Tuning forks with optimized geometries for quartz-enhanced ......Tuning forks with optimized geometries for quartz-enhanced photoacoustic spectroscopy PIETRO PATIMISCO, 1 ANGELO SAMPAOLO,1

Tuning forks with optimized geometries for quartz-enhanced photoacoustic spectroscopy

PIETRO PATIMISCO,1 ANGELO SAMPAOLO,1 MARILENA GIGLIO,1 STEFANO DELLO RUSSO,1 VERENA MACKOWIAK,2 HUBERT ROSSMADL,2 ALEX CABLE,3 FRANK K. TITTEL

4 AND VINCENZO SPAGNOLO1*

1PolySense Lab - Dipartimento Interateneo di Fisica, University and Politecnico of Bari, Via Amendola 173, Bari, Italy 2Thorlabs GmbH, Hans-Boeckler-Straße 6, 85221 Dachau, Germany 3Thorlabs, Inc., 56 Sparta Ave., Newton, NJ 07860, USA 4Department of Electrical and Computer Engineering, Rice University, 6100 Main Street, Houston, TX 77005, USA *[email protected]

Abstract: We report on the design, realization, and performance of novel quartz tuning forks (QTFs) optimized for quartz-enhanced photoacoustic spectroscopy (QEPAS). Starting from a QTF geometry designed to provide a fundamental flexural in-plane vibrational mode resonance frequency of ~16 kHz, with a quality factor of 15,000 at atmospheric pressure, two novel geometries have been realized: a QTF with T-shaped prongs and a QTF with prongs having rectangular grooves carved on both surface sides. The QTF with grooves showed the lowest electrical resistance, while the T-shaped prongs QTF provided the best photoacoustic response in terms of signal-to-noise ratio (SNR). When acoustically coupled with a pair of micro-resonator tubes, the T-shaped QTF provides a SNR enhancement of a factor of 60 with respect to the bare QTF, which represents a record value for mid-infrared QEPAS sensing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical techniques operating in the mid-infrared spectral regions are capable of excellent trace gas sensing performances, together with high sensitivity and selectivity [1,2] due to the presence of strong ro-vibrational absorption bands of many molecules. Photoacoustic spectroscopy (PAS) is a sensing technique that does not require the use of an optical detector and troublesome optical alignments, but nevertheless is capable of performing trace gas measurements at sub-parts-per-trillion concentration levels [3,4]. PAS is based on the detection of sound waves generated by gas absorption of modulated optical radiation. Quartz tuning forks (QTFs) have shown a great potential as sound transducers, leading to a well-established variant of PAS, named quartz-enhanced photoacoustic spectroscopy (QEPAS) [5]. The confinement of the acoustic energy between the prongs of the QTF, combined with high quality factors, enabled the detection of weak photoacoustic excitation within very small gas volumes. Since its introduction in 2002, standard low-cost QTFs with resonance frequencies at 32.7 kHz are typically employed in QEPAS sensors [6]. The QTF is typically coupled with a pair of tubes, acting as an organ pipe resonator to probe the sound wave [7,8]. The acoustic detection module composed of the QTF and micro-resonator tubes constitutes the QEPAS spectrophone, which is the core of any QEPAS sensor. In QEPAS sensing, the light source is focused between QTF prongs and sound waves produced by the modulated absorption of the gas are generated between the QTF prongs, forcing them to oscillate back and forth (in-plane anti-symmetrical modes). The main problem in the realization of a standard QEPAS sensor is the focalization of the laser beam within the 300 μm-gap between the standard QTF prongs without touching both micro-resonator tubes and the QTF. This is crucial in order to avoid the generation of a photo-thermal noise contribution which would be added to the piezoelectric

