Fibre Fabry-P\'erot Astrophotonic Correlation Spectroscopy for Remote Gas Identification and Radial Velocity Measurements

We present a novel remote gas detection and identification technique based on correlation spectroscopy with a piezoelectric tunable fibre-optic Fabry-P\'erot filter. We show that the spectral correlation amplitude between the filter transmission window and gas absorption features is related to the gas absorption optical depth, and that different gases can be distinguished from one another using their correlation signal phase. Using an observed telluric-corrected, high-resolution near-infrared spectrum of Venus, we show via simulation that the Doppler shift of gases lines can be extracted from the phase of the lock-in signal using low-cost, compact, and lightweight fibre-optic components with lock-in amplification to improve the signal-to-noise ratio. This correlation spectroscopy technique has applications in the detection and radial velocity determination of faint spectral features in astronomy and remote sensing. We experimentally demonstrate remote CO2 detection system using a lock-in amplifier, fibre-optic Fabry-P\'erot filter, and single channel photodiode.