Multiple light scattering, medical imaging, and random lasers

Multiple scattering of light in biological tissue provides a safe, inexpensive, and noninvasive probe of brain, breast, and skin tumors. Unlike, magnetic resonance imaging (MRI) which relies on very long wavelength radiation, or X-ray based tomography which relies on very short wavelength radiation, the optical method utilizes an intermediate wavelength window. This window is sensitive to the concentration of oxygenated haemoglobin in tissue, and thereby provides an early diagnostic image of metabolic processes leading to cancer, prior to structural damage caused by the tumor. We are developing a microscopic theory of the propagation of the Wigner coherence function (two-point electric field correlation function) of near infra-red light propagating and scattering in biological tissue which contains a statistical inhomogeneity (tumor). The inhomogeneity exhibits preferential absorption of light and may have different scattering characteristics than healthy tissue. The optical Wigner function is sensitive to these different absorption and scattering characteristics. The difficulty of the optical method is that, unlike X-ray and MRI techniques in which radiation propagates in a straight line, light undergoes a complicated multiple scattering path in the medium. Our work is aimed at unscrambling the information about tissue characteristics contained in the optical wave-field after it has been scattered many times. Most other researchers in this field have adopted the simplistic assumption that photons (particles of light) can be regarded as classical particles undergoing diffusion in the tissue. Using this assumption, tissue properties can only be resolved on the scale of a millimeter. Our approach, which for the first time solves the wave equation and relates the Wigner coherence function to the tissue dielectric constant, will improve the resolution of the optical method by several orders of magnitude. Our microscopic theory will facilitate the reconstruction of tissue images with a resolution on the scale of the optical wavelength. Imaging devices based on our theory will be safe, inexpensive, and suitable for use in the office of the general practitioner. Other applications include the ability to diagnose skin tumors without recourse to a biopsy and the ability to perform a blood test without having to draw blood.

Biological tissue is a weakly absorbing, multiple light scattering medium. A closely related problem is that of stimulated emission, optical amplification and lasing in a random medium with gain. Recent experiments have revealed that a multiple scattering medium doped with dye molecules can exhibit isotropic laser action when suitably pumped. We are currently developing a microscopic theory of these "Laser Paints".