Vol. 27, No. 2 | 21 Jan 2019 | OPTICS EXPRESS 1401

#340626 https://doi.org/10.1364/OE.27.001401 Journal © 2019 Received 25 Jul 2018; revised 31 Oct 2018; accepted 4 Nov 2018; published 16 Jan 2019

https://doi.org/10.1364/OA_License_v1

signal [9]. When laser modulation occurs at one of resonance frequencies of in-plane piezoelectrically active modes, the induced strain field generates surface electric charges proportional to the intensity of the sound waves incident on the QTF prongs. When the light is periodically absorbed by the gas, the energy excess is mainly dissipated through non-radiative relaxation processes, involving vibrational and rotational excited states. Sound waves are then generated via energy transfer from excited states to translational degrees of freedom. The ability of the gas target to periodically relax the excess of energy depends on the modulation frequency (i.e. the resonance frequency of the QTF in-plane mode) of the incident laser radiation and differs for each gas [10,11]. With respect to the standard PAS, QEPAS operates at higher resonance frequencies. For slow relaxing gases, such as CO, CO2 and NO a QEPAS sensor operational frequency as high as 32.7 kHz, like in standard QTFs, can limit the sound wave generation efficiency [12]. These considerations suggested directions for the realization of improved QTFs: i) reduction of the QTF fundamental frequency, ii) increase the prongs spacing in order to facilitate the optical alignments and minimize the photo-thermal noise level. Starting in 2013, custom QTFs have been realized in QEPAS sensors following these two guidelines [13]. Larger prongs spacing led to the use of the QEPAS technique with laser sources having a poor spatial beam quality as well as operating in the terahertz spectral range [13,14]. The implementation of a single-tube as acoustic micro-resonator system is another achievement [15]. Lowering the fundamental frequency also opened the way to the use of first overtone mode in QEPAS sensing [16,17], leading to a double-antinode QEPAS configuration [18] and simultaneous dual-gas detection by exciting with two laser sources both the fundamental and first overtone QTF flexural modes, simultaneously [19]. However, guidelines for QTFs optimized for QEPAS operation are still not well defined.

This paper reports an investigation of the influence of prong sizes on both the resonance frequency and on the quality factor of the fundamental flexural mode, leading to the design of a quartz tuning fork optimized for QEPAS sensing. Starting from this design, two novel geometries were proposed: one with T-shaped prongs to optimize the strain field between the prongs and their support and the other one having prongs with grooves carved on the central sides in order to reduce the QTF electrical resistance. After determining the resonance properties, the investigated QTF samples were implemented in a QEPAS setup to test their photoacoustic response. The QTF providing the best performance in terms of signal-to-noise ratio (SNR) was acoustically coupled with a dual-tube micro-resonator system. The influence of the geometrical parameters on the photoacoustic response, namely the internal diameter and the length of the two tubes together with the spacing between the tube and the QTF, was also investigated to determine the optimal micro-resonator geometry.

2. Guidelines for the design of quartz tuning forks

The photoacoustic signal is proportional to the product Q·P·α, where Q is the QTF resonance quality factor, α is the gas target absorption coefficient and P is the laser power [17]. The straightforward approach to design QTFs optimized for QEPAS sensing is to reduce the resonance frequency while keeping high the quality factor. The dependence of the resonance frequency and related quality factor on the QTF relevant dimensions has been investigated in [20], where a set of QTFs with different values of spacing between the prongs and their sizes was analyzed. This study showed that resonance frequencies of in-plane flexural modes can be well predicted by using the Euler-Bernoulli equation. Considerations about the quality factor are more challenging. The Q-factor depends on all the energy dissipation mechanisms occurring in a vibrating prong of a QTF. The main contributions are due to damping by the surrounding fluid, the interaction of the prong with its support and thermo-elastic damping [21]. All these loss mechanisms strongly depend on the QTF prongs size. Although several theoretical models have been proposed to describe the dependence of each loss mechanism on the prongs geometry [22–24], there is no theoretical model capable to take into account all the


dissipation mechanisms in one, consistent formulation. An experimental investigation described in [21] on the QTF fundamental flexural mode resonance at atmospheric pressure demonstrates that the overall quality factor can be phenomenologically related to the prong sizes by:

