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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 8 — Apr. 9, 2012
  • pp: 9187–9196
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T-shape microresonator-based high sensitivity quartz-enhanced photoacoustic spectroscopy sensor

Hongming Yi, Weidong Chen, Shanwen Sun, Kun Liu, Tu Tan, and Xiaoming Gao  »View Author Affiliations


Optics Express, Vol. 20, Issue 8, pp. 9187-9196 (2012)
http://dx.doi.org/10.1364/OE.20.009187


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Abstract

A novel spectrophone sensor prototype consisting of a T-shaped acoustic microresonator (T-mR) in off-beam quartz-enhanced photoacoustic spectroscopy (T-mR QEPAS) is introduced for the first time. Its performance was evaluated and optimized through an acoustic model and experimental investigation via detection of water vapor in the atmosphere. The present work shows that the use of T-mR in QEPAS based sensor can improve the detection sensitivity by a factor of up to ~30, compared with that using only a bare QTF. This value is as high as that obtained in a conventional “on-beam” QEPAS, while keeping the advantages of “off-beam” QEPAS configuration: it is no longer necessary to couple excitation light beam through the narrow gap between the QTF prongs. In addition, the T-mR is really suitable for mass production with high precision.

© 2012 OSA

1. Introduction

In this paper, we introduce a novel T-shaped mR (T-mR) for use, for the first time, in “off-beam” QEPAS sensor (Fig. 1
Fig. 1 T-shaped mR based QEPAS spectrophone configuration. (a1) 3D map of an ideal T-shaped mR based QEPAS approach; (a2) 3D map of a T-mR made with a cubic aluminum block in the present work; (a3) cross section profile along axis of the main pipe of an ideal T-shaped mR; (a4) orifice formed by a QTF placed as close as possible to the branch pipe end of an ideal T-shaped mR; (a5) setup consisting of an ideal T-shaped mR and a QTF observed from the cross section along axis of the branch pipe.
(a1)). As shown in the present work, the use of T-mR in QEPAS sensor can improve the detection sensitivity by a factor of up to ~30, compared with that using only a bare QTF. This signal-to-noise ratio (SNR) gain is as high as that obtained in a conventional “on-beam” QEPAS, while keeping the advantages of “off-beam” QEPAS configuration: it is easier for optical alignment and mechanical assembling. Performance of the T-mR based QEPAS sensor is evaluated and optimized through an acoustic model and experimental investigation via detection of water vapor in the atmosphere.

2. Theoretical background

In fact, T-shaped photoacoustic (PA) cell has been successfully used in conventional microphone-based photoacoustic spectroscopy (PAS) [9

9. B. Baumann, B. Kost, H. Groninga, and M. Wolff, “Eigenmode analysis of photoacoustic sensors via finite element method,” Rev. Sci. Instrum. 77(4), 044901 (2006). [CrossRef]

, 10

10. A. Elia, V. Spagnolo, C. D. Franco, P. M. Lugarà, and G. Scamarcio, “Trace gas sensing using quantum cascade lasers and a fiber-coupled optoacoustic sensor: application to formaldehyde,” 15th International Conference on Photoacoustic and Photothermal Phenomena (ICPPP15),” J. Phys.: Conference Series 214, 012037 (2010). [CrossRef]

]. Similar to the T-shaped PA cell, a T-mR for use in QEPAS (Fig. 1(a3)) consists of a long main pipe of length l (diameter D) and a short branch pipe of length l1 (diameter D1). The branch pipe is perpendicularly intersected the main pipe in the middle of the main pipe. The QTF is placed at the end of the branch pipe to “off-beam” probe the PA signal excited inside the main pipe (Fig. 1(a4) and 1(a5)). The gap g between the QTF and the branch pipe end (Fig. 1(a5)) is set as small as possible (commonly, the gap is g ~10 μm, measured with a High-Definition USB scientific digital microscope). Because the dimension of the T-shaped mR is in the range of submillimeter to millimeter, it is difficult to acquire a tube with such dimension in real condition. Instead of using a stainless steel or glass tube, the T-mR is made of a cubic aluminum block with dimension of 2 × 3 × 9 mm in the present work (Fig. 1(a2)). A drilling with a diameter D1 and a real length l1 was made to form the short branch pipe, and another drilling of diameter D and a real length l formed the main pipe. The averaged wall thickness of the main pipe and branch pipe are noted as T and T1, respectively. In order to reduce the viscous drag [11

11. S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing sensitivity in tuning fork photoacoustic spectroscopy systems,” in Sensor Application Symposium (SAS), 23–25 Feb. (IEEE Press, New York 2010), 30–35.

