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Concentration measurement of gas embedded in scattering media by employingabsorption and time-resolved laser spectroscopy

Somesfalean, Gabriel; Sjöholm, Mikael; Alnis, J; af Klinteberg, C; Andersson-Engels, Stefan;Svanberg, SunePublished in:Applied Optics

DOI:10.1364/AO.41.003538

2002

Link to publication

Citation for published version (APA):Somesfalean, G., Sjöholm, M., Alnis, J., af Klinteberg, C., Andersson-Engels, S., & Svanberg, S. (2002).Concentration measurement of gas embedded in scattering media by employing absorption and time-resolvedlaser spectroscopy. Applied Optics, 41(18), 3538-3544. https://doi.org/10.1364/AO.41.003538

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Concentration measurement of gas embedded inscattering media by employing absorption andtime-resolved laser spectroscopy

Gabriel Somesfalean, Mikael Sjoholm, Janis Alnis, Claes af Klinteberg,Stefan Andersson-Engels, and Sune Svanberg

Diode-laser-based absorption spectroscopy for the evaluation of embedded gas concentrations in porousmaterials is demonstrated in measurements of molecular oxygen dispersed throughout scattering poly-styrene foam, used here as a generic test material. The mean path length of light scattered in thematerial is determined with the temporal characteristics of the radiation transmitted through thesample. This combined with sensitive gas-absorption measurements employing wavelength-modulationspectroscopy yields an oxygen concentration in polystyrene foam of 20.4% corresponding to a foamporosity of 98%, which is consistent with manufacturing specifications. This feasibility study opensmany possibilities for quantitative measurements by using the method of gas-in-scattering-media ab-sorption spectroscopy. © 2002 Optical Society of America

OCIS codes: 290.7050, 300.1030, 290.4210, 300.6380, 300.6390.

1. Introduction

Embedded gas is often found in porous materials ofboth organic and synthetic origin. Monitoring thedistributed free gas can convey the internal gas con-centration, pressure, and temperature and can re-veal useful information about the bulk material,e.g., internal structure and diffusion characteris-tics. Recently, we demonstrated a new technique,called gas in scattering media absorption spectros-copy �GASMAS�,1 used for the characterization anddiagnostics of free gas in scattering solids and tur-bid liquids. Initial demonstrations included proof-of-principle measurements of the embedded oxygenconcentration relative to an equivalent column of airand of the internal gas pressure as well as assess-ment of the gas exchange. We analyzed the dis-persed gas in situ by using absorption spectroscopy,employing a single-mode probing diode laser tunedover a sharp absorption feature of the free gas mole-cule. The absorption and scattering cross sections of

The authors are with the Department of Physics, Lund Instituteof Technology, P.O. Box 118, Lund, Sweden. S. Svanberg can bereached at sune.svanberg@fysik.lth.se.

Received 23 July 2001; revised manuscript received 2 January2002.

0003-6935�02�183538-07$15.00�0© 2002 Optical Society of America

3538 APPLIED OPTICS � Vol. 41, No. 18 � 20 June 2002

the bulk material display slow wavelength depen-dence; thus these properties can be assumed to beconstant over the wavelength range tuned. Wave-length modulation techniques2 are used to increasethe detection sensitivity and to discriminate effec-tively against background signals, allowing for detec-tion of around 10�4–10�5 absorption fractions of thelight received.

Owing to inhomogeneities on the microscopic scalein the optical properties of the turbid medium, theradiation is scattered multiple times in the material.This prevents a straightforward application of theBeer–Lambert law, which requires well-defined pathlengths. However, using a temporally resolved tech-nique, as is routinely done in tissue optics studies,3,4

a mean path length of the diffused light can be esti-mated, which together with the strength of the gasabsorption determines the concentration of the dis-persed gas. In this paper we demonstrate the possi-bility of quantitative concentration measurements byusing polystyrene foam as a generic test material.