53.78 10wT

QL

= ⋅ (1)

where w, T and L are the crystal thickness, the prongs width and the prongs length, respectively, all expressed in mm-units. This relation suggests that the overall quality factor of the fundamental mode can be increased by reducing the prong length and increasing both thickness and crystal width. Conversely, according to Euler-Bernoulli model, the resonance frequency of the fundamental flexural mode increases as the ratio between the prong thickness and its squared length [20]. When the crystal thickness is fixed, the quality factor scales linearly as the ratio T/L and Eq. (1) becomes Q = 9.45·104 T/L, for w = 0.25 mm, at atmospheric pressure. A MATLAB-based software was realized to relate the quality factor and the resonance frequency at different prong geometries. For each fixed prong geometry (T, L), the software calculates the resonance frequency and the related Q-factor, and plots ordered points on the x- (frequencies, f) and y- (Q-factors) axis of the coordinate plane. By ranging L from 3 mm to 20 mm and T from 0.2 mm to 3.0 mm, while keeping w at a fixed value of 0.25 mm, the calculated ordered points (Q, f) are shown in Fig. 1.

Fig. 1. Q-factor values plotted as a function of the resonance frequency for different prong lengths and thicknesses of quartz tuning fork of crystal width w = 0.25 mm, at atmospheric pressure.

The graph clearly shows that for a selected resonance frequency, different prong sizes can be chosen, providing quality factors values spanning in a certain range. Moving to low resonance frequencies, this range of possible quality factor values, as well as the Q-factor values itself, is reduced. In particular, QTFs with a resonance frequency lower than 10 kHz cannot ensure a Q-factor higher than 15,000, at atmospheric pressure. For a novel generation of QTFs optimized for QEPAS operation, a resonance frequency of ~16 kHz (a half of the standard 32.7 kHz) was selected. At f = 16 kHz, L and T values (with w = 0.25 mm) maximizing the quality factor (18,000) are 9.4 mm and 2.0 mm, respectively. In a first step, starting with this prong geometry we designed two QTFs differing only in the prong spacing: QTF-S08 having a prong spacing of 0.8 mm, and QTF-S15 with a prong spacing of 1.5 mm. With all other geometrical parameters being identical, a comparison between them in terms of QEPAS performance will allow establishing the influence of the prong spacing on the QTF frequency and Q-factor, as well as on the amount of radiation incident on the prong surface, which typical affects the QEPAS sensor noise level.


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Fig. 5(a)-(d).

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QTF-S08 differ only in resonance freof the QTF aQTF-S15 also13% different

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frequencies (f0), qG, QTF-S08-T, Q

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2 kHz-QTF 3

5 share the sametween the proies that the proe two prongs cthe same Q-fa

dicted value of

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ated an uncerta

quality factors (QQTF-S15, QTF#1,

QTF.

f0 (Hz) Q15841.92 15715801.66 15412460.55 155

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me geometricaongs. The smalong spacing docan be consideactor value (15~ 18,000. This

15 (), (c) QTF-S= 0.5 mV at atmose red solid lines

onents with resce between the

28]. In Table 1,gated QTFs are787.95 Hz andrd 32.7 kHz-QTion process, L

gation of unceainty of both th

Q) and electrical r, QTF#2 and stan

Q R (kΩ) 710 162.8 400 141.7

40 157.5

050 104.3 890 183.0 10 301.7 690 94.6

al characteristill difference (~oes not affect thered almost un5,710 and 15,4s means that th

S08-T () and (c)spheric pressure in

indicate the best

spect to the cue two pins of , resonance free compared wid fundamental TF [20]. Assumand T uncerta

ertainty for bohe resonance an

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ncoupled. QTF00, respectivel