] between the branch pipe and the QTF, the side surface of the branch pipe end was shaped as shown in a 3D map in Fig. 1(a2). Optimum parameters of the T-mR can be determined via an acoustic model, originated from references [12

12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

].

2.1. Acoustic impedance - Determination of the main pipe’s effective length

Based on the theoretical analysis of acoustic resonator given in [14

14. A. Miklós, P. Hess, and Z. Bozóki, “Application of acoustic resonators in photoacoustic trace gas analysis and metrology,” Rev. Sci. Instrum. 72(4), 1937–1955 (2001). [CrossRef]

], a mR tube used in QEPAS can be treated as one-dimensional acoustic resonator, and only longitudinal acoustic resonance occurs inside the mR. Optimum parameters of a T-mR should match the T-mR resonant frequency to the QTF resonant frequency. These parameters can be determined through the resonant condition of the T-mR. Acoustic impedance Z inside the resonator at acoustic boundary condition [12

12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

] is usually used to describe the characteristics of a T-mR, including its resonant condition which allows determining the effective length of the main pipe. It is usually expressed as Z = p/(uS) [12

12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

] (where p, u are the acoustic pressure and fluid velocity inside the pipe, respectively, S is the cross section area of the pipe).

In acoustic resonator modeling, it is convenient to use effective length L0 rather than its real physical length l0. In the following analysis, the main pipe is divided into two parts: branches 2 and 3, respectively; branch pipe denoted as branch 1. For an acoustic resonator pipe with a length of L 0 and an inner radius of r0, the input acoustic impedances Z at x = 0 (one end of the resonator) and x = L0 (the other end of the resonator), noted as Z(0) and Z(L0) respectively, are expressed by Eq. (1) [11

11. S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing sensitivity in tuning fork photoacoustic spectroscopy systems,” in Sensor Application Symposium (SAS), 23–25 Feb. (IEEE Press, New York 2010), 30–35.

, 12

12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

]:
Z(L0)=(Z(0)jρυS0tan(kL0))/(1+S0jρυZ(0)tan(kL0))
(1)
where x is the position coordinate, as shown in Fig. 2
Fig. 2 Theoretical model for calculation of the optimum T-mR parameters. (b1) T-shaped mR and coordinate system; (b2) orifice area Ω1 of the branch pipe end close to the QTF (seen from the axis of the branch pipe and the gap between QTF prongs); (b3) gap (between the QTF and the branch pipe end) district surface area Ω0; (b4) equivalent of a circular orifice (Fig. 2(b4)) to the real non-circular orifice (b2) with an effective area Ω = Ω1.
(b1): x1 and x2 stand for position coordinate of the branch pipe and the main pipe, respectively; ρ is the density of the fluid inside the pipe; S0 the cross section area of the pipe. The axis origin is noted as 0. k = ω/υ = 2πf/υ is the wave number, f is the acoustic frequency (that should be equal to the QTF resonant frequency f0 = 32.740 kHz, in our case), υ the acoustic wave velocity and j2 = −1.

The acoustic impedance at A (x2 = -L2), E (x2 = 0) for branch 2, at F (x2 = 0), B (x2 = L3) for branch 3, at 0 (x1 = 0), C (x1 = -L1) for branch 1 are noted as Z2A(-L2), Z2E(0), Z3F(0), Z3B(L3), Z10(0), Z1C(-L1) (shown in Fig. 2(b1)), respectively. Zo, Zs are the input acoustic impedances of the orifice and the gap between the QTF and the end of the branch pipe (Fig. 2(b1)), respectively. L1 is the effective length of the branch 1 (its corresponding physical length is l1).

