Modelling of ATR-FTIR MEMS Spectrometer Under Partially-Coherent Multimode-Fiber Illumination

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.