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mode of ming that

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prong and measured properties F-S08 and ly), about n between


the Euler-Bernoulli model and the empirical dependence of the quality factor with prong width/length ratio is an efficient tool for the prediction of the quality factor values. Even if the resonance frequency of both QTF-S08 and QTF-S15 is almost a half of the standard 32.7 kHz-QTF, higher quality factors were measured. QTF-S08-G showed a resonance frequency about 4% lower than QTF-S08. Although the Euler-Bernoulli model does not predict a dependence of the resonance frequency on the crystal thickness w, 50 μm-grooves carving on both surface slightly affects the rectangular geometry of the prong and produces a small shift of the resonance frequency. For QTF-S08-T, a lower resonance frequency was measured with respect to QTF-S08 and QTF-S15, as predicted by COMSOL simulations, due to the non-uniformity of the moments of inertia along the prong section. For QTF-S08-T, a quality factor of 15,260 was measured. Although the prong T-geometry leads to a decrease of the prong width from 2 mm to 1.4 mm starting from 2.4 mm far from prong top, the quality factor was not affected. A comparison of the QTF#2 with the new generation QTFs shows that the latter exhibits higher quality factors and higher resonance frequencies, in agreement with the calculation shown in Fig. 1. A more interesting comparison can be performed when considering QTF#1 operating at the first overtone mode. QTF#1 has the fundamental flexural mode at 2.87 kHz with a quality factor of ~ 5,000 and the first overtone mode at 17.8 kHz with a quality factor as high as ~ 14,890. Therefore, by moving from the fundamental to the overtone mode leads to an increase of the resonance quality factor. This behavior can be explained by considering that air damping is strongly reduced when the resonance frequency increases [29] and support losses start to dominate when overtone modes are excited [30]. The new generation QTFs reached the same Q-factor values range of QTF#1 when they vibrate at the fundamental mode and this is useful in terms of QEPAS performance. T-shaping the prongs does not affect the electrical resistance, being nearly identical the electrical resistance measured for QTF-S08 and QTF-S08-T. While, a comparison of QTF-S08 and QTF-S08-G, clearly demonstrates that adding grooves on the prongs surfaces reduces the electrical resistance from 162.9 kΩ (QTF-S08) to 104.3 kΩ (QTF-S08-G), while Q-factor and resonance frequency are only slightly affected and thereby providing an improvement in terms of the QEPAS performance.

4. Photoacoustic response

To verify all assumptions, we employed all QTFs in the QEPAS setup, depicted in Fig. 4(b). A single-mode continuous-wave quantum cascade laser (QCL) was used as the excitation source to generate photoacoustic signals. The QCL targeted a water vapor absorption line falling at 1297.19 cm−1, having intensity of 3.6·10−22 cm/molecule [31]. The laser beam was focused between the QTF prongs using a ZnSe lens with a focal length of 50 mm. An aluminum enclosure equipped with two mid-IR AR-coated windows was realized in order to accommodate and easily switch the QTFs. The housing was filled by standard air with a fixed 1.7% water vapor concentration at atmospheric pressure. The QEPAS sensor operated with a wavelength modulation and dual-frequency detection approach, i.e. the laser beam is wavelength-modulated at a half of the selected resonance frequency while the lock-in amplifier demodulates the QTF signal at the resonance frequency. The absorption line is acquired by applying a slow ramp to the current driver allowing a linear wavelength-scan. As a first step, the vertical position of the laser beam focus along the QTF axis (as shown in Fig. 6(a)) has to be optimized in terms of the QEPAS signal. To study the dependence of the QEPAS signal intensity (proportional to the total momentum generated by the pressure wave) as a function of the vertical position of the laser beam, the laser beam focus was moved from the top to the bottom along the QTF axis between the two prongs.


Fig. 6acousNormtop of

The experQTF-S08-T aposition maxiprongs. The fundamental mrespect to thecan be explainspherical-likeprong [17]. Inmm far from obtained for tFig. 7(a)-(d).