2. Theoretical Background

To extract the concentration of gas embedded in aturbid sample, we employ two independent mea-surements to obtain the gas absorbance a and theabsorption path length L, respectively. The Beer–Lambert law yields the transmitted intensity over afree path length L of a species with a concentration

c and a wavelength-dependent absorption cross sec-tion ���� according to

I��� � I0���exp������cL� � I0���exp��a�, (1)

where I0��� is the initial injected intensity and I��� isthe recorded intensity of the transmitted light. Oneobtains the gas absorbance using Eq. �1� by measur-ing the transmitted intensity through the sample atwavelengths on and off the gas absorption line. Theexpression cL can thus be determined from the trans-mission measurement, assuming that the absorptioncross section is known. The optical path length in ascattering medium Lsm is, however, not simply thethickness of the sample but is determined by theabsorption and scattering properties of the materialas well as by measurement geometry. Independentmeasurements of both the absorbance and the opticalpath length are thus necessary to obtain the concen-tration. The absorption of the gas is often smallcompared with the bulk material absorption, and willthus essentially not influence the optical path length.The influence of gas absorption on the optical pathlength is neglected below.

The absorption path length can be estimated as themean path length traveled by the photons �l. Twodifferent approaches can be used to determine thepath length, by a direct time-resolved measurementor indirectly by assessing the optical properties of themedium, making it possible to calculate Lsm with theuse of a transport model for the light propagationwithin the sample. In the limit of small absorptionsthe mean traveled path length can be estimated fromthe experimentally determined average time of flightof the photons �t according to

Lsm � �l � v�t, (2)

where v is the velocity of light in the scattering ma-terial. The material optical properties can be as-

sessed experimentally in three different ways: bytime-resolved, spatially resolved, and frequency-domain measurements.

In this research the powerful technique of time-resolved measurements utilizing ultrashort lightpulses and fast optical detection was used for study-ing photon propagation in multiple-scattering mate-rials.3,4 The analysis of the time-resolved data wasbased on the diffusion approximation to theradiative-transfer theory. When solving the diffu-sion equation, one must specify the boundary condi-tions. In the case of simple geometries, such as a

slab with finite thickness and infinite expansion, themost common approach is to mirror an infinite set ofimaginary positive and negative isotropic sources inan extrapolated boundary at some distance beyondthe actual surface, to insure that the fluence rate ofphotons is fully canceled. It yields an analytic ex-pression for the transmitted pulse shape in terms ofthe absorption coefficient a and the reduced scatter-ing coefficient s� of the sample material. In thecase of an infinitely extended slab of scattering ma-terial the time-dependent transmitted intensity canbe expressed as5

I��, d, t� � �4 Dv��3�2 t�5�2

� exp��avt ��2

4Dvt�� �

k�0

�� �z�k exp�� r�k2

4Dvt�� z�k exp��

r�k2

4Dvt�� , (3)

where � is the lateral injection–detection separation,d is the slab thickness, D � �3�a � s���

�1 is thediffusion coefficient, z0 � �s��

�1 is the mean free pathof isotropic scattering, z�k � �2k � 1�d � z0 is thedepth of the imaginary sources used to fulfill theboundary conditions, and r�k � ��2 � z�k

2�1�2 is thedistance between the detector position and thesources used in the calculations. One can evaluatethe optical properties of a sample by fitting such ananalytical expression to the experimentally acquiredtemporal dispersion curve by adjusting the free pa-rameters: the absorption, and reduced scatteringcoefficients. For a slab of thickness d the expressionfor the average time of flight of the photons, calcu-lated by integration of Eq. �3�, is given by6

where eff � �a�D�1�2 is the effective attenuationcoefficient. If the distribution of gas in the porousmaterial is assumed to be homogeneous and theabsorption is of the order of a few percent, the de-tected gas absorption signal can be considered theintegrated contribution from all exiting photons.A typical theoretical time-dispersed curve for lighttransmitted through a 39-mm-thick sample withthe optical parameters a � 0.002 cm�1 and s� �40 cm�1 is shown in Fig. 1. The broad time-of-flight distribution of the photons, corresponding tothe absorption path lengths through the embedded

�t �

�k�0

� �z�k

r�kexp��eff r�k� �

z�k

r�kexp��eff r�k��

2vD �k�0

� � z�k

r�k3 �1 � eff r�k�exp��eff r�k� �

z�k

r�k3 �1 � eff r�k�exp��eff r�k�� , (4)

20 June 2002 � Vol. 41, No. 18 � APPLIED OPTICS 3539

gas, gives rise to varying absorption signalstrengths, which are also schematically shown inFig. 1. Thus the gas absorption can be used as ameans to track the history of the photons in thematerial.

