Standard Fourier Transform Infrared Spectrometers (FTIR) rely on a Michelson Interferometer scheme which uses a linear delay line to retrieve an interference pattern. Here, we demonstrate a fast FTIR based on a rotational delay line which allows us to achieve kHz acquisition rates. We perform spectrometry measurements using it in combination either with a Mid-IR Quantum Cascade Laser (QCL) frequency comb or a strongly, low-frequency, RF-modulated QCL. Regarding the latter, the modulation enables to broaden the laser emission up to 250cm^-1 (from 6.5µm to 7.5µm) and to reduce its amplitude noise compared to the free-running case. The combination of a strongly modulated QCL with a rotational FTIR opens the possibility to fast and broadband spectroscopy in the Mid-IR region, with possible applications spanning from gas detection to process control
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