Nonlinear inversion for optical tomography

Optical tomography is a recent addition to the available set of computerized imaging methods available to characterize live or inanimate matter. It uses light in the optical and nearinfrared ranges and is thus particularly suited to study samples that exhibit significant variation in their optical properties in this wavelength range. This includes, for example, biological tissues as well as some inhomogenous fluids of industrial interest. We will focus here on the use of the method for biomedical imaging. One of the advantages of optical tomography over many of the established methods is that it is relatively fast, inexpensive, and does not use ionizing radiation. The latter is particularly important when studying live tissue as the near infrared radiation does not induce ionization. Another advantage is that the variant of optical tomography described here, namely fluorescence enhanced optical tomography, can be made molecularly targeted, i.e. it can be used to determine the three-dimensional distribution of biochemical events of interest, as long as they can be targeted by antibodies or other targeting moeties. In contrast to most traditional imaging methods such as X-ray tomography, optical tomography does not use a linear mapping from the desired description of an object to the detected signal. Consequently, we can not hope for explicit inversion formulas such as the inverse Radon transform, and have to resort to numerical procedures for imaging. We will explain and demonstrate such a procedure in this contribution.