Differential imaging in heterogeneous media: limitations of linearization assumptions in optical tomography

Image reconstruction and data collection in optical tomography can be achieved in a number of different ways. This paper explores the limitations of using assumptions of linearity, particularly in the case where image data is acquired before and after a change in optical properties within an object with heterogeneous optical properties. The effects of using a 2 dimensional (2D) reconstruction scheme for changes in 3D measurements are also demonstrated. Problems are a direct result of the inherent non-linearity of optical tomographic image reconstruction. We show how these assumptions affect images of changes in absorption in the presence of a) heterogeneous background scatter, and b) heterogeneous background absorption using both simulations and time-resolved experimental data. Comparisons of results using non-linear and linear image reconstruction techniques are included throughout. The origin and dependence of the error are investigated. Methods to improve results by using estimates of background structure from baseline images are shown to improve quantitation and object localization in simple images. The potential significance of this error is discussed in relation to successful, reliable clinical imaging of the neonatal brain.