**1. Introduction**

Public concern about the adverse health effects of air pollution has increased considerably in recent years. This growing concern is being progressively translated into more restrictive legislation [1]: new emission limit values (ELVs) are set for previously unregulated pollutants, and more stringent levels are established for those already regulated. There is thus an increasing need to develop reliable methods for the measurement of atmospheric gases at immission levels. An example of this trend is the IMPRESS 2 project, funded by the research program EMPIR (European Metrology Programme for Innovation and Research) of the European Association of National Metrology Institutes (EURAMET), with the aim of improving measurement of pollutant gases at several levels: to develop new reference measurement methods for gases not yet regulated, to improve hyperspectral techniques, to determine uncertainty and traceability of mass emission measurements, etc. [2].

Ideally, a measurement method for air pollutants should be both versatile and accurate. Since all pollutant gases show characteristic absorption–emission bands in the infrared (IR) spectral region, IR optical techniques are such a versatile method with the additional advantage of providing remote and non-intrusive measurements. There are many techniques for IR optical gas sensing (see [3] for a comprehensive review) but high resolution spectroscopy is the most wide ranging in its applications, being able to detect several gases at the same time, and has the potential for high accuracy, since the dependence of line intensities on temperature and concentration is very well known.

Due to these features, Fourier transform spectrometry has been used for a long time to measure emissions from smokestack effluents and other industrial sources [4–6], but in

**Citation:** Meléndez, J.; Guarnizo, G. Fast Quantification of Air Pollutants by Mid-Infrared Hyperspectral Imaging and Principal Component Analysis. *Sensors* **2021**, *21*, 2092. https://doi.org/10.3390/s21062092

Academic Editor: Krzysztof M. Abramski

Received: 29 January 2021 Accepted: 8 March 2021 Published: 17 March 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

recent years, imaging spectrometers have conferred additional power to this technique [7]: it has become possible to map column densities *Q* (concentration·path product) of pollutants and plume temperatures *T* [8] over a large area, or to track gas flows and estimate effluent mass flow rates [9]. Cooler sources, such as automobile exhaust emissions, have also been measured in absorption mode [10], as well as ambient-temperature greenhouse emissions [11].

These studies apply techniques originally developed for non-imaging absorption spectroscopy to each pixel of the acquired datacube. It is possible, however, to take advantage of the large amount of data provided by imaging instruments to improve the sensitivity and signal to noise ratio. The objective of this paper is to study the absorption spectroscopy of pollutant gases in the atmosphere in the context of hyperspectral imaging, taking advantage of those possibilities. In particular, the well-known statistical technique of principal component analysis (PCA) is applied to gas spectra in the datacube, first to filter out noise and then to fasten retrieval of T and Q values. A simple radiative model applicable to field measurements is defined, although in this work it has been used only for laboratory measurements with a gas cell in order to evaluate its accuracy for the determination of gas concentrations.

Three gases have been studied: methane (CH4), nitrous oxide (N2O) and propane (C3H8). The first two are greenhouse gases and the third is a hydrocarbon that frequently appears jointly with methane and whose spectral features are in the same spectral region. For each of them, a mixture of known concentration has been prepared, and measured with a hyperspectral imager that operates in the mid-infrared band. Values of T and Q have been retrieved by fitting experimental spectra with simulated ones, and have been compared with the nominal values to assess the accuracy of the method. It has been demonstrated that processing with PCA increases signal to noise ratio which, in turn, improves the accuracy of retrieval, without losing spatial resolution or increasing acquisition time.

The basics of our approach are described in Section 2. After briefly explaining the radiative model in Section 2.1, the retrieval procedure is outlined in Section 2.2 and detailed in Section 2.3. The experimental setup and the measurements performed are described in Section 3. Principal component analysis is exposed and applied to noise filtering of spectra in Section 4; then it is applied, in Section 5, to reduce the dimensionality of spectra, thus making possible a faster retrieval of column density *Q* and temperature *T*. Retrieval is further simplified in Section 5.3 by defining polynomial functions that provide *Q* and *T* directly as functions of the principal components of the spectra. Finally, conclusions are summarized in Section 6.