A simpler alternative to the time-resolved mea-surement technique, also explored in the present re-search, is to use a cw laser source and to spatiallymonitor the diffuse light-intensity distribution at thesample surface.7,8 When the recorded light inten-sity is plotted versus, e.g., the injection–detectionseparation distance, the final slope of the curve atlarge distances is found to be determined by the ef-fective attenuation coefficient eff. The spatially re-solved measurement method also requires that theabsolute intensities of the injected and scattered lightbe measured, which may be difficult to perform ex-perimentally because of unknown conditions regard-ing the coupling of light at the medium boundary.Solving the diffusion equation in the steady-statecase yields a transmitted intensity for an infinite slabof scattering material:

I��, d� �1

2 �k�0

� � z�k

r�k3 �1 � eff r�k�exp��eff r�k�

�z�k

r�k3 �1 � eff r�k�exp��eff r�k�� . (5)

In our previous research on measurements of molec-ular oxygen,1 we expressed the concentration of thegas in a scattering medium by introducing an equiv-alent mean path length Leq. It is defined as thedistance traversed by light in air, yielding a detectedsignal of the same magnitude as that from the ab-sorption of photons by oxygen embedded in the po-rous material according to

cairLeq � csmLsm, (6)

where cair is the oxygen concentration in air and csm isthe oxygen concentration in the scattering medium.The purpose of the present paper is to demonstrate

quantitative gas concentration measurements. Thusdetermination of an effective absorption path lengthcan be performed by means of time-resolved and spa-tially resolved measurements.

3. Experiment

The experimental setup for GASMAS measure-ments has been described in detail.1 Basic exper-iments of the GASMAS type are convenientlyperformed on molecular oxygen, because this gas isnormally diffused from the surrounding atmo-sphere into porous materials. A near-IR single-mode diode laser �Sharp LT031MDO� was placed ina nitrogen-flushed chamber, and the light wasbrought to the sample through a 0.6-mm-core-diameter optical fiber to ensure that the ambient airdid not influence the measurements. A transillu-minating geometry was chosen, in that the sampleswere placed on a long-pass colored-glass filter�Schott RG 695� attached directly to the cathodesurface of a photomultiplier tube 2 in. ��50 mm� indiameter �EMI 9558 QA�. A very high sensitivityand a large dynamic range were achieved with thisdetector setup, which is necessary when only smalland variable amounts of light seep through the scat-tering materials under observation. In the mea-surements performed in this study, relatively hightransmitted light intensities were available, and itwas thus possible to spatially limit the detectionarea by using a mask with a circular aperture 3 mmin diameter. Thus spatially resolved measure-ments could also be performed.

The experiments were performed on the strong,isolated R7R7 line at 761.003 nm in the oxygen Aband. Wavelength-modulation spectroscopy �WMS�employing lock-in techniques was used to pick up thesecond-harmonic component, which produces a signalsimilar to the second derivative of the original ab-sorption line shape. An experimental signal for oxy-gen in free air is shown in Fig. 2, where a directabsorption recording is also included. In our casemodulation at 55 kHz �Philips PM5139� effectivelydiscriminated the background signals by shifting the

Fig. 1. Analytical time dispersion curve obtained for transillumi-nation of a 39-mm-thick slab with optical parameters a � 0.002cm�1 and s� � 40 cm�1 by using short-pulsed light. For claritythe direct absorption signals corresponding to photons that havetraveled distances of different lengths in the material are inten-tionally exaggerated. The mean traveling time in the limit ofsmall absorptions is shown in the inset.

Fig. 2. �a� Direct absorption and �b� second-harmonic componentof the WMS spectrum for the R7R7 line in the oxygen A bandmeasured along a 10-m-long path in air. �c� Low-finesse fringesfrom a 2.43-GHz free spectral range Fabry–Perot etalon used forcalibration of the frequency scale.

