Optical gas sensors based on correlation spectroscopy using a Fabry-Perot interferometer

Abstract

In this work we present an analysis of gas sensors based on correlation spectroscopy with a Fabry-Perot interferometer (FPI). In this technique the spectral FPI transmission fringe pattern is matched with ro-vibrational absorption lines. To produce the cross correlation principle the FPI fringe pattern must be shifted along the frequency axis. Hence as the spectral FPI fringes are equidistant and symmetric therefore the ro-vibrational absorption lines of the target molecule must be almost equidistant. Well resolved ro-vibrational lines with Lorentzian line shapes and with almost equidistant spectral separation are characteristics of most diatomic and linear molecules, i.e. CO₂, CO, N₂O, and some specific absorptions bands of symmetric top and spherical top molecules eg. NH3, CH4 at one atmosphere pressure.

In this work we review two general sensor designs, in the first the FPI it is illuminated with a collimated beam and in the second design the FPI it is illuminated by a converging beam. In the collimated beam design all the rays reaching the FPI have the same angle of incidence whilst in converging beam the incident rays have different angles of incidence. Hence the spectral FPI fringe pattern it is affected by the different angles of incidence and therefore it is essential to consider these effects during the evaluation of the sensor response.

A novel analytical method based on the Fourier transform which gives a good insight of the gas sensor design based on correlation spectroscopy with a FPI it is presented which we call the convolution method. The method provides a simple way to evaluate much faster the sensor response, and using the Fourier transform characteristics the functions involved in the mathematical model of the sensor response the optimal cavity length of the FPI can be directly determined and it is shown that if the sensor signal will be recovered by a Phase Sensitivity Detector the optimum mirror reflectivity is 0.41 regardless of the other parameters. Moreover using the convolution method the optimal FPI mirror reflectivity can be quickly evaluated. The method also gives us guidance on selecting the best bandpass filter for the application. In this work we also review the effects of the blackbody converging beam and some possible solutions to minimize the effect of the degraded FPI fringe pattern are proposed. In this case it is important to consider the spurious FPI fringe patterns produced by reflection within the mirrors substrates of FPI mirrors.

Finally based on all these knowledge we describe a full methodology to simulate the sensor response. It is important to mention that in our methodology we not use 'fitting parameters’ to adjust the simulated results with experimental measurements. Our experimental measurements strongly support the simulated sensor response obtained with our methodology. Therefore the methodology can be applied to design other gas sensors based on cross correlation spectroscopy with a FPI as a modulator. Moreover it is shown that these sensors present an almost negligible sensitivity to molecules other than the target. Finally based on our simulated and experimental results we can conclude that this sensor design configuration is viable to fabricate commercial gas sensors if the FPI and the detector are integrated within a MEMS structure.

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