Depth sensitivity of frequency domain optical measurements in diffusive media.

Tiziano Binzoni,Lorenzo Spinelli,Angelo Sassaroli,Fabrizio Martelli,Turgut Durduran,Antonio Pifferi,Andrea Farina,Stefano Cavalieri,Alessandro Torricelli

doi:10.1364/boe.8.002990

Abstract

The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been obtained in the frequency domain (where the source amplitude is modulated at radio-frequencies) by making use of analytical solutions of the photon diffusion equation in an infinite slab geometry. Furthermore, solutions for the relative contrast of AC, PH and DC signals when a totally absorbing plane is placed at a fixed depth of the slab have also been obtained. The solutions have been validated by comparisons with gold standard Monte Carlo simulations. The obtained results show that the AC signal, for modulation frequencies < 200 MHz, has a depth sensitivity with similar characteristics to that of the continuous-wave (CW) domain (source modulation frequency of zero). Thus, the depth probed by such a signal can be estimated by using the formula of penetration depth for the CW domain (Sci. Rep.6, 27057 (2016)). However, the PH signal has a different behavior compared to the CW domain, showing a larger depth sensitivity at shallow depths and a less steep relative contrast as a function of depth. These results mark a clear difference in term of depth sensitivity between AC and PH signals, and highlight the complexity of the estimation of the actual depth probed in tissue spectroscopy.

Highlights

Depth information is crucial in biomedical optics applications since it can help to identify the part of tissue probed by the detected light
The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been obtained in the frequency domain by making use of analytical solutions of the photon diffusion equation in an infinite slab geometry
Translating the similarity between AC and CW depth sensitivity and contrast in a practical guideline for the experimenter, we propose to use the theoretical tool for the penetration depth available for the CW domain signal to obtain an estimation of the depth probed by AC signal

Summary

Introduction

Depth information is crucial in biomedical optics applications since it can help to identify the part of tissue probed by the detected light. Analytical formulae based on the diffusion equation (DE) for the mean maximum depth and the mean average depth reached by the detected photons have been obtained [11]. Another common domain in biomedical diffuse optics is the so-called “frequency-domain (FD)” where the light source is amplitude modulated at radio-frequencies (tens of megahertz), and, often, in a sinusoidal fashion. In the FD we do not have anymore this intuitive relationship between observable quantities, e.g. the phase, and the number of detected photons This fact marks a clear difference between FD and TD/CW, where results from TD/CW cannot be generalized to FD

Methods

Results

Discussion

Conclusion