Modeling and Design Optimization of a Resonant Optothermoacoustic Trace Gas Sensor

Trace gas sensors that are compact and portable are being deployed for use in a variety of applications including disease diagnosis via breath analysis, monitoring of atmospheric pollutants and greenhouse gas emissions, control of industrial processes, and for early warning of terrorist threats. One such sensor is based on optothermal detection and uses a modulated laser source and a quartz tuning fork resonator to detect trace gases. In this paper we introduce the first mathematical model of such a resonant optothermoacoustic sensor. The model is solved via the finite element method and couples heat transfer and thermoelastic deformation to determine the strength of the generated signal. Numerical simulations validate the experimental observation that the source location that produces the maximum signal is near the junction of the tines of the tuning fork. Determining an optimally designed sensor requires maximizing the signal as a function of the geometry of the quartz tuning fork (length and width of the tines, etc). To avoid difficulties from numerical differentiation we chose to solve the optimization problem using the derivative-free mesh adaptive direct search algorithm. An optimal tuning fork constrained to resonate at a frequency close to the 32.8 kHz resonance frequency of many commercially available tuning forks produces a signal that is three times larger than the one obtained with the current experimental design. Moreover, the optimal tuning fork found without imposing any constraint on the resonance frequency produces a signal that is 24 times greater than that obtained with the current sensor.

[1]  M. Fraser,et al.  Application of quantum cascade lasers to trace gas analysis , 2008 .

[2]  M. Stein.  Large sample properties of simulations using latin hypercube sampling , 1987 .

[3]  J. Dennis,et al.  Pattern search algorithms for mixed variable general constrained optimization problems , 2003 .

[4]  Virginia Torczon,et al.  On the Convergence of Pattern Search Algorithms , 1997, SIAM J. Optim..

[5]  Andreas Mandelis,et al.  Photoacoustic and thermal wave phenomena in semiconductors , 1987 .

[6]  Samara L. Firebaugh,et al.  Modeling the Response of Photoacoustic Gas Sensors , 2009 .

[7]  K. Kokubun,et al.  Size effect of a quartz oscillator on its characteristics as a friction vacuum gauge , 1985 .

[8]  Charles Audet,et al.  A Pattern Search Filter Method for Nonlinear Programming without Derivatives , 2001, SIAM J. Optim..

[9]  Robert D. Grober,et al.  Piezo-electric tuning fork tip—sample distance control for near field optical microscopes , 1995 .

[10]  D. Wasserman,et al.  High-Performance Quantum Cascade Lasers: Optimized Design Through Waveguide and Thermal Modeling , 2007, IEEE Journal of Selected Topics in Quantum Electronics.

[11]  Andreas Mandelis,et al.  Diffusion Waves and their Uses , 2000 .

[12]  John A. Pelesko,et al.  Nonlinear Stability Considerations in Thermoelastic Contact , 1999 .

[13]  Sungkyu Lee,et al.  Design optimization of surface mount device 32.768kHz quartz tuning fork-type crystals using finite element method and statistical analysis of test samples manufactured using photolithography , 2002 .

[14]  A A Kosterev,et al.  Numerical and experimental investigation for a resonant optothermoacoustic sensor , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[15]  Gustav Gautschi.  Amplifiers for Piezoelectric Sensors , 2002 .

[16]  Comandur Venkatesan,et al.  Electro-thermo-elastic formulation for the analysis of smart structures , 2006 .

[17]  Robert Michael Lewis,et al.  Pattern Search Algorithms for Bound Constrained Minimization , 1999, SIAM J. Optim..

[18]  A. Morse,et al.  Fundamental limits to force detection using quartz tuning forks , 2000 .

[19]  Alexander Graham Bell,et al.  Upon the production of sound by radiant energy , 1881, American Journal of Science.

[20]  Matthias K. Gobbert,et al.  Parallel Performance Studies for COMSOL Multiphysics Using Scripting and Batch Processing , 2009 .

[21]  John Zweck,et al.  Theoretical analysis of a quartz-enhanced photoacoustic spectroscopy sensor , 2009 .

[22]  A. Schawlow.  Lasers , 2018, Acta Ophthalmologica.

[23]  John A. Pelesko,et al.  Generic unfolding of the thermoelastic contact instability , 2002 .

[24]  T. Risby,et al.  Current status of clinical breath analysis , 2005 .

[25]  A. Mandelis.  Diffusion-wave fields : mathematical methods and Green functions , 2001 .

[26]  Bret D. Cannon,et al.  Gas-phase photoacoustic sensor at 8.41 μm using quartz tuning forks and amplitude-modulated quantum cascade lasers , 2006 .

[27]  A. Kosterev,et al.  Resonant optothermoacoustic detection: technique for measuring weak optical absorption by gases and micro-objects. , 2010, Optics letters.

[28]  John A. Pelesko.  Nonlinear Stability, Thermoelastic Contact, and the Barber Condition , 2001 .

[29]  Vladilen S. Letokhov,et al.  Tuning-fork-based fast highly sensitive surface-contact sensor for atomic force microscopy/near-field scanning optical microscopy , 2002 .

[30]  A. Authier,et al.  Physical properties of crystals , 2007 .

[31]  András Miklós,et al.  Experimental and theoretical investigation of photoacoustic-signal generation by wavelength-modulated diode lasers , 1994 .

[32]  F. Tittel,et al.  Recent advances of laser-spectroscopy-based techniques for applications in breath analysis , 2007, Journal of breath research.

[33]  D. B. Sullivan,et al.  Time and frequency measurement at NIST: the first 100 years , 2001, Proceedings of the 2001 IEEE International Frequncy Control Symposium and PDA Exhibition (Cat. No.01CH37218).

[34]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[35]  P. Griffiths,et al.  Photoacoustics and Photoacoustic Spectroscopy , 1981 .

[36]  Cleve Ashcraft,et al.  SPOOLES: An Object-Oriented Sparse Matrix Library , 1999, PPSC.

[37]  Gene H. Golub,et al.  Matrix computations , 1983 .

[38]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[39]  Samara L. Firebaugh,et al.  Enhancing sensitivity in tuning fork photoacoustic spectroscopy systems , 2010, 2010 IEEE Sensors Applications Symposium (SAS).

[40]  W. Marsden.  I and J , 2012 .

[41]  A. Kosterev,et al.  Applications of quartz tuning forks in spectroscopic gas sensing , 2005 .

[42]  Hideaki Itoh,et al.  Model for a Quartz-Crystal Tuning Fork Using Plate Spring Approximated to Torsion Spring Adopted at the Joint of the Arm and the Base , 2003 .

[43]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[44]  A. Bell.  On the production and reproduction of sound by light , 1880, American Journal of Science.

[45]  Claire F. Gmachl,et al.  Coupled Monitoring and Modeling of Air Quality and Regional Climate during the 2008 Beijing Olympic Games , 2009 .

[46]  Gang Li,et al.  The HITRAN 2008 molecular spectroscopic database , 2005 .

[47]  W. A. Marrison.  The evolution of the quartz crystal clock , 1948, Bell Syst. Tech. J..

[48]  Alexander Graham Bell,et al.  Upon the production and reproduction of sound by light , 1880 .

[49]  A. Kosterev,et al.  Quartz-enhanced photoacoustic spectroscopy. , 2002, Optics letters.

[50]  A. Miklós,et al.  Application of acoustic resonators in photoacoustic trace gas analysis and metrology , 2001 .

[51]  A. P. French,et al.  Vibrations and Waves , 1971 .

[52]  Frank K Tittel,et al.  First experimental studies of the resonant optothermoacoustic detection technique , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.