Samuele Del Bianco

Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation

The depth at which photons penetrate into a diffusive medium before being re-emitted has been investigated with reference to a semi-infinite homogeneous medium illuminated by a pencil beam. By using the diffusion equation analytical expressions have been obtained for the probability that photons penetrate at a certain depth before being detected, and for the mean path length they travel inside each layer of the medium. Expressions have been obtained both for the cw and the time domain, and simple approximate scaling relationships describing the dependence on the scattering properties of the medium have been found. For time-resolved measurements both the probability and the mean path length are expected to be independent of the distance from the light beam at which the detector is placed and of the absorption coefficient of the medium. The penetration depth increases as the time of flight increases. In contrast, for cw measurements both the probability and the mean path length strongly depend on the distance and absorption. The penetration depth increases as the distance increases or absorption decreases. The accuracy of the analytical expressions has been demonstrated by comparisons with cw experimental results. The penetration depth and the mean path length provide useful information, for instance, for measurements of tissue oxygenation and for functional imaging of muscle and brain. In particular, the depth reached by received photons provides overall information on the volume of the tissue actually investigated, while the mean path is strictly related to the sensitivity to local variations of absorption.

Light Propagation through Biological Tissue and Other Diffusive Media

Acknowledgements Preface List of Acronyms List of Symbols 1. Introduction Part I: Theory 2. Scattering and Absorption Properties of Diffusive Media 2.1 Approach Followed in this Book 2.2 Optical Properties of a Turbid Medium 2.2.1 Absorption properties 2.2.2 Scattering properties 2.3 Statistical Meaning of the Optical Properties 2.4 Similarity Relation and Reduced Scattering Coefficient 2.5 Examples of Diffusive Media.

Phantom validation and in vivo application of an inversion procedure for retrieving the optical properties of diffusive layered media from time-resolved reflectance measurements

An experimental validation of an inversion procedure for retrieving the optical properties of layered media from multidistance time-resolved reflectance measurements is presented. The results cover a wide range of optical properties, showing excellent effectiveness and reliability of the procedure in reconstructing the optical properties of a two-layered medium. The optical properties of the first layer and the absorption of the second layer could be retrieved with excellent precision, whereas the reduced scattering coefficient of the second layer was reconstructed with a large error. The first layer thickness could be retrieved with an error less than 50%. An example of retrieval of the optical properties of muscle from in vivo measurements during an arterial occlusion is shown.

Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements.

A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the diffusion equation and on relative multidistance time-resolved reflectance measurements is presented. The method overcomes some limitations of previously developed procedures. Five parameters of the medium have been fitted: the absorption and the reduced scattering coefficients of both layers and the thickness of the first layer. The actual values of the parameters are correctly retrieved by the procedure. The inversion procedure does not require an initial guess for the unknown optical properties, but the starting value for the thickness of the first layer needs to be estimated with an error smaller than 50%.

Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model.

A diffusion-based model for photon migration through a three-layer medium is described. The main purpose of this work is to investigate the performance of a diffusion equation (DE)-based forward model for studying photon migration through a diffusive layered medium having a low scattering layer. This geometrical model can be used as a simple model of the adult head. Numerical results are shown for a set of values of the optical properties typical of the adult human head, where scalp and skull are lumped in the first layer while the second and third layer are associated with the cerebrospinal fluid (CSF) and the brain, respectively. Due to the presence of the CSF, which is a relatively clear layer, the diffusion-based model yields an approximate solution of photon migration. Nevertheless, comparisons with MC simulations show that the model can predict the total and the partial mean path length in the different layers with an error less than 20%. In particular, the partial mean path length in the third layer, representative of the brain, is calculated with an error less than 10% if the reduced scattering coefficient of the second layer, representative of the CSF, is assumed 0.25 mm(-1).

Perturbation model for light propagation through diffusive layered media

A fast and novel perturbation approach is proposed to account for the effects of absorbing inhomogeneities on light propagation through layered media. The calculation has been implemented with the Born approximation. Examples of results are reported both for a two- and for a three-layered medium. The method presented has been validated with the results of Monte Carlo simulations. The forward solver presented in this paper can be of significant use in investigating the feasibility of real experiments, e.g. for functional imaging studies.

Sun-induced leaf fluorescence retrieval in the O 2 -B atmospheric absorption band

Sun-induced leaf fluorescence was inferred by using high resolution (0.5 cm(-1)) radiance measurements and simulated spectra of the solar irradiance at the ground level, in the region of the O(2)-B absorption band. The minimization of a cost function was performed in the Fourier transform domain in order to make an accurate fit of the Instrumental Line- Shape that convoluted the simulated spectrum. Second- order polynomials were used to fit the leaf fluorescence and reflectance in the 100-cm(-1)-wide spectral window. The scale and the instrumental conversion factor were also fitted in order to obtain an accuracy that could not be attained by using the radiance measurements alone.

Optimal estimation reconstruction of the optical properties of a two-layered tissue phantom from time-resolved single-distance measurements

Abstract. In this work, we have tested the optimal estimation (OE) algorithm for the reconstruction of the optical properties of a two-layered liquid tissue phantom from time-resolved single-distance measurements. The OE allows a priori information, in particular on the range of variation of fit parameters, to be included. The purpose of the present investigations was to compare the performance of OE with the Levenberg–Marquardt method for a geometry and real experimental conditions typically used to reconstruct the optical properties of biological tissues such as muscle and brain. The absorption coefficient of the layers was varied in a range of values typical for biological tissues. The reconstructions performed demonstrate the substantial improvements achievable with the OE provided a priori information is available. We note the extreme reliability, robustness, and accuracy of the retrieved absorption coefficient of the second layer obtained with the OE that was found for up to six fit parameters, with an error in the retrieved values of less than 10%. A priori information on fit parameters and fixed forward model parameters clearly improves robustness and accuracy of the inversion procedure.

A phantom for investigating light propagation through layered diffusive media

A phantom for investigating light propagation through layered diffusive media is described. The diffusive medium is an aqueous suspension of calibrated scatterers and absorbers and a thin membrane separates layers with different optical properties.

Wide-band spectrally resolved measurement of the Earth's up-welling radiation with the REFIR-PAD spectroradiometer

The REFIR-PAD (Radiation Explorer in the Far InfraRed-Prototype for Applications and Development) Fourier transform spectroradiometer has successfully performed, at the end of June, 2005, a stratospheric balloon flight from Teresina, Brazil. The instrument has provided 8 hours worth of nadir-looking spectra acquired with a resolution of 0.5 cm-1 in the 100 to 1400 cm-1 spectral range, thus covering both the far-infrared range, containing the radiative signature of the upper tropospheric water vapour, and the better-known mid-infrared range, which provides validation with existing instruments. From the analysis of the calibrated spectra we obtain valuable information on the contribution to the Earths outgoing long-wave radiation of water, both in the vapour and cloud form, in a region of the atmosphere, the upper-troposphere/lower-stratosphere, in which this contribution has a critical role.