3540 APPLIED OPTICS � Vol. 41, No. 18 � 20 June 2002

detection band to a high-frequency region where thenoise level is low.2 An absolute absorption calibra-tion was established by performing a long-path mea-surement in free atmosphere, where the directabsorption signal could also be observed. Curves �a�and �b� in Fig. 2 are recordings obtained for a 10-m-long absorption path length in air. To compensatefor variations in the detected light intensity, the ex-perimental WMS signal SWMS was normalizedagainst the interpolated intensity of the diffused lightat the line center SDir, defining a GASMAS differen-tial absorption signal

g �SWMS

SDir, (7)

determined for the selected modulation parameters.The Fabry–Perot etalon fringes in Fig. 2�c� allow theoxygen linewidth to be evaluated to �3.6 GHz.

Figure 3 shows a schematic diagram of the exper-imental setup used for the time-resolved measure-ments. Two different laser sources were used forgeneration of picosecond-long light pulses: a diodelaser with a repetition rate of 10 MHz �MitsubishiML4405 with a Bios Quant DL4040 driver� and amode-locked Ti:Sapphire laser with a repetition fre-quency of 76 MHz �Coherent MIRA 900�. Diode la-sers are particularly convenient to use in suchapplications because of their simple operation, com-pact size, and ability to produce short light pulseswhen high-frequency components are applied to thedriving current. The average output power of thediode laser was less than 1 mW, while only a smallfraction of the available radiation of the Ti:Sapphirelaser was used. Both lasers were tuned near theselected absorption wavelength of oxygen around 761nm. Owing to the broadened linewidths of theshort-pulsed lasers and low gas absorption, the gashas no significant influence on the photon propaga-tion through the scattering medium. A transillumi-nation arrangement was used, as shown in Fig. 3,although a backscattering detection scheme can in

certain cases be more appropriate. Optical fiberswith a core diameter of 0.6 mm were employed forlight injection and for collection of scattered radia-tion, with the samples placed between the fiber ends.The injector–detector separation could be varied bytranslating the collecting fiber. The transmittedlight was detected with a microchannel plate photo-multiplier tube �Hamamatsu R2566U-07�, whichensured high detection sensitivity. The time-correlated single-photon detection technique was em-ployed, including a constant fraction discriminator, atime-to-amplitude converter TAC, and a multichan-nel analyzer.4,9 The photon arrival time distribu-tion was recorded, and the overall temporal responsefunction of the system was �140 ps for the diode laserand �60 ps for the Ti:Sapphire laser. The latternumber corresponds essentially to the electronic re-sponse time, since the Ti:Sapphire laser has a subpi-cosecond pulse length.

Spatially resolved gas absorption measurements ofGASMAS type combined with transmitted light in-tensity measurements were also performed withtransilluminating geometry. The incident beam di-ameter was 3 mm, and the receiving photomultipliertube, with a detection area masked down to 3 mm indiameter, could be translated sideways.

The measurements were performed on polystyrenefoam samples of different thicknesses but of the samekind. We have chosen polystyrene foam as a modelscattering material, owing to its relatively high ho-mogeneity, strong scattering properties, and high gascontent, i.e., factors that contribute to a strong gassignature. This material also has a great industrialand commercial importance since it is extensivelyused as an insulation and packaging material.

4. Results

Figure 4 shows the recorded photon-arrival-time dis-tribution curve for a 39-mm-thick slab of polystyrenefoam measured with the diode laser. The time re-sponse of the system itself, the apparatus function,was obtained at time t � 0 by using a separate fiber,transmitting part of the laser pulse directly to thedetector �see Fig. 3�. This signal also provided a

Fig. 3. Experimental setup used for time-resolved measure-ments: PD, photodiode; PMT, photomultiplier tube; Amp, ampli-fier; CFD, constant fraction discriminator; TAC, time-to-amplitudeconverter.

Fig. 4. Recorded time dispersion curve obtained when transillu-minating a 39-mm-thick slab of polystyrene foam by using a diodelaser source pulsed at 10 MHz. A fit of a theoretical curve and theinstrumental transfer function are also depicted.