At the junction of the three branches as shown in Fig. 2(b1), Z2E(0), Z3F(0) and Z10(0) satisfy the following relation deduced by continuity equations [12

12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

, 13

13. D. Li and J. S. Vipperman, “On the design of long T-shaped acoustic resonators,” J. Acoust. Soc. Am. 116(5), 2785–2792 (2004). [CrossRef]

, 15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

]:

1Z10(0)=1Z2E(0)+1Z3F(0)
(2)

For the T-shaped mR used in the present work, S2 = S3 = S = πR2, with R = D/2, the radius of the main pipe branches 2 and 3; S1 = πR12, with R1 = D1/2, the radius of the short branch 1.

According to Eq. (1), Z10(0), Z2A(-L2) and Z3B(-L3) can be given by:

Z10(0)=(Z1C(-L1)jρυS0tan(kL1))/(1+S0jρυZ1C(-L1)tan(kL1))
(3)
Z2A(-L2)=(Z2E(0)jρυS2tan(kL2))/(1+S2jρυZ2E(0)tan(kL2))
(4)
Z3B(L3)=(Z3F(0)jρυS3tan(kL3))/(1+S3jρυZ3F(0)tan(kL3))
(5)

When acoustic resonance occurs in the T-mR, the acoustic boundary condition at A (x2 = -L2) and B (x2 = L3) satisfies the following relationship [11

11. S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing sensitivity in tuning fork photoacoustic spectroscopy systems,” in Sensor Application Symposium (SAS), 23–25 Feb. (IEEE Press, New York 2010), 30–35.

, 12

12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

]:
Z2A(L2)=Z3B(L3)=0
(6)
where L2 = L3, L2 and L3 are the effective length of the main pipe branches 2 and 3, respectively (their corresponding physical length are l2 and l3, respectively).

Based on Eqs. (4)(6), Z2E (x2 = 0) and Z3F (x2 = 0) can be given as follows:

Z2E(0)=jρυtan(kL2)/S2
(7)
Z3F(0)=jρυtan(kL3)/S3
(8)

We will now consider the acoustic impedance of the gap between the QTF and the end of the branch pipe. For the branch pipe (branch 1), one end is connected to the middle of the main pipe (inserted with branches 2 and 3), and the other end close to the QTF is partially masked which can be considered as a terminal orifice (Fig. 1(a4) and Fig. 2(b2)). The acoustic impedance of the partially masked end at x1 = -L1 was denoted as Z1C(-L1) = jρω/α [13

13. D. Li and J. S. Vipperman, “On the design of long T-shaped acoustic resonators,” J. Acoust. Soc. Am. 116(5), 2785–2792 (2004). [CrossRef]

], and it is determined by the acoustic impedance of the orifice Zo = jρω/αο (see Fig. 2(b1)) and the acoustic impedance of the gap between the QTF and the end of the branch pipe Zs = jρω/αs (see Fig. 2(b1)) [8

8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

]. In fact, this gap part can be considered as a narrow side slit of branch pipe with a surface area of Ω0 = πD1g and a thickness of T1 [8

8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

]. Analogous to the boundary condition at the junction 0, Z1C(0), Zo and Zs satisfy the following equation at the junction of x1 = -L1:
1Z1C(0)=αjρυk=1Zo+1Zs=αojρυk+αsjρυk=αo+αsjρυk
(9)
where α is the total acoustic conductivity of the partially masked end that is the sum of the acoustic conductivity of the orifice αο (Fig. 2(b2) and 2(b4), dash area) and the acoustic conductivity of the gap αs [8

8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

] (Fig. 2(b3), dash area):

α=αo+αs
(10)

Using the theory outlined in [8

8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

, 15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

], αο and αs can be calculated using the following equations:
αo=d(1+d/D1)1.19
(11)
αs=Ω0/T1=πD1g/T1
(12)
α=αo+αs=d(1+d/D1)1.19+πD1g/T1
(13)
with d=2(Ω/π)1/2
(14)
and Ω=Ω1=2R12arcsin(w/(2R1))+w(R12w2/4)1/2
(15)
where w is the gap between two QTF prongs, w = 0.30 mm, and d is the equivalent diameter of the orifice. In reality, the orifice is not circular; the diameter d may be derived from a circular orifice with a cross section Ω (Fig. 2(b4), dash area) equivalent to the real orifice area Ω1 (Fig. 2(b2), dash area).