Fig. 7mode record

6. (a) Sketch of a tic source is loc

malized QEPAS pef the QTF axis.

rimental QEPAat different laseimizing the Qsame result wmode, the optie antinode vibrned by conside acoustic sourn all new genethe top. The Q

the new genera

7. QEPAS spectralof QTF-S08 (a),

ded with a 100 ms

QTF depicting thecated between theeak signal acquired

AS peak signaer focused spo

QEPAS signal was obtained fimum laser berational point, ering that the crce, the larger eration QTFs, QEPAS spectraation QTFs, al

l scans of 1.7% w, QTF-S08-G (b),lock-in integration

e prong deflectione prongs. The ard at different laser

als, normalizeot positions areis 2 mm far ffor QTF-S08, am position istheoretically l

closer to the pris the fractionthe laser beamal scans of thell operating at

water concentration, QTF-S08-T (c) n time.

n at the fundamentrrow indicates thr focus position m

d to the highee shown in Figfrom the QTFQTF-S08-G a

s shifted towarlocated on the rong top is then of the press

m was focusede selected wate

the fundamen

n in air for the funand QTF-S15 (d

tal mode while anhe QTF axis. (b)measured from the

est value, obtag. 6(a). The laF top, betweenand QTF-S15rds the prong b

top of the proe vertical positisure wave not d between the per vapor absorpntal mode, are

ndamental flexurald). All scans were

n ) e

ained for aser focus n the two . For the base with ong. This ion of the hitting a

prongs, 2 ption line shown in

l e


The largeshigher than trectangular prinfluence on surface, leadibeneficial forthan QTF-S1influenced btransduction ein piezoelectrwave intensity1.36 times higslightly affectis more benefQTF were alsmm, 1.2 mm respectively [respect QTF#best QTF of tthan QTF#1. absorption feafour QTFs. Thboth prong spdemonstratingportion of ligh

Fig. 8acquir

However, signal-to-noisfluctuations oabsorptions awith QTF#1, All new gener

st QEPAS signthat measured rong provided the quality faing to an inc

r QEPAS senso15. This meanby the prong efficiency, i.e.,ric charge prody hitting the ingher than QTFt the resonanceficial in terms so tested with t

and 0.6 mm f[17]. All new #1 and QTF#2 the new QTF gIn the graphs satures. Hence, he 1σ noise lev

pacings of 0.8 mg that a pronght hits the inter

8. SNR of QTF-red for QTF#1, QT

the most impse ratio (SNR)of the signal are detected. In

QTF#2 and a ration QTFs sh

nal was measurwith QTF-S0

two advantageactor; ii) an increase of colleor performancens that even i

spacing, thi, the conversioduction. The lnternal surface F-S08, demonste frequency and

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generation (QTshown in Fig. 7this range was

vel measured fmm (QTF-S08g spacing of 0rnal surface of

-S08, QTF-S08-GTF#2 and standard

portant param) defined as thin a spectral n Fig. 8, a comstandard 32.7

howed the high

red with the QT08. The T-shaes: i) a reductioncrease of the ected piezoelee. QTF-S08 prif the electro-is parameter on efficiency olarger is the pof the prong.

trating that eved the Q-factor,ormance. QTF#rimental conditop for QTF#1, TFs resulted inak signal. In pa

TF-S08-T) exhi7(a)-(d), the ras used for the efor all bare new, QTF-S08-T, .8 mm is largprongs.

G, QTF-S08-T and 32.7 KHz-QTF (b

meter to compahe ratio betwerange (i.e. lasmparison betwkHz-QTF, is

hest SNR valu

TF-S08-T (5.4aped prong deon of the reson

stress field alectric charges.rovides a QEP-elastic propercan influence

of the amplitudprong spacing

QTF-S08-G shen if the groov, a decrease of #1, QTF#2 antions. The laserQTF#2 and st

n a better QEParticular, a comibits a QEPAS ange between 0estimation of thw generation QQTF-S08-G) ae enough to e

nd QTF-S15 comblack bars).

