scattering and lower for those with high scattering. At wavelengths above 700 nm, measured μ_a values do not vary significantly with amount of scattering. For 1.0 vol.% ink absorbers, measured spectra do not change with low scattering. These results indicate that the method can be used for measuring absorption spectra of scattering liquid samples with optical properties similar to biological absorbers, particularly at wavelengths above 700 nm, which is difficult to accomplish with standard transmission spectrophotometry.