Near-IR diffuse optical spectroscopy (DOS) is commonly used to determine

*in vivo* tissue absorption coefficient

*μ*_{a} and reduced scattering coefficient

, from which tissue functional information, such as hemoglobin concentration, oxygen saturation, water concentration, and averaged scatter size and density can be deduced.

^{1}^{,}^{2} Both of these parameters are important in noninvasive tissue diagnostics, since the scattering coefficient of tissue can provide information about the mean size of the tissue scatterers, while the absorption coefficient of tissue can be used to determine chromophore species and concentrations.

^{3}^{,}^{4} The interrogation depth of DOS measurements is generally proportional to the source-detector separation of the probe employed and it also depends on the optical properties of tissues under investigation.

^{5}^{,}^{6} DOS methods with source-detector separation larger than 20 mm have performed quite well in the 600 to 1000-nm spectral range for the purpose of determining optical properties and chromophore concentrations of thick tissues (depths greater than 10 mm) such as breast and brain.

^{7}^{,}^{8} DOS techniques have been applied to investigate optical properties of superficial tissues as well. Bevilacqua et al. used a fiber probe having source-detector separations in the range from 0.3 to 1.4 mm along with a Monte Carlo model to recover optical properties of a human skull and brain.

^{9} Bays et al.

^{10} employed spatially resolved reflectometry to determine optical properties of human esophageal wall with a probe having source-detector separations ranging from 3 to 20 mm. Amelink et al. developed differential path-length spectroscopy to investigate optical properties of bronchial mucosa.

^{11} In all cases, DOS techniques require either a photon transport model or an empirical model to determine

*μ*_{a} and

from the reflectance.

The photon transport model most often utilized for determining optical properties from DOS measurements is the standard diffusion model derived from the radiative transport theory. Because of its simplicity and computational efficiency, the standard diffusion model has been used widely and successfully to recover optical properties of deep tissues.

^{12}^{,}^{13} While the standard diffusion model is derived from the radiative transport theory with diffusion approximations, the model cannot be used reliably for recovering the optical properties of typical biological tissues when (

*ρ/l*_{t}) is smaller than 10, where

*ρ* is the source-detector separation and

*l*_{t} is

^{14}^{-}^{16} the transport mean free path

. To reliably determine optical properties of superficial tissue volumes lying between the tissue surface and 1 to 2 mm deep using DOS, measurements with source-detector separation shorter than 3 mm are necessary.

^{6} This regime is of great interest for skin-cancer-oriented applications, oral cancer applications, and numerous applications accessible via endoscope in which functional characterization of tissue is desirable. Several alternative approaches to diffusion approximation such as Monte Carlo simulations,

*P*_{3} approximation, and

*δ*-

*P*_{1} approximation have been proposed for short source-detector separation DOS applications.

^{17}^{-}^{19}Although methods based on Monte Carlo techniques have, in certain circumstances, been shown to provide the most accurate results among the aforementioned models, the need for intensive computation resources to build a data library in advance limits its applicability. Several researchers have developed the so-called “white Monte Carlo model,” which enables the calculation of optical properties based on a single Monte Carlo simulation to bring the computation time similar to the diffusion theory based models.

^{17} However, it is shown that even with the white Monte Carlo method, a data library containing various single scattering phase functions still must be established in advance to properly recover optical properties of superficial tissues, since the single scattering phase function of tissue actively affects the measured reflectance especially when the source-detector separation is

^{20} shorter than 1 to 2 mm. By changing the scattering phase function used in the Monte Carlo model, Liu and Ramanujam reported the reflectance generated with different scattering phase functions could have deviation larger than 20% at source-detector separations shorter than 1 mm. This deviation in calculated reflectance resulted in 31.4% error in the recovered absorption coefficient.

^{21} In contrast, the diffusion-based models do not require a phase function to recover

*μ*_{a} and

. We demonstrated that using a novel optical probe to facilitate the usage of the diffusion model to recover the optical properties of superficial volume of a tissue phantom

with less than 8% error.

^{16}The diffusing probe we proposed employs a slab of highly scattering Spectralon (Labsphere, New Hampshire) (

,

*μ*_{a}~10

^{−6}/mm) that is placed in contact with the surface of the sample under investigation (). This scattering layer causes photons emitted from the source optical fiber to undergo multiple scattering. This enables us to employ a modified two-layer (MTL) standard diffusion model to recover the sample optical properties, even under the condition that the source-detector separation is less than 3 transport mean free paths.

^{16}We successfully applied the diffusing probe to study the optical properties of *in vivo* human skin.^{22} We are planning to use the diffusing probe in many clinical applications. To correctly interpret *in vivo* measurement results obtained from the diffusing probe, it is critical to characterize and understand the effects of parameters of the diffusing probe that may impact the interrogation volume. The primary objective of this paper is to methodically examine the influence of sample optical properties and probe parameters on the depth of interrogation of the diffusing probe.

In this paper, we first demonstrate the accuracy and the advantage of the MTL diffusion model over a standard diffusion approach. The performance of the diffusion model, in either MTL geometry or semiinfinite geometry, was evaluated by a benchmark Monte Carlo model. While the reflectance generated from the Monte Carlo model is sensitive to the choice of the scattering phase function when the source-detector separation is smaller than 1 mm, the Monte Carlo model is usually employed^{23}^{,}^{24} as the gold standard method to calculate diffuse reflectance when the source-detector separation is larger than 1 mm. It was reported that when using different scattering phase functions in the Monte Carlo model, the difference in generated reflectance was less than 10% when the source-detector separation was^{21} larger than 1 mm. Thus, in this study, to use the Monte Carlo model as a benchmark method, we limit the source-detector separations to be larger than 1 mm in all simulations.

We also conducted numerous Monte Carlo simulations with the objective of investigating the dependence of the probing depth of the diffusing probe on the optical properties of samples, scattering, absorption, and thickness of the diffusing layer of the probe, as well as dependence on the source-detector separation. The simulation results presented provide design guidelines for a diffusing probe having specific interrogation depth characteristics.