In accordance with the invention, a low coherence interferometer is used to non-invasively monitor the concentration of glucose in blood by shining a light over a surface area of human or animal tissue, continuously scanning the light over a two dimensional area of the surface, collecting the reflected light from within the tissue and constructively interfering this reflected light with light reflected along a reference path to scan the tissue in depth. Since the reflection spectrum is sensitive to glucose concentration at particular wavelengths, measurement and analysis of the reflected light provides a measure of the level of glucose in the blood. The measurement of glucose is taken from multiple depths within blood-profused tissue, and sensitivity is preferably enhanced by the use of multiple wavelengths. Noise or speckle associated with this technique is minimized by continuously scanning the illuminated tissue in area and depth.