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Topological complexity of photons' paths in biological tissues
In the present contribution three means of measuring the geometrical and
topological complexity of photons' paths in random media are proposed. This is
realized by investigating the behavior of the average crossing number, the mean
writhe, and the minimal crossing number of photons' paths generated by Monte
Carlo (MC) simulations, for different sets of optical parameters. It is
observed that the complexity of the photons' paths increases for increasing
light source/detector spacing, and that highly "knotted" paths are formed. Due
to the particular rules utilized to generate the MC photons' paths, the present
results may have an interest not only for the biomedical optics community, but
also from a pure mathematical point of view
The use of India ink in tissue-simulating phantoms
The optical properties of India ink, an absorber often used in preparation of tissue simulating phantoms, have been investigated at visible and near infrared wavelengths. The extinction coefficient has been obtained from measurements of collimated transmittance and from spectrophotometric measurements, the absorption coefficient from multidistance measurements of fluence rate in a diffusive infinite medium with small concentrations of added ink. Measurements have been carried out on samples of India ink from five different brands, and for some brands also from different batches. As also reported in previously published papers the results we have obtained showed large inter-brand and inter-batch variations for both the absorption and the extinction coefficient. On the contrary, our results showed small variations for the ratio between the absorption and the extinction coefficient. The albedo is therefore similar for all samples: The values averaged over all samples investigated were 0.161, 0.115, and 0.115 at λ = 632.8, 751, and 833 nm respectively, with maximum deviations of 0.044, 0.019, and 0.035. These results indicate that, using the values we have obtained for the albedo, it should be possible to obtain with uncertainty smaller than about 4% the absorption coefficient of a sample of unknown ink from simple measurements of extinction coefficient. A similar accuracy is not easily obtained with the complicated procedures necessary for measurements of absorption coefficient
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