We present a novel instrument to measure the spectral, angular, azimuthal, and polarization dependence of light backscattered by living biological tissues, thus providing the most comprehensive description of the light scattering to obtain unique quantitative information about the microarchitecture of living cells and tissues. We show the potential of this technique to characterize and diagnose early premalignant changes in the epithelia. In studies with a rodent model of colon carcinogenesis, we show that several parameters obtained using this technique, such as the number density of red blood cells in the capillary network immediately underlying the epithelium, the fractal dimension of the tissue, and the average roundness of subcellular structures, are significant for detection of precancerous changes at a very early stage of the carcinogenic process, at which no other histological or molecular markers have been identified.