20 June 2002 � Vol. 41, No. 18 � APPLIED OPTICS 3541

time reference during the measurement. As can beseen from the time distribution curve, a certain frac-tion of the photons has traveled more than 15 nsthrough the material, i.e., corresponding to a pathlength of 4.5 m, although the physical thickness of theslab is only 0.039 m. The absorption and scatteringcoefficients of the polystyrene foam were determinedby first convolving the solution of the diffusion equa-tion, Eq. �3�, to the impulse response of the systemand then fitting the resulting curve to the detectedtime dispersion curve, as shown in Fig. 4. Note thatthe scale is logarithmic, causing small discrepanciesin the low-intensity region at late times to be clearlyvisible. No extrapolated boundary condition wasemployed in the model owing to the resultingnegligible corrections. In principle, laser-inducedfluorescence could perturb the measurements.However, because of the long excitation wavelength,the fluorescence is negligible compared with the di-rectly scattered light. The evaluated absorption co-efficient is a � 0.002 cm�1, and the transportscattering coefficient is s� � 40 cm�1, yielding aneffective attenuation coefficient eff � 0.5 cm�1.

Gas-absorption spectroscopy data for a 9.4-mm-thick slab of polystyrene foam embedded with at-mospheric oxygen are shown in Fig. 5. Itillustrates the amplitude variation of the GASMASsignal for several added free columns of air and isused to estimate an extrapolated equivalent meanpath length in polystyrene foam according to thestandard-addition method. Since the fraction oflight absorbed by the gas within the medium issmall, corresponding to only a few percent of theincident light, the absorption signal g is approxi-mately linearly proportional to the concentration.We denote the slope of the curve

kgL �gL

, (8)

where L is the absorption path length in air. Theoxygen concentration in the polystyrene foam cannow be estimated as

csm �cairLeq

v�t�

g�t

cair

vkgL, (9)

where Eqs. �2� and �6� and substitution of L � Leq inEq. �8� have been utilized. To minimize the influ-ence of material inhomogeneities, temporal disper-sion curves were also recorded for various lateralpositions of the detector. The pulsed Ti:Sapphirelaser was employed in such a measurement on a 9.4-mm-thick polystyrene foam slab. An experimentalplot of the directly evaluated mean photon arrivaltime versus various injector–detector separations isshown in Fig. 6�a�, derived from these measurements.A theoretical curve corresponding to the evaluatedoptical parameters is also plotted according to Eq. �4�.In Fig. 6�b� the experimental value at differentinjection–detection separations of the ratio betweenthe GASMAS signal and the mean time of flight, kgt �g��t, is shown together with a least-squares fit. Theuncertainty in the ratio was 1.3%, evaluated by usinga 95% confidence interval of the experimental values.The only unknown factor left is the index of refractionof the scattering material nsm, which determines thelight velocity in the medium according to v � c0�nsmwhere c0 is the light velocity in vacuum. Owing tothe homogeneous and isotropic nature of the porousmaterial, the macroscopic index of refraction was es-timated as a weighted mean of the refractive indicesof the individual compounds contained, i.e.,

nsm � Pnair � �1 � P�nb, (10)

where P is the material porosity, nair and nb are theindices of refraction of air and of the bulk material,respectively. In the case of gas equilibrium with thesurrounding atmosphere we can derive the foam po-

Fig. 5. Standard-addition plot for molecular oxygen obtainedwith the GASMAS setup showing the extrapolated equivalentmean path length for a 9.4-mm-thick slab of polystyrene foam.The WMS signal obtained with the light-injecting collimator indirect contact with the sample is shown in the inset.

Fig. 6. �a� Recorded mean time of flight through a 9.4-mm-thickslab of polystyrene foam measured with a pulsed Ti:Sapphire laser.Solid curve, theoretical curve corresponding to the evaluated op-tical parameters �a � 0.002 cm�1, s� � 40 cm�1�. �b� Dottedline, quotient between the GASMAS signal and the mean travelingtime of the photons together with a least-squares fit of the factorkgt.

3542 APPLIED OPTICS � Vol. 41, No. 18 � 20 June 2002

rosity P from the embedded gas concentration by us-ing

P �Vgas

Vtot�

csm

cair, (11)

where Vgas is the volume of gas in the porous materialand Vtot is the total volume of the porous material.With an index of refraction of the polystyrene bulkmaterial, nb � 1.4, and an atmospheric oxygen con-tent of 20.8%, the oxygen concentration in the poly-styrene foam can be evaluated accordingly with Eqs.�9�–�11� to yield csm � 20.4% and the correspondingfoam porosity P � 98%.

