Much effort has been devoted in recent years to quantify the optical properties of superficial biological tissue from spatially resolved reflectance measurement

as they can be used to infer important physiological information. Some examples include the noninvasive measurement of the concentration of chemotherapy drugs or exogenous chromophores used for photodynamic cancer treatment and the assessment of hemoglobin oxygenation in tissue. The diffusion approximation to the Boltzmann equation has become the current standard for making theoretical predictions of spatially resolved reflectance because of its higher mathematical tractability compared with the general transport equation. In this regime

the parameters of interest are the absorption(μ

α

)and the effective isotropic transport scattering(μ′

s

)coefficients. To a first crude approximation

superficial tissue can be considered as a semi-infinite turbid medium. Diffuse reflectance models have been developed for that geometry. In reality

superficial tissue is a multi-layered structure with each component having a different μ

α

and μ′

s

. Recovery of the complete spatial distribution of μ

α

and μ′

s

is the goal of optical tomography

and it is an open question as to whether this can be accomplished with sufficient accuracy. In an attempt to mimic tissue structure more realistically than the semi-infinite medium model

an improved

yet still crude

two-layer turbid medium model of tissue structure can be utilized. In this model

a top-layer thickness of 1~10mm that includes the epidermis and the dermis lies on top of a semi-infinite homogeneous medium that could be fat or muscle. In this article

a solution of the diffusion equation for a two-layered turbid medium having a semi-infinite second layer is derived by using the Fourier transform. Naturally

the assumptions that are inherent in each model will be reflected in the accuracy of its predictions and

consequently

the accuracy of the optical properties that can be inferred from it. The comparisons of the reflectance in the steady-state showed that the derived solutions of the two-layer model are close to the results obtained from two-layer Monte Carlo simulations. Thus

for many applications the reflectance calculated with the derived solution is exact enough to replace the time-consuming Monte Carlo simulations. Nonlinear regressions of these solutions of the diffusion equation to reflectance data obtained from two-layer Monte Carlo simulations in the steady-state showed the absorption and the effective isotropic transport scattering coefficients of the two layers can

in principle

be obtained. It was also shown by fitting the solutions of the diffusion equation to results obtained from Monte Carlo data that the optical parameters are obtained with different accuracy.