On Path Length, Beam Divergence, and Retroreflector Array Size in Open-Path FTIR Spectroscopy

Abstract. Open-Path Fourier Transform InfraRed (OP-FTIR) spectroscopy is an established technique used to measure boundary layer trace gas concentrations, consisting (in this work) of a spectrometer with an active mid-IR source coupled to a single transmitting and receiving telescope, and a cube-corner retroreflector array separated from the spectrometer and telescope by an atmospheric path. The detection limit is directly proportional to the optical path length in the atmosphere, which controls target gas spectral absorption depth; however, open-path beam divergence can lead to overfilling of the distant retroreflector array for one-way paths greater than ~300 m (details depend on specifics of spectrometer and telescope optics, plus array size), resulting in decreased returning radiation at the detector. In this case, the absorption signature of the target gas increases, but the signal to noise ratio of the recorded spectrum decreases.  We present the results of theoretical spectral simulations for formaldehyde (HCHO) that show how path length, interfering water concentration, and HCHO target concentration affect the expected differential absorption spectrum of the HCHO target. We demonstrate that two-way path lengths > ~300 m are necessary for robust HCHO spectral signatures (at typical random plus systematic noise levels).  Next, we present the results of two field experiments where the retroreflector array area was increased to collect a larger fraction of returning radiation, at two-way path lengths ranging from 50 m to 1300 m. We demonstrate that the larger retroreflector array resulted in a smaller decrease in the signal-to-noise ratio as a function of measurement path, ~1.5 m⁻¹ for the larger array as compared to ~3.6 m⁻¹ for the smaller array. Finally, we perform retrievals of HCHO concentrations from spectra collected at the same field site and path length in Halifax Harbour during 2018 and 2021, with a smaller and a larger retroreflector array, respectively.  We demonstrate that retrievals based on larger retroreflector array spectra exhibit higher precision (average standard deviation of 0.352 ppb for 2021 and 0.678 ppb for 2018 in hourly formaldehyde data bins over two days), even though systematic errors remain in the fitted spectra, due to water vapour.  Where systematic fitting errors in interfering species are significant, a longer path may not be optimal for a given target gas, leading instead to biased retrievals; moreover, at very long pathlengths signal-to-noise ratio decreases with increasing water vapour conditions due to broadband spectrum signal reduction effects in water-saturated regions.  We discuss factors to consider in the choice of path length and retroreflector array size in open-path FTIR spectroscopy, which must be made with care.