are different Qeen the QEPAser current ra

ween the invesshown in term

ues with respec

48 mV), about esigned startingnance frequencylong the prong. Both advant

PAS signal ~ 6rties of QTFse the acoustde of the acousthe lower is thowed a QEPA

ves on the pronthe electrical rd a standard 3r beam was fotandard 32.7 kPAS performa

mparison show signal 4.2 tim

0 s and 24 s is he 1σ noise lev

QTFs was ~0.26and 1.5 mm (Qensure that a n

mpared with those

QEPAS sensoAS peak signaange) where nstigated QTFs,ms of the QEPAct to QTF#1 an

1.5 times g from a y with no gs lateral tages are

6% higher s are not o-electric stic wave the sound AS signal ng surface resistance 32.7 kHz-cused 9.5

kHz-QTF, ance with

ws that the mes higher

free from vel for all 6 mV, for

QTF-S15), negligible

e

ors is the al and 1σ no optical , together AS SNR.

nd QTF#2


and the standhigher than th

5. T-shaped

As demonstraexcellent candis typically coacting as ampprobe the acoV-groove withQTF. The gediameter and surface of thmicroresonatoThe first paraof the prong.controlled duperformance. placed at diffpeak signal m

Fig. 9lines s

The distanrange 150 µmtube-QTF disQEPAS signabetween the tudistance is reacoustical codecreases becthe QTF. Thresonance freconsidered asmm) to form make them altested tubes hmm and 15 mtube diameter

dard 32.7 kHz-he new generati

d tuning fork

ated in Sectiondidate for the romposed by a

plifiers for the soustic vibrationh a cylindrical eometrical parthe length of t

he QTF. In [or tubes as weameter to be op The gaps siz

uring the specTwo tubes hav

ferent distancesmeasured as a fu

9. QEPAS peak sigserve as convenien

nce between Qm - 300 µm, the

tance from 10al approaches aubes and the Qeduced, confirupling betwee

cause of dampihe length of twequency (λ = a single tube na half-wave relmost indepen

having lengths mm. The choice

r is larger than

-QTF, the lattion QTFs) due

with dual-tu

4, QTF-S08-Trealization of a

a QTF acousticsound wave. Tn excited in the

hole was usedrameters influthe two tubes, 8], a detailed

ell as their influptimized is the e between the

ctrophone asseving a length os from the pronunction of the t

gnal as a function nt visual guides.

QTF and tubes e curve in Fig. 00 µm to 380 µasymptotically QTF becomes lrming that theen them. Wheing effects genwo tubes is c

27.6 mm) [7neglecting the esonator. Instedent, each tubbetween λ/4 a

e of the optiman the prongs

er showing alse to its small pr

be micro-res

T provides the a spectrophonecally coupled w

The QTF is typie absorbing gad to locate the tuencing the se

together with d investigationuence on QEPdistance betw

e QTF and theembly and it hof 13.3 mm anngs, spanning tube-QTF dista

of the distance be

maximizing t9 shows a quaµm the QEPAthat achieved arger than 200

e shorter the Qen the distancenerated by theorrelated with7,8]. Assumingap, each tube

ead, if the gap be length shouand λ/2, i.e., 1l ID is related spacing, the g

so the highestrong spacing of

sonator

highest QEPAe for QEPAS swith a pair of ically position

as contained intwo tubes at a ensor performthe spacing be

n of geometriPAS sensing p

ween the tubes e tubes is a dihas a signific

nd internal diamfrom 70 µm to

ance is plotted

etween the tube an

the SNR is 20si-plateau. Ind

AS signal variewith the bare

00 µm and rapiQTF-tube diste is shorter th

e short distanceh the sound wng that the lefe should be cutbetween the tu

uld be λ/2 (l =0 mm, 11 mmto the QTF pro

gap between tw

t noise level (9f 0.3 mm.

AS SNR. Hencsensors. A specf micro-resonatned between thenside the tubes

fixed distancemance are: theetween the tubical parametererformance is and the internaifficult paramecant effect on meter of 1.52 mo 2.0 mm. Thein Fig. 9.

nd the QTF. Solid

0 µm. Howevdeed, when chas by less than QTF when theidly increases wtance the highhan 120 µm, e between the

wavelength at ft and right tt to a λ/4 lengtubes is large e

= 13.8 mm). Hm, 12.4 mm, 13ongs spacing. Wwo tubes beco

9.4 times

e, it is an ctrophone tor tubes, e tubes to [5–8]. A

e from the e internal be and the rs of the reported.

