Abstract
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 mm-1 at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys.19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.
Highlights
Interpretation of diffuse optical reflectance spectra requires translating the remitted detected light flux from the turbid material into an absorption coefficient by applying photon transport models.[1,2] radiative transport theory is the gold standard here,[3] it cannot be used because it lacks analytical solutions that allow general analysis of diffuse reflectances
We restrict ourselves to medicine and forensic science, where diffuse reflection spectroscopy is used to assess the state of health or disease of patients,[1,2,6] and for example, the age of a blood stain found at crime scenes[7] or the age of bruises when abuse is suspected.[8]
We evaluate the asymptotic behavior of the reflectance ratio, Eq (8), for small and large μa, μs[0]
Summary
Interpretation of diffuse optical reflectance spectra requires translating the remitted detected light flux from the turbid material into an absorption coefficient by applying photon transport models.[1,2] radiative transport theory is the gold standard here,[3] it cannot be used because it lacks analytical solutions that allow general analysis of diffuse reflectances. The diffusion approximation of radiative transport theory[2,4] or empirical relations between reflectance and tissue optical properties[5] is often used as a best approach. Diffusion theory requires the reduced scattering coefficient, μs[0], to be much larger than the absorption coefficient, μa. We restrict ourselves to medicine and forensic science, where diffuse reflection spectroscopy is used to assess the state of health or disease of patients,[1,2,6] and for example, the age of a blood stain found at crime scenes[7] or the age of bruises when abuse is suspected.[8] In medicine, tissues have μs[0] values in the visible part of the spectrum that vary between 0.5 and 10 mm−1, whereas μa of whole blood ranges from 0.1 to 30 mm−1.
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