Substituting the acoustic impedances Z2E(0), Z3F(0) and Z10(0) (Eqs. (3), (7)(9)) into Eq. (2) with L2 = L3 = L/2, we can deduce the following equation for the main pipe effective length L:

tan(kL2)/2S=(kαtan(kL1)S1)/(1+kαS1tan(kL1))
(16)

2.2. End correction - determination of the resonator physical length

Due to the fact of the mismatch between the one dimensional acoustic wave inside the mR and the three dimensional field (of spherical wave front) radiated from the opening end of the mR tube to free space [14

14. A. Miklós, P. Hess, and Z. Bozóki, “Application of acoustic resonators in photoacoustic trace gas analysis and metrology,” Rev. Sci. Instrum. 72(4), 1937–1955 (2001). [CrossRef]

], end (ends at A, B and C, shown in Fig. 2(b1)) corrections for the main and branch pipes should be performed. On the other hand, interior end corrections at the junction of the branch pipe (at 0 as shown in Fig. 2(b1)) should be taken into account too. The end corrections result in a longer effective length than its real physical length. The theories of end corrections given in [13

13. D. Li and J. S. Vipperman, “On the design of long T-shaped acoustic resonators,” J. Acoust. Soc. Am. 116(5), 2785–2792 (2004). [CrossRef]

16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

] were adopted to calculate effective lengths.

(1) Wirz suggested [15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

] an approximate formula for end-correction Δl of circular tubes based on the flange width T (T is the wall thickness of the mR tube here):
Δl=(0.60+0.22exp(kT/r))×r
(17)
where k is the acoustic wave number, r is the radius of the tube. In real application, if T is rather thin, the tube end can be treated as unflanged, the end correction is Δl≈0.6r [15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

, 16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

]. When T becomes thicker (T≥3r), the tube end forms a flange, the end correction for such a flanged end can be expressed as Δl≈0.85r [15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

, 16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

].

In our designed T-mR, the main pipe was formed by drilling a hole on a flat surface with a cross section area of 2 × 3 mm2 (see Fig. 1(a2)), two ends of the main pipe can be treated as flanged [16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

]. As a result, for the ends at A and B of the main pipe, the end corrections Δl2A and Δl3B can be approximately calculated by:

Δl2A=Δl3B0.85R
(18)

(2) For the outer end of the branch pipe, which is partially masked (treated as an orifice), the end correction Δl1C can be determined by the following equation [15

15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

]:

tan(kΔl1C)=kS1/α
(19)

(3) Because D1 and D have the same order of magnitude, the interior end of the branch pipe at junction 0 (shown in Fig. 2(b1)) can be seen as unflanged [16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

], the end corrections, denoted as Δl10, may be determined by Hybrid Rayleigh’s end corrections outlined in [13

13. D. Li and J. S. Vipperman, “On the design of long T-shaped acoustic resonators,” J. Acoust. Soc. Am. 116(5), 2785–2792 (2004). [CrossRef]

16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

]:

 Δl100.60R1
(20)

As a result, the effective length of the main and branch pipe are then calculated as follows:
L1=l1+Δl10+Δl1C
(21)
for the branch pipe, and
L=l+Δl2A+Δl3B
(22)
for the main pipe with both ends treated as flanged.

The real physical length of the main pipe can thus be deduced by:

lLΔl2AΔl3B=L1.70R
(23)

2.3. General consideration of T-mR design

For a T-mR used in QEPAS, D1 is usually limited by the value of w = 0.30 mm and l1 is taken as short as possible to avoid coupling losses of sound wave. D would be a choice depending on the light beam diameter that we can obtain, with such a pre-determination of these 3 parameters, we can determine the parameters l of the main pipe using Eqs. (11)(22). The wall thickness can be approximately estimated as:

T(6/πR2)1/2R
(24)
T1(1.5/π)1/2R1
(25)

In the present work, we evaluated the performances of the T-mR based QEPAS sensor with different geometrical dimension: D1 = 0.34-0.50 mm, T1≈0.44-0.52 mm and l1 = 0.10-0.85 mm for the branch pipe, D between 0.46 and 1.50 mm for the main pipe with a cross section of 2 × 3 mm2 (not circular, see Fig. 1(a2)) and an approximate wall thickness T ≈0.63-1.15 mm. The corresponding real lengths of the main pipe were calculated based on the acoustic model described above and compared with the optimum experimental values.