al surface eter to be

its final mm were e QEPAS

d

ver, in the anging the

7%. The e distance when this

her is the the SNR tube and the QTF

tubes are th (l = 6.9 enough to

Hence, we 3 mm, 14 When the omes less


important andbecomes comdecreases. In QEPAS signaFor this reasotubes with intmm have beenas a function o

Fig. 1resonatube l

For all inlength is l = result allows tThe internal dmeasured in t1.59 mm and value measurhitting the intconfigurationand ID = 1.5signal (480.8spectrophone have to be co(SNRE) as thethe QTF couinternal diamthe SNRE rappronounced w

With QTFnew record fowith QTF#1, the T-shape othis result.

d the tubes are mparable with t

addition, for al can arise, duon, tubes with Iternal diametern investigated.of the tube leng

0. QEPAS peak sator tubes with anength. Solid lines

ternal diamete12.4 mm and to affirm that tdiameter maximthe same way l = 12.4 mm),

red for the barternal surface s investigated,9 mm showed

8 mV). The Qis shown in Fi

ompared with e ratio between

upled with the eter for tubes

pidly decreaseswhen higher innF-S08-T a signor mid-IR QEPQTF-S08-T re

of the prong, al

well acousticathe prongs spac

small tube diue to portion ofIDs < 1 mm hars ID = 1.36 mm As representagths, for ID =

ignals measured wn ID = 1.41 mm (aserve as convenien

ers investigatedrapidly decrea

the optimal tubmizing the QEPas reported in

, the 1σ noise le QTF-S08-T.of tubes. The

, within a discd the highest SQEPAS scan ig. 11(a). The the SNR of t

n the SNR meamicro-resonat

having l = 12.s when movingner diameters anal-to-noise raPAS spectroscoeaches a 50% hlthough a more

ally coupled wcing, the acousiameters a phof the laser beamave not been tam, 1.41 mm, 1

atives, in Fig. 11.41 mm, 1.59

with three differena), 1.59 mm (b) annt visual guides.

d, the QEPASases when a s

be length is notPAS signal is In Section 4. Wlevel results in This can be a 1σ noise leverepancy below

SNR of ~1380,of the water SNR values obthe bare QTF.asured for the tor. In Fig. 11.4 mm is reporg to lower inneare employed.atio enhancemeopy. With resphigher SNRE. e detailed calcu

with the QTF. Wstic coupling botothermal nom touching paraken into accou1.52 mm, 1.59 0, the QEPAS

9 mm and 2.06

nt spectrophones emnd 2.06 mm (c) as

S signal is maxshorter or longt dependent froID = 1.59 mm.

With the optiman 0.38 mV, ~1.attributed to aels were simil

w 5%. The tub, as well as thabsorption lin

btained with th. We defined bare QTF and1(b), the SNRrted. Starting fer diameter wh

ent of ~60 wapect to the besThis improvemulation is need

When the tube between tubes oise contributiorts of the spectunt. Hence, sixmm, 1.83 mm peak values armm.

mploying acoustics a function of the

ximized whenger length is uom its internal The 1σ noise al tube geomet.5 times higher

a small fractionar for all speces having l =

he highest QEPne measured whe spectrophonthe SNR Enha

d the SNR meaRE as a functiofrom the highehile the decrea

as obtained, wst spectrophonement can be asded to better un

diameter and QTF

on to the trophone.

x different m and 2.06

re plotted

c e

the tube used. This diameter. level was try (ID = r than the n of light ctrophone 12.4 mm

PAS peak with this ne system ancement

asured for on of the est value, ase is less

which is a e realized scribed to nderstand


Fig. 1(dasheresona200 μthe spthe tub

6. Conclusio

In this work, investigated. straightforwarlinear dependwith the EulerQTFs were prkHz with a qthree novel vwhile keepingQ-factors of stress-field sidemonstrated when QTF pgeometry, thenot affected. between the factor not affedetection of exhibited the selected to beenhance the Qdiameter of 1performance ithe SNR withobtained is aAlthough thevalidated, anaacoustic coupestimation ofmodel based osimulate the stube symmetr

