The purpose of this work is twofold. First we obtain a series expansion for the Voigt function that is valid for all values of the dimensionless parameter a (a measure of the ratio between the Lorentzian and Gaussian widths). Furthermore, the resulting coefficients are independent of the generalized coordinate b (the wavelength measured in units of the Gaussian width). In the second place, we fit an experimental “shaped bell” curve to a Voigt profile using certain theoretical restrictions that relate the maximum height and the full width at half-maximum.

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In the present contribution we investigate the images of CW diffusely reflected light for a point-like source, registered by a CCD camera imaging a turbid medium containing an absorbing lesion. We show that detection of μa variations (absorption anomalies) is achieved if images are normalized to background intensity. A theoretical analysis based on the diffusion approximation is presented to investigate the sensitivity and the limitations of our proposal and a novel procedure to find the location of the inclusions in 3D is given and tested. An analysis of the noise and its influence on the detection capabilities of our proposal is provided. Experimental results on phantoms are also given, supporting the proposed approach.

In diffuse optical tomography (DOT) the main objective is to estimate the absorption coefficent and the reduced scattering coefficient of a certain media given a set of boundary measurements. Biological tissues contains many objects such as arteries, skin and fat whose optical properties are rather different than those of the media. When these values are near to those of the background, linear techniques are usually used to estimate them. However, certain objects, such as tumors, may have properties which cannot be well estimated with linear models. In this article we present a non-linear approach for the frequency-domain problem based on an improvement of the extended Kalman filter (EKF) which is used in estimation-observation problems, and modified to the DOT parameter estimation problem. The EKF allows to incorporate prior information of the measurement noise as well as certain characteristics of the objective media. We show that the proposed methodology is equivalent to existing methods but can be applied to other schemes such as model reduction as suggested in previous works. Some computer simulations as well as experimental results are shown to validate our proposal.

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