Composition-Aware Spectroscopic Tomography

Abstract: 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.