1. (a) QEPAS speed red line) and ator tubes having aμm far from the QTpectrophone with rbe length is 12.4 m

ons

new designs oLowering the rd approach to

dence of the qur-Bernoulli moroposed and requality factor avariants were pg the same proa QTF are noimulations wer

that the stressprongs with ae QTF resonancIn the third delectrodes, lea

fected. All novewater vapor, best QEPAS

e acoustically cQEPAS sensor.59 mm, positin terms of QE

h respect to thea record value dependence oalytical modelpling between f all geometricon the propagasound field exitry axis. In this

ectral scan of watewith a spectrophoa length of 12.4 mTF (solid black linrespect to the baremm. The solid line

of quartz tuninresonance fre

o enhance the puality factor froodel for the prealized. The rea

as high as 15,0proposed. In thong geometry, at affected by re implementes field intensita T-shape geoce frequency w

design, groovesading to a reduel QTFs were exploiting a mperformance icoupled with ar performance.tioned about 2EPAS SNR ope bare QTF of ae for QEPAS of QEPAS pers proposed in a QTF a dua

cal parameters ation of the souting from tube case, the intera

er absorption line one composed by

mm and internal diane). (b) Signal-to-e QTF as a functi

e is a visual guide.

ng forks optimiequency while performance oom the prong thediction of the alized QTF pos000 at atmosphhe first design,allowing to veprong spacing

ed to generate ty generated byometry were

was reduced to s were applieduction of the implemented i

mid-IR range in terms of thea dual-tube mi. Tubes having

200 µm far froptimization. Wia factor of 60 wsystems oper

rformance on the literature

al-tube systeminvolved, it i

und wave insideedges, as a fun

action between

acquired with they QTF-S08-T andameter of 1.59 mm-noise ratio enhanion of tubes intern

ized for QEPAkeeping the q

of a QEPAS sehickness/lengtresonance freqssessed a resonheric pressure, a larger pronerify that the reg ≤ 1.5 mm. C

the second dy the prong deemployed. W12.4 kHz whil

d on prongs toelectrical resisin a QEPAS seabsorption line signal-to-noiicro-resonator g length of 12

om the QTF suith this conditiwas achieved. rating in the mthe tube geomdo not allow

m. In order to is necessary toe the micro res

unction of the an the exiting so

e bare QTF-S08-Td a pair of micro-m, both positionedcement (SNRE) ofnal diameter when

AS operation hquality factor ensor. Starting th ratio (T/L), cquency, new denance frequenc. Based on thi

ng spacing wasesonance propeCOMSOL Muldesign. The simeformation is

With a T-shapele the quality fao increase the stance with thensor and testene. The T-shapise ratio. Hencsystem with th

2.4 mm and anurface, provideion, an enhancThe SNR enhamid-IR spectrmetry was ver

w to exactly probtain a mor

o develop a thsonator tubes cangle with respound wave and

T -d f n

have been high is a from the

combined esigns for cy of 15.8 is design, s adopted erties and ltiPhysics mulations increased ed prong

factor was coupling

he quality ed for the ped QTF ce, it was he aim to n internal e the best cement of ancement ral range. rified and redict the re precise heoretical capable to pect to the d the QTF


prongs should be related with the geometrical properties of both acoustic resonators. Hence, the experimental results achieved in this work can be also used as a basis for theoretical and computational approaches (for example, finite element method analysis), mandatory for a precise prediction of an acoustic detection module performance.

Funding

Welch Foundation (Grant C0586).

Acknowledgment

The authors from Dipartimento Interateneo di Fisica di Bari acknowledge financial support from THORLABS GmbH, within the joint-research laboratory PolySense.

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Tuning forks with optimized geometries for quartz-enhanced ......Tuning forks with optimized geometries for quartz-enhanced photoacoustic spectroscopy PIETRO PATIMISCO, 1 ANGELO SAMPAOLO,1