Abstract
In this paper, we report the first analytical model for quartz-enhanced photoacoustic spectroscopy in combination with an acoustic resonator. A generalized fundamental equation is proposed to model the photoacoustic effect, taking into account the coupling between the tuning fork and the surrounding fluid. The analytical signal-to-noise ratio is derived, yielding a direct physical insight with respect to the system design. Experimental behaviors are very well reproduced, and numerical finite elements methods are implemented to successfully confirm the relevance of our approach. We also provide a detailed explanation of the coupling dynamics between the quartz tuning fork and the acoustically resonant tube.
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References
C.K.N. Patel, Laser photoacoustic spectroscopy helps fight terrorism: high sensitivity detection of chemical Warfare Agent and explosives. Eur. Phys. J. Special Topics 153(1), 1–18 (2008)
S.M. Cristescu, S.T. Persijn, S. TE Lintel Hekkert, F.J.M. Harren, Laser-based systems for trace gas detection in life sciences. Appl. Phys. B 92(3), 343–349 (2008)
A. Miklós, P. Hess, Z. Bozóki, Application of acoustic resonators in photoacoustic trace gas analysis and metrology. Rev. Sci. Instrum. 72(4), 1937 (2001)
A.A. Kosterev, F.K. Tittel, Chemical sensors based on quantum cascade lasers. IEEE J. Quantum Electron. 38(6), 582–591 (2002)
L. Dong, A.A. Kosterev, D.M. Thomazy, F.K. Tittel, QEPAS spectrophones: design, optimization, and performance. Appl. Phys. B 100(3), 627–635 (2010)
H. Yi, K. Liu, S. Sun, W. Zhang, Xiaoming Gao, Theoretical analysis of off beam quartz-enhanced photoacoustic spectroscopy sensor. Optics Commun. 285(24), 5306–5312 (2012)
H. Yi, W. Chen, A. Vicet, Z. Cao, T-shape microresonator-based quartz enchanced photoacoustic spectroscopy for ambient methane monitoring using 3.38 \(\mu\)m antimonide-distributed feedback laser diode. Appl. Phys. B 116, 423–428 (2014)
P. Patimisco, G. Scamarcio, F.K. Tittel, V. Spagnolo, Quartz-enhanced photoacoustic spectroscopy: a review. Sensors 14, 6165–6206 (2014)
A.A. Kosterev, J.H. Doty, Resonant optothermoacoustic detection: technique for measuring weak optical absorption by gases and micro-objects. Optics Lett. 35(21), 3571–3573 (2010)
N. Petra, J. Zweck, S.E. Minkoff, A.A. Kosterev, J.H. Doty III, Modeling and design optimization of a resonant optothermoacoustic trace gas sensor. SIAM J. Appl. Math. 71(1), 309–332 (2011)
N. Petra, J. Zweck, A.A. Kosterev, S.E. Minkoff, D. Thomazy, Theoretical analysis of a quartz-enhanced photoacoustic spectroscopy sensor. Appl. Phys. B 94(4), 673–680 (2009)
D.V. Serebryakov, I.V. Morozov, A.A. Kosterev, V.S. Letokhov, Laser microphotoacoustic sensor of ammonia traces in the atmosphere. Quantum Electron. 40(2), 167–172 (2010)
H. Yi, W. Chen, S. Sun, K. Liu, T. Tan, T-shape microresonator-based high sensitivity quartz-enhanced photoacoustic spectroscopy sensor. Optics Express 20(8), 9187–9196 (2012)
S.L. Firebaugh, F. Roignant, E.A. Terray. Modeling the response of photoacoustic gas sensors. In COMSOL, number 1 (2009)
S.L. Firebaugh, E.A. Terray, L. Dong. Optimization of resonator radial dimensions for quartz enhanced photoacoustic spectroscopy systems. Proc. SPIE 8600, 86001S-1–86001S-12 (2013)
Yingchun Cao, Wei Jin, Hoi Lut Ho, Optimization of spectrophone performance for quartz-enhanced photoacoustic spectroscopy. Sensors Actuators B 174, 24–30 (2012)
U. Willer, M. Köhring, M. Mordmüller, W. Schade, Photoacoustic sensing with micro-tuning forks. Proceedings of SPIE 9482B, 1–11 (2015)
G. Aoust, R. Levy, B. Bourgeteau, O. Le Traon, Viscous damping on flexural mechanical resonators. Sensors Actuators A Phys. 230, 126–135 (2015)
L. Meirovitch. Elements of Vibration Analysis (McGraw-Hill, Singapore, 1986). ISBN 0-07-041342-8
G. Aoust, R. Levy, B. Bourgeteau, O. Le Traon, Acoustic damping on flexural mechanical resonators. Sensors Actuators A Phys. 238, 158–166 (2016)
M.P. Morse, H. Feshbach, Methods of Theoretical Physics (Mc Graw-Hill Book Compagny Inc, New York, 1953)
R.M. Sillitto, Angular distribution of the acoustic radiation from a tuning fork. Am. J. Phys. 34(8), 639–644 (1966)
A.A. Kosterev, F.K. Tittel, D.V. Serebryakov, A.L. Malinovsky, I.V. Morozov, Applications of quartz tuning forks in spectroscopic gas sensing. Rev. Sci. Instrum. 76(4), 043105 (2005)
G. Wysocki, A.A. Kosterev, F.K. Tittel, Influence of molecular relaxation dynamics on quartz-enhanced photoacoustic detection of CO2 at \(\lambda\) = 2 microns. Appl. Phys. B 85, 301–306 (2006)
L.S. Rothman, I.E. Gordon, A. Barbe, D.C. Benner, P.F. Bernath, M. Birk, V. Boudon, L.R. Brown, A. Campargue, J. Champion, K. Chance, L.H. Coudert, V. Dana, V.M. Devi, S. Fally, J. Flaud, R.R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W.J. Lafferty, J. Mandin, S.T. Massie, S.N. Mikhailenko, C.E. Miller, N. Moazzen-ahmadi, O.V. Naumenko, A.V. Nikitin, J. Orphal, V.I. Perevalov, A. Perrin, A. Predoi-cross, C.P. Rinsland, M. Rotger, S.A. Tashkun, J. Tennyson, R.A. Toth, A.C. Vandaele, J. Vander Auwera, The HITRAN, molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transfer 110(533–572), 2009 (2008)
S. Paquay. Développement d ’ une méthodologie de simulation numérique pour les problèmes vibro-acoustiques couplés intérieurs / extérieurs de grande taille. 2001
s. a. Open Engineering. OOFELIE::Multiphysics (2013)
M.J. Moloney, D.L. Hatten, Acoustic quality factor and energy losses in cylindrical pipes. Am. J. Phys. 69(3), 311 (2001)
L.D. Landau, E.M. Lifshitz. Fluid Mechanics (Pergamon Press, Oxford, 1959)
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Aoust, G., Levy, R., Raybaut, M. et al. Theoretical analysis of a resonant quartz-enhanced photoacoustic spectroscopy sensor. Appl. Phys. B 123, 63 (2017). https://doi.org/10.1007/s00340-017-6640-z
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DOI: https://doi.org/10.1007/s00340-017-6640-z