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 (RSNR) 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 RSNR 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.

中文翻译：

---

光栅光谱和空间外差傅里叶变换光谱：拉曼测量的比较噪声分析

对便携式拉曼光谱仪的需求不断推动新型光谱仪架构的发展，在这种架构中，可以实现小型化而不会降低检测性能。空间外差光谱仪正成为挑战传统光栅光谱仪主导地位的潜在候选者，这要归功于它们更大的展量和更大的小型化潜力。本文通过推导出两种类型光谱仪的性能估计器（信噪比，SNR）的解析表达式，提供了一个通用的分析模型，用于估计和比较基于光栅光谱仪和空间外差光谱仪设计的拉曼光谱仪的检测性能. 分析表明，根据拉曼光的光谱特性和某些仪器特定参数的值，两个光谱仪 (RSNR) 的 SNR 估计值之比可能相差两个数量级。这些方程的极限情况是针对在拉曼光谱的实际应用中具有实际重要性的光谱范围的子集提出的。特别是，在背景信号与目标拉曼线相当或大于目标拉曼线且散粒噪声是主要噪声贡献的实验条件下，RSNR 的值是一阶近似值，仅取决于每个的相对值光谱仪的集光率和探测器阵列中的行像素数。对于关键仪器特定参数的典型值（例如，集光率、像素数、