3. Experiment and results

Performances of the T-mR based QEPAS spectrophone were evaluated using water vapor detection in ambient air at normal atmospheric pressure and temperature between 24.2 and 27.2 °C. The used H2O line intensity is 1.174 × 10−20 cm−1/ (mol.cm−2) at 7161.41 cm−1. Output power of the used fiber-coupled DFB laser (NLK1E5GAAA, NEL) was ~8 mW. The ambient H2O vapor relative humidity (RH) was determined with a hygrometer (humidity sensor, SHT75) with an uncertainty of 2% and the temperature of the ambient air was measured by a temperature sensor (PT100) with a precision of 0.1°C. The absolute concentration of water vapor was deduced from the measured RH value and the temperature. The uncertainty of the deduced absolute concentration of H2O in volume mixing ratio is about 3%. As the concentration of the ambient H2O varied over time, all measured QEPAS signals were normalized to the H2O vapor concentration for instrument performance comparison.

The experimental arrangement of the T-mR QEPAS, similar to that used in [6

6. K. Liu, X. Guo, H. Yi, W. Chen, W. Zhang, and X. Gao, “Off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 34(10), 1594–1596 (2009). [CrossRef] [PubMed]

, 7

7. K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: optimization and performance evaluation,” Rev. Sci. Instrum. 81(10), 103103 (2010). [CrossRef] [PubMed]

], is schematically presented in Fig. 3
Fig. 3 Experimental set up of a T-mR based QEPAS. RS232: communication port for remote control and data exchange; PC: personal computer; GPIB: General Purpose Interface Bus; DAQ card: data acquisition card.
.

SNR Gain is used to describe the sensitivity enhancement factor of QEPAS spectrophone. The definition of SNR Gain is given as follow [5

5. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

, 7

7. K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: optimization and performance evaluation,” Rev. Sci. Instrum. 81(10), 103103 (2010). [CrossRef] [PubMed]

, 8

8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

]:
SNRGain=(Sa/Sb)×(Qb/Qa)1/2=(QSEfactor)×(Qb/Qa)1/2
(26)
where Sa and Qa are the QEPAS signal normalized to the H2O vapor concentration and the corresponding QTF Q factor, respectively for T-mR enhanced QEPAS. Sb and Qb are the H2O vapor concentration normalized QEPAS signal and the corresponding QTF Q factor for bare QTF-QEPAS. QSE factor, standing for QEPAS signal enhancement factor, is defined as Sa/Sb. Acoustic velocity υ (m/s) in ambient air at normal atmospheric pressure was calculated using the following expression [8

8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

, 16

16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

]:
υ(t)=331.6+0.6t
(27)
where t is the centigrade temperature (°C).

As can be seen in Table 1, the theoretically calculated T-mR parameters closely match the experimental results. With the optimum parameters, the highest SNR gain of ~30 was obtained by using T-mR1 and T-mR5. Due to the acoustic coupling between the high-Q QTF and the low-Q mR resonator [5

5. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

], the QTF Q factor in the T-mR QEPAS setup changes from Qb~9000 to Qa~5000 (see Table 1). It is worth noting that the change of QTF’s Q factor in the T-mR QEPAS versus the bare QTF QEPAS is smaller than that in the “on beam” QEPAS, in which Q changes from more than 10000 (bare QTF QEPAS) to even below 2500 (mR enhanced “on beam” QEPAS) [5

5. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

]. This results show that T-mR possesses smaller energy accumulation wastage inside the tube compared with the mR tube used in “on beam” configuration. For sensitivity evaluation, a photoacoustic 2f signal of a 1.816% of H2O vapor in air at 1 atm and 25.6°C was acquired using T-mR1 based QEPAS spectrophone (see Fig. 4
Fig. 4 Second harmonic QEPAS signal of H2O vapor absorption at 7161.41cm−1 using T-mR1 based QEPAS sensor.
).

