Theoretical analysis of off beam quartz-enhanced photoacoustic spectroscopy sensor

Off beam quartz-enhanced photoacoustic spectroscopy (OB-QEPAS) sensors are based on a recently developed approach to off-beam photoacoustic (PA) detection which employs a quartz tuning fork (QTF) as an acoustic transducer. A microresonator (mR) with a side slit in the middle is used to enhance PA signal. This paper describes a theoretical model of an OB-QEPAS-based sensor. By deriving the acoustic impedances of the mR at two ends and the side slit in the middle in the model, we obtain a formula for numerically calculating the optimal mRs' parameters of OB-QEPAS-based sensor. We use the model to calculate the optimal mRs' lengths with respect to the resonant frequency of the QTF, acoustic velocities inside mRs, inner diameters of mRs, and acoustic conductivities of the mRs' side slits, and found out that the calculated results closely match experimental data. We also investigated the relationship between the mR selected in “on beam” QEPAS, OB-QEPAS, and an acoustic resonator (AR) excited in its first longitudinal mode used in conventional photoacoustic spectroscopy (PAS).