Grating Spectrometry and Spatial Heterodyne Fourier Transform Spectrometry: Comparative Noise Analysis for Raman Measurements.

The desire for portable Raman spectrometers is continuously driving the development of novel spectrometer architectures where miniaturisation can be achieved without the penalty of a poorer detection performance. Spatial heterodyne spectrometers are emerging as potential candidates for challenging the dominance of traditional grating spectrometers, thanks to their larger etendue and greater potential for miniaturisation. This paper provides a generic analytical model for estimating and comparing the detection performance of Raman spectrometers based on grating spectrometer and spatial heterodyne spectrometer designs by deriving the analytical expressions for the performance estimator (signal-to-noise ratio, SNR) for both types of spectrometers. The analysis shows that, depending on the spectral characteristics of the Raman light and on the values of some instrument-specific parameters, the ratio of the SNR estimates for the two spectrometers () can vary as much as by two orders of magnitude. Limit cases of these equations are presented for a subset of spectral regimes which are of practical importance in real-life applications of Raman spectroscopy. In particular, under the experimental conditions where the background signal is comparable or larger than the target Raman line and shot noise is the dominant noise contribution, the value of is, to a first order of approximation, dependent solely on the relative values of each spectrometer's etendue and on the number of row pixels in the detector array. For typical values of the key instrument-specific parameters (e.g., etendue, number of pixels, spectral bandwidth), the analysis shows that spatial heterodyne spectrometer-based Raman spectrometers have the potential to compete with compact grating spectrometer designs for delivering in a much smaller footprint (10-30 times) levels of detection performance that are approximately only five to ten times poorer.