Multiscale Reconstruction for Photon-Limited Shifted Excitation Raman Spectroscopy

Shifted excitation Raman spectroscopy results in multiple observations of the sum of a material´s fluorescent and Raman spectra. The fluorescent spectrum is typically stationary with respect to the excitation frequency induced by the instrument, while the Raman spectrum is subject to a nonlinear shift which depends explicitly and in a known manner upon the excitation frequency. This phenomenon has been exploited to reconstruct Raman spectra indirectly by subtracting spectra observed at two closely spaced excitation frequencies. The technique, known as shifted excitation Raman difference spectroscopy (SERDS), is of limited utility, however, in that observations with low photon counts are difficult to process accurately, and that one must still reconstruct the spectrum from the estimate of the derivative. This paper presents an innovative alternative approach to Raman spectrum reconstruction based on an expectation-maximization algorithm and multiresolution photon-limited signal analysis. Using this method, it is shown that using multiple excitation frequencies (while keeping the total excitation laser power and total expected photon counts constant) can result in dramatic improvements in reconstruction accuracy.