The mean time of flight of the photons, and conse-quently the embedded gas concentration, can as de-scribed above also be evaluated indirectly by spatiallyresolved measurement techniques. Experimentalcurves recorded with the GASMAS setup are shownfor a 9.4-mm-thick �Figs. 7�a�, 7�b��, and a 39-mm-thick �Figs. 7�c�, 7�d�� slab of polystyrene foam. Fig-ures 7�a� and 7�c� show the total transmitted lightintensity as a function of lateral displacement, wherethe zero separation corresponds to the position wherethe injector and the detector are placed opposite toeach other. Figures 7�b� and 7�d� display the GAS-MAS signal of the embedded oxygen. Note that thetransmitted light intensity falls off laterally as theGASMAS signal increases. The distributions are, asexpected, broader in the case of the thicker slab.The experimental points are plotted in Fig. 7 togetherwith theoretical curves �Eqs. �4� and �5�� where theeffective attenuation coefficient evaluated above isused. In the general case the mean time of flight canthus be evaluated when we insert the obtained opti-cal parameters into the analytical formula, Eq. �4�.However, a fit of the theoretical curve to the spatiallyresolved steady-state data measured at longinjection–detection separation �� �� z0� can provide

only an unambiguous value for the lumped coefficienteff and not for a and s� separately. The embed-ded gas concentration can thus not readily be as-sessed by using only these kinds of steady-statemeasurements.

Measurements on polystyrene foam slabs of differ-ent thicknesses were also performed, and the varia-tion in the equivalent mean path length with the slabthickness is plotted in Fig. 8. It can be seen in Fig.8 that in the case of polystyrene foam, which hasweak absorption and strong scattering properties, themean time of flight related to the equivalent meanpath length is proportional to the square of the thick-ness of the slab, i.e., �t � d2, as predicted by Eq. �4� forthe case of low gas absorption. A similar relation-ship was also obtained by considering the relatedtopic of light propagation through clouds.10

5. Conclusions and Discussions

We have shown that the embedded gas concentrationcan be estimated by using time-resolved measure-ments together with the newly developed GASMAStechnique. The proof-of-principle measurementswere performed on atmospheric oxygen at a wave-length characterized by weak absorption. The gaswas embedded in polystyrene foam, which is a modelmaterial with high porosity and strong scatteringproperties. The evaluated porosity of polystyrenefoam is comparable with manufacturing specifica-tions. However, in the more general case of moder-ate porosity or of substantial gas absorption, it is stilla subject for further investigation whether there isany preference for the photons to travel through thediffused gas or through the bulk material when beingmultiply scattered inside the porous material. Thisis a research topic that might reveal novel insightsinto the field of light propagation through confiningmedia.

Note that some aspects of the GASMAS technique

Fig. 7. Spatially resolved transmission recordings measured withthe GASMAS setup on two polystyrene foam slabs �a�, �b� 9.4 mmand �c�, �d� 39 mm thick: upper curves, transmitted intensity;lower curves, detected oxygen absorption signal amplitude for dif-ferent injector–detector separation distances. Fits according tothe evaluated effective attenuation coefficient �eff � 0.5 cm�1� arealso indicated. A schematic of the transillumination setup isshown in the insets, and dashed lines at the zero position mark thesymmetry axis.

Fig. 8. Plot of the equivalent mean path length corresponding tooxygen absorption measured through slabs of polystyrene foamwith different thicknesses by using a diode laser. The mean timeof flight is proportional to the square of the slab thickness. Solidline, theoretical curve evaluated with a � 0.002 cm�1 and s� �40 cm�1.

20 June 2002 � Vol. 41, No. 18 � APPLIED OPTICS 3543

do not require detailed knowledge about light prop-agation, as in the present case of an absolute concen-tration measurement. For example, gas pressure,temperature, and ratios between gas concentrationsare quantities that can be readily evaluated, beinglargely independent of light scattering inside the po-rous medium.

Gas tomography is another possible application ofthe technique. This extension corresponds to theone done for optical mammography and skull hema-toma detection.

An alternative to the time and spatially resolvedtechniques presented in this paper is to performphase-sensitive measurements in the frequency do-main.11,12 A major advantage of such a method isthat it needs only one single diode laser both for theGASMAS measurements and for determination of op-tical properties of the bulk material by using modu-lation techniques.

This research was supported by the Swedish Re-search Council for Engineering Sciences �TFR�, theKnut and Alice Wallenberg Foundation, and theSwedish Institute.

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