Based on the experimentally measured noise in the QEPAS baseline, a noise level (1σ) of ~1µV was deduced at the output of the transimpedance amplifier which included the noise resulting from the transimpedance amplifier and the fundamental thermal noise of the used QTF [2

2. F. K. Tittel, G. Wysocki, A. A. Kosterev, and Y. Bakhirkin, “Semiconductor laser based trace gas sensor technology: recent advances and applications,” in Mid-Infrared Coherent Sources and Applications, Ebrahim-Zadeh, M., Sorokina, I.T., Eds. (Springer, 2007), 467–493.

, 5

5. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

7

7. K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: optimization and performance evaluation,” Rev. Sci. Instrum. 81(10), 103103 (2010). [CrossRef] [PubMed]

]. This thermal noise<VN2>≈0.80 μV (rms, root mean square) can be determined using the following equation:
<VN2>=ΔfRg(4kBT)/R
(28)
where R = 246 kΩ is the QTF equivalent dynamic resistance, Δf = 0.094 Hz is the detection bandwidth and kB is the Boltzmann constant. The corresponding minimum detectable concentration (MDC) of 165 ppbv (parts per billion by volume) for H2O was achieved which led to a normalized noise equivalent absorption coefficient (NNEAC) of 3.9 × 10−9 cm−1W/Hz1/2.

4. Conclusions

In comparison with the currently used QEPAS spectrophone configurations, T-shaped mR based QEPAS combines the advantages from “on beam” and “off beam” QEPAS schemes while offsetting their shortages: high sensitivity (equivalent to that in the “on beam” QEPAS) and easy for optical alignment and suited for sensor applications using low cost exciting light sources (like the “off beam” QEPAS approach). In addition, the T-shaped mR design permits for precise manufacture. All these characteristics would make “T-mR QEPAS” an optimal choice for QEPAS sensor applications.

Acknowledgments

This research was supported by National Natural Science Foundation of China (Foundation No. 41175036). The support of the Groupement de Recherche International SAMIA between CNRS (France), RFBR (Russia) and CAS (China) is acknowledged.

References and links

1.

A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 27(21), 1902–1904 (2002). [CrossRef] [PubMed]

2.

F. K. Tittel, G. Wysocki, A. A. Kosterev, and Y. Bakhirkin, “Semiconductor laser based trace gas sensor technology: recent advances and applications,” in Mid-Infrared Coherent Sources and Applications, Ebrahim-Zadeh, M., Sorokina, I.T., Eds. (Springer, 2007), 467–493.

3.

H. Yi, K. Liu, W. Chen, T. Tan, L. Wang, and X. Gao, “Application of a broadband blue laser diode to trace NO2 detection using off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 36(4), 481–483 (2011). [CrossRef] [PubMed]

4.

S. Böttger, M. Angelmahr, and W. Schade, “Photoacoustic Gas Detection with LED QEPAS,” in CLEO/Europe and EQEC 2011 Conference Digest, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CH_P14.

5.

L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

6.

K. Liu, X. Guo, H. Yi, W. Chen, W. Zhang, and X. Gao, “Off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 34(10), 1594–1596 (2009). [CrossRef] [PubMed]

7.

K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: optimization and performance evaluation,” Rev. Sci. Instrum. 81(10), 103103 (2010). [CrossRef] [PubMed]

8.

H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI . [CrossRef] [PubMed]

9.

B. Baumann, B. Kost, H. Groninga, and M. Wolff, “Eigenmode analysis of photoacoustic sensors via finite element method,” Rev. Sci. Instrum. 77(4), 044901 (2006). [CrossRef]

10.

A. Elia, V. Spagnolo, C. D. Franco, P. M. Lugarà, and G. Scamarcio, “Trace gas sensing using quantum cascade lasers and a fiber-coupled optoacoustic sensor: application to formaldehyde,” 15th International Conference on Photoacoustic and Photothermal Phenomena (ICPPP15),” J. Phys.: Conference Series 214, 012037 (2010). [CrossRef]

11.

S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing sensitivity in tuning fork photoacoustic spectroscopy systems,” in Sensor Application Symposium (SAS), 23–25 Feb. (IEEE Press, New York 2010), 30–35.

12.

P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]

13.

D. Li and J. S. Vipperman, “On the design of long T-shaped acoustic resonators,” J. Acoust. Soc. Am. 116(5), 2785–2792 (2004). [CrossRef]

14.

