Apparatus and method to measure optical absorption spectra with spatial resolution on the micron scale. An exemplary setup combines a continuous white light excitation beam in transmission geometry with a confocal microscope. Spatial resolution better than 1.4 μm in the lateral and 3.6 μm in the axial, directions was obtained. The detection and measurement of the absorption spectrum of hemoglobin in a single red blood cell under physiological conditions on the timescale of seconds was realized. The apparatus and method enables the investigation of spatial variations in the optical density of small samples on the micron scale and the study of biological assemblies at the single cell level, leading to applications in optical diagnostics, microfluidics, and other areas.