A method of imaging an optically thin sample is described wherein a collimated beam is directed through the sample and then reflected back through the sample one or more times. The beam is then directed toward a detector which collects and analyzes the spatial and spectral composition of the beam. In some embodiments, the detector is a focal plane array with a large number of detector elements. In other embodiments the relative position of a single detector or a small detector array and the sample is altered and the process is repeated, thereby tracing out a large virtual detector array. In either case, the spectral information received by the detector elements can be related, by methods which are elaborated below, to information about the spatial distribution of absorption in the sample.