A. Miklós, P. Hess, and Z. Bozóki, “Application of acoustic resonators in photoacoustic trace gas analysis and metrology,” Rev. Sci. Instrum. 72(4), 1937–1955 (2001). [CrossRef]

15.

E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.

16.

L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

OCIS Codes
(230.0230) Optical devices : Optical devices
(280.3420) Remote sensing and sensors : Laser sensors
(300.6260) Spectroscopy : Spectroscopy, diode lasers
(300.6430) Spectroscopy : Spectroscopy, photothermal

ToC Category:
Spectroscopy

History
Original Manuscript: February 9, 2012
Revised Manuscript: March 28, 2012
Manuscript Accepted: March 28, 2012
Published: April 5, 2012

Virtual Issues
Vol. 7, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Hongming Yi, Weidong Chen, Shanwen Sun, Kun Liu, Tu Tan, and Xiaoming Gao, "T-shape microresonator-based high sensitivity quartz-enhanced photoacoustic spectroscopy sensor," Opt. Express 20, 9187-9196 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-9187


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References

  1. A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 27(21), 1902–1904 (2002). [CrossRef] [PubMed]
  2. F. K. Tittel, G. Wysocki, A. A. Kosterev, and Y. Bakhirkin, “Semiconductor laser based trace gas sensor technology: recent advances and applications,” in Mid-Infrared Coherent Sources and Applications, Ebrahim-Zadeh, M., Sorokina, I.T., Eds. (Springer, 2007), 467–493.
  3. H. Yi, K. Liu, W. Chen, T. Tan, L. Wang, and X. Gao, “Application of a broadband blue laser diode to trace NO2 detection using off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 36(4), 481–483 (2011). [CrossRef] [PubMed]
  4. S. Böttger, M. Angelmahr, and W. Schade, “Photoacoustic Gas Detection with LED QEPAS,” in CLEO/Europe and EQEC 2011 Conference Digest, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CH_P14.
  5. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]
  6. K. Liu, X. Guo, H. Yi, W. Chen, W. Zhang, and X. Gao, “Off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 34(10), 1594–1596 (2009). [CrossRef] [PubMed]
  7. K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: optimization and performance evaluation,” Rev. Sci. Instrum. 81(10), 103103 (2010). [CrossRef] [PubMed]
  8. H. Yi, W. Chen, X. Guo, S. Sun, K. Liu, T. Tan, W. Zhang, and X. Gao, “An acoustic model for microresonator in on beam quartz-enhanced photoacoustic spectroscopy,” Appl. Phys. B (2012). DOI 10.1007/s00340-012-4988-7. [CrossRef] [PubMed]
  9. B. Baumann, B. Kost, H. Groninga, and M. Wolff, “Eigenmode analysis of photoacoustic sensors via finite element method,” Rev. Sci. Instrum. 77(4), 044901 (2006). [CrossRef]
  10. A. Elia, V. Spagnolo, C. D. Franco, P. M. Lugarà, and G. Scamarcio, “Trace gas sensing using quantum cascade lasers and a fiber-coupled optoacoustic sensor: application to formaldehyde,” 15th International Conference on Photoacoustic and Photothermal Phenomena (ICPPP15),” J. Phys.: Conference Series 214, 012037 (2010). [CrossRef]
  11. S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing sensitivity in tuning fork photoacoustic spectroscopy systems,” in Sensor Application Symposium (SAS), 23–25 Feb. (IEEE Press, New York 2010), 30–35.
  12. P. Merkli, “Acoustic resonance frequencies for a T-tube,” Z. Angew. Math. Phys. 29(3), 486–498 (1978) (ZAMP). [CrossRef]
  13. D. Li and J. S. Vipperman, “On the design of long T-shaped acoustic resonators,” J. Acoust. Soc. Am. 116(5), 2785–2792 (2004). [CrossRef]
  14. A. Miklós, P. Hess, and Z. Bozóki, “Application of acoustic resonators in photoacoustic trace gas analysis and metrology,” Rev. Sci. Instrum. 72(4), 1937–1955 (2001). [CrossRef]
  15. E. G. Richardson, Technical Aspects of Sound: Sonic Range and Airborne Sound (Elsevier Pub. Co., 1957), pp. 12–13 and 487–496.
  16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley& Sons, Inc., 1962), pp. 116–118 and 186–213.

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