Theoretical optimal modulation frequencies for scattering parameter estimation and ballistic photon filtering in diffusive media

TL;DR

This paper theoretically determines the optimal modulation frequencies for estimating scattering parameters and filtering ballistic photons in diffusive media, providing analytical bounds and insights into their dependence on medium properties.

Contribution

It introduces a theoretical framework for optimal modulation frequency selection and a metric for ballistic photon filtering efficiency in turbid media.

Findings

Existence of a variance-minimizing optimal modulation frequency.

Optimal frequency depends on the medium's reduced scattering coefficient.

Minimum modulation frequency for ballistic discrimination is linearly related to scattering coefficient.

Abstract

The efficiency of using intensity modulated light for estimation of scattering properties of a turbid medium and for ballistic photon discrimination is theoretically quantified in this article. Using the diffusion model for modulated photon transport and considering a noisy quadrature demodulation scheme, the minimum-variance bounds on estimation of parameters of interest are analytically derived and analyzed. The existence of a variance-minimizing optimal modulation frequency is shown and its evolution with the properties of the intervening medium is derived and studied. Furthermore, a metric is defined to quantify the efficiency of ballistic photon filtering which may be sought when imaging through turbid media. The analytical derivation of this metric shows that the minimum modulation frequency required to attain significant ballistic discrimination depends only on the reduced scattering coefficient of the medium in a linear fashion for a highly scattering medium.