Miniaturization of attenuated total reflectance (ATR) spectrometers has been an emerging field applying such powerful surface sensing method for in-situ spectroscopic analysis. In this work, we present a model for field propagation through ATR element under the illumination of multimode fiber (MMF) in a micro-electro-mechanical-systems (MEMS) based ATR Fourier transform infrared (FTIR) spectroscopic system. The core spectrometer is based on micro-fabricated Michelson interferometer using deep etching technology, in which the light propagates in-plane with respect to the silicon substrate. An ATR multiple reflection crystal is illuminated with infrared (IR) thermal blackbody radiation source through an MMF. The output light of the crystal is fiber-coupled to the MEMS interferometer then to an IR broadband photodetector. The optical system is modelled using scaler Fourier optics, where the fiber output field is represented by a group of spatially shifted elementary sources, to predict the ATR absorbance response, taking into account the partial spatial coherence nature of the MMF output. The model output leads to the requirements on the ATR measurement conditions and numerical aperture (NA) of the system. The model is compared to practical results of MEMS spectrometer which is experimentally characterized over the mid-infrared (MIR) wavenumber range from 5000 cm ⁻¹ to 2100 cm ⁻¹ , lower limited by the used fiber and photodetector cut-off. Spectra of liquid samples are obtained using two different crystals and total internal reflection (TIR) angles showing good agreement with theoretical prediction.

中文翻译：

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部分相干多模光纤照明下 ATR-FTIR MEMS 光谱仪的建模

衰减全反射 (ATR) 光谱仪的小型化一直是一个新兴领域，应用如此强大的表面传感方法进行原位光谱分析。在这项工作中，我们提出了在基于微机电系统 (MEMS) 的 ATR 傅里叶变换红外 (FTIR) 光谱系统中，在多模光纤 (MMF) 的照射下通过 ATR 元件的场传播模型。核心光谱仪基于使用深蚀刻技术的微制造迈克尔逊干涉仪，其中光相对于硅基板在平面内传播。ATR 多重反射晶体通过 MMF 用红外 (IR) 热黑体辐射源照射。晶体的输出光通过光纤耦合到 MEMS 干涉仪，然后耦合到红外宽带光电探测器。光学系统使用定标傅里叶光学建模，其中光纤输出场由一组空间位移的基本源表示，以预测 ATR 吸收响应，同时考虑到 MMF 输出的部分空间相干性质。模型输出导致对系统的 ATR 测量条件和数值孔径 (NA) 的要求。该模型与 MEMS 光谱仪的实际结果进行了比较，该光谱仪在 5000 cm 的中红外 (MIR) 波数范围内进行了实验表征 模型输出导致对系统的 ATR 测量条件和数值孔径 (NA) 的要求。该模型与 MEMS 光谱仪的实际结果进行了比较，该光谱仪在 5000 cm 的中红外 (MIR) 波数范围内进行了实验表征 模型输出导致对系统的 ATR 测量条件和数值孔径 (NA) 的要求。该模型与 MEMS 光谱仪的实际结果进行了比较，该光谱仪在 5000 cm 的中红外 (MIR) 波数范围内进行了实验表征 ^-1到 2100 cm ^-1 ，下限受所用光纤和光电探测器截止。使用两种不同的晶体和全内反射 (TIR) 角获得液体样品的光谱，显示与理论预测非常吻合。