  Chemical imaging provides information about the distribution of chemicals
within a target. When combined with structural information about the target, in
situ chemical imaging opens the door to applications ranging from tissue
classification to industrial process monitoring. The combination of infrared
spectroscopy and optical microscopy is a powerful tool for chemical imaging of
thin targets. Unfortunately, extending this technique to targets with
appreciable depth is prohibitively slow.
  We combine confocal microscopy and infrared spectroscopy to provide chemical
imaging in three spatial dimensions. Interferometric measurements are acquired
at a small number of focal depths, and images are formed by solving a
regularized inverse scattering problem. A low-dimensional signal model is key
to our approach: we assume the target comprises a finite number of distinct
chemical species. We establish conditions on the constituent spectra and the
number of measurements needed for unique recovery of the target. Simulations
illustrate imaging of cellular phantoms and sub-wavelength targets from noisy
measurements.
