Improved solutions of the diffusion equation for time-resolved and steady-state spatially resolved reflectance are investigated for the determination of the optical coefficients of semi-infinite turbid media such as tissue. These solutions are derived for different boundary conditions at the turbid-medium-air interface and are compared with Monte Carlo simulations. Relative reflectance data are fitted in the time domain, whereas relative and absolute reflectance are investigated in the steady-state domain. It is shown that the error in deriving the optical coefficients is, especially for steady-state spatially resolved reflectance, considerably smaller for the solutions under study than for the commonly used solutions. Analysis of experimental measurements of absolute steady-state spatially resolved reflectance confirms these results.

The absorption and transport scattering coefficients of biological tissues determine the radial dependence of the diffuse reflectance that is due to a point source. A system is described for making remote measurements of spatially resolved absolute diffuse reflectance and hence noninvasive, noncontact estimates of the tissue optical properties. The system incorporated a laser source and a CCD camera. Deflection of the incident beam into the camera allowed characterization of the source for absolute reflectance measurements. It is shown that an often used solution of the diffusion equation cannot be applied for these measurements. Instead, a neural network, trained on the results of Monte Carlo simulations, was used to estimate the absorption and scattering coefficients from the reflectance data. Tests on tissue-simulating phantoms with transport scattering coefficients between 0.5 and 2.0 mm(-1) and absorption coefficients between 0.002 and 0.1 mm(-1) showed the rms errors of this technique to be 2.6% for the transport scattering coefficient and 14% for the absorption coefficients. The optical properties of bovine muscle, adipose, and liver tissue, as well as chicken muscle (breast), were also measured ex vivo at 633 and 751 nm. For muscle tissue it was found that the Monte Carlo simulation did not agree with experimental measurements of reflectance at distances less than 2 mm from the incident beam.

We present measurements of the optical properties of six different fat emulsions from three different brands, Clinoleic, Lipovenoes and Intralipid, with fat concentrations from 10% to 30%. The scattering coefficient, the reduced scattering coefficient, and the phase function of each sample are measured for wavelengths between 350 nm and 900 nm. A method for the calculation of the particle size distribution of these fat emulsions is introduced. With the particle size distribution the optical properties of the fat emulsions are obtained with Mie theory. Simple equations for the calculation of the absorption coefficient, the scattering coefficient, the reduced scattering coefficient, the g factor, and the phase function of all measured samples are presented.

Light propagation in two-layered turbid media having an infinitely thick second layer is investigated in the steady-state, frequency, and time domains. A solution of the diffusion approximation to the transport equation is derived by employing the extrapolated boundary condition. We compare the reflectance calculated from this solution with that computed with Monte Carlo simulations and show good agreement. To investigate if it is possible to determine the optical coefficients of the two layers and the thickness of the first layer, the solution of the diffusion equation is fitted to reflectance data obtained from both the diffusion equation and the Monte Carlo simulations. Although it is found that it is, in principle, possible to derive the optical coefficients of the two layers and the thickness of the first layer, we concentrate on the determination of the optical coefficients, knowing the thickness of the first layer. In the frequency domain, for example, it is shown that it is sufficient to make relative measurements of the phase and the steady-state reflectance at three distances from the illumination point to obtain useful estimates of the optical coefficients. Measurements of the absolute steady-state spatially resolved reflectance performed on two-layered solid phantoms confirm the theoretical results.