We investigated the relationship between chromophore concentrations in two-layered scattering media and the apparent chromophore concentrations measured with broadband optical spectroscopy in conjunction with commonly used homogeneous medium inverse models. We used diffusion theory to generate optical data from a two-layered distribution of relevant tissue absorbers, namely, oxyhemoglobin, deoxyhemoglobin, water, and lipids, with a top-layer thickness in the range 1–15 mm. The generated data consisted of broadband continuous-wave (CW) diffuse reflectance in the wavelength range 650–1024 nm, and frequency-domain (FD) diffuse reflectance at 690 and 830 nm; two source-detector distances of 25 and 35mm were used to simulate a dual-slope technique. The data were inverted using diffusion theory for a semi-infinite homogeneous medium to generate reduced scattering coe±cients at 690 and 830nm (from FD data) and effective absorption spectra in the range 650–1024nm (from CW data). The absorption spectra were then converted into effective total concentration and oxygen saturation of hemoglobin, as well as water and lipid concentrations. For absolute values, it was found that the effective hemoglobin parameters are typically representative of the bottom layer, whereas water and lipid represent some average of the respective concentrations in the two layers. For concentration changes, lipid showed a significant cross-talk with other absorber concentrations, thus indicating that lipid dynamics obtained in these conditions may not be reliable. These systematic simulations of broadband spectroscopy of two-layered media provide guidance on how to interpret effective optical properties measured with similar instrumental setups under the assumption of medium homogeneity.

The concept of region of sensitivity is central to the field of diffuse optics and is closely related to the Jacobian matrix used to solve the inverse problem in imaging. It is well known that, in diffuse reflectance, the region of sensitivity associated with a given source–detector pair is shaped as a banana, and features maximal sensitivity to the portions of the sample that are closest to the source and the detector. We have recently introduced a dual-slope (DS) method based on a special arrangement of two sources and two detectors, which results in deeper and more localized regions of sensitivity, resembling the shapes of different kinds of nuts. Here, we report the regions of sensitivity associated with a variety of source–detector arrangements for DS measurements of intensity and phase with frequency-domain spectroscopy (modulation frequency: 140MHz) in a medium with absorption and reduced scattering coe±cients of 0.1 and 12 cm-1, respectively. The main result is that the depth of maximum sensitivity, considering only cases that use sourcedetector separations of 25 and 35 mm, progressively increases as we consider single-distance intensity (2.0 mm), DS intensity (4.6 mm), single-distance phase (7.5 mm), and DS phase (10.9 mm). These results indicate the importance of DS measurements, and even more so of phase measurements, when it is desirable to selectively probe deeper portions of a sample with diffuse optics. This is certainly the case in non-invasive optical studies of brain, muscle, and breast tissue, which are located underneath the superficial tissue at variable depths.