Transformational change in the field of diffuse optics: From going bananas to going nuts

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 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 dual-slope measurements of intensity and phase with frequency-domain spectroscopy (modulation frequency: 140 MHz) in a medium with absorption and reduced scattering coefficients of 0.1 cm^-1 and 12 cm^-1, respectively. The main result is that the depth of maximum sensitivity, considering only cases that use source-detector separations of 25 and 35 mm, progressively increases as we consider single-distance intensity (2.0 mm), dual-slope intensity (4.6 mm), single-distance phase (7.5 mm), and dual-slope phase (10.9 mm). These results indicate the importance of dual-slope 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 superficial tissue at variable depths.