Measurement and analysis of OH emissionspectra following laser-induced opticalbreakdown in air

Christian G. Parigger, Guoming Guan, and James O. Hornkohl

The measured emission spectra of the OH radical subsequent to laser-induced optical breakdown in airare analyzed to infer spectroscopic temperature and species number density. Emissions from the UVA2��3X2IIi transition dominate the spectra in the wavelength range of 306–322 nm and for time delaysfrom the optical breakdown of 30–300 �s. Contributions from other species to the recorded OH emissionspectra were also investigated for spectroscopic temperature measurements in the range of 2000–6000K and for OH number densities in the range of 1014–2 � 1016 cm�3. Monte Carlo simulations are appliedto estimate errors in the analysis of the hydroxyl spectra. © 2003 Optical Society of America

OCIS codes: 140.3440, 350.5400, 280.1740.

1. Introduction

Rich emission spectra typically can be recorded fol-lowing laser-induced optical breakdown. Investiga-tions where laser-induced breakdown spectroscopy�LIBS� is used show the occurrence of molecular re-combination spectra a few to a few tens of microsec-onds after nominal nanosecond breakdown in air.The emission spectra can be used to infer the compo-sition of the gas sample. For example, LIBS hasbeen successfully demonstrated for the detection ofice1 by using spectroscopic signatures in measuredspectra. The focus of this work is the measurementand analysis of OH emission spectra in laboratory airfor the determination of temperature and the OHnumber density.

An accurate diatomic spectrum can be computedfrom an electronic table, called a line-strength file, ofupper and lower term values and electric dipole linestrength.2 The temperature can be inferred by find-ing the temperature for which a computed spectrumbest fits an experimental spectrum. The determina-

C. G. Parigger and J. O. Hornkohl are with the Center for LaserApplications, The University of Tennessee Space Institute, 411B. H. Goethert Parkway, Tullahoma, Tennessee 37388. G. Guanis with the Microparticle Photophysics Laboratory �MP3L�, Poly-technic University, 6 MetroTech Center, Brooklyn, New York11201.

Received 20 January 2003, revised manuscript received 26 May2003.

0003-6935�03�305986-06$15.00�0© 2003 Optical Society of America

5986 APPLIED OPTICS � Vol. 42, No. 30 � 20 October 2003

tion of the species number density by use of emissionspectroscopy is challenging because the spectral anal-ysis involves the superimposed spectra of multiplespecies. We apply the computer code for nonequilib-rium air radiation �NEQAIR� in our analysis.3–5 Thespecies number densities �input to NEQAIR96� werecalculated by the use of the NASA chemical equilib-rium code.6,7 The NEQAIR code is used, for exam-ple, in interpreting the plasma torch spectra8 and thespectral analysis of transient microplasma.9–11

For a detailed analysis of laser-induced breakdownspectra with NEQAIR, the computed files for the ro-tational energy levels are replaced with line-strengthfiles for selected transitions of specific diatomic mol-ecules. These modifications are required for an ac-curate prediction of the wavelength positions ofmeasured, highly excited molecular spectra. Alter-natively, if a particular species dominates the emis-sion spectrum, the codes’ predictions can be combinedin the data reduction of a spectrum from an individ-ual diatomic molecule for which an accurate line-strength file is available. For thermodynamicequilibrium the so-called Boltzmann EquilibriumSpectrum Program �BESP� can be utilized12 in theanalysis of OH A2�� 3 X2IIi emission spectra byusing published OH databases.13–16 The Nelder–Mead17 least-squares-fitting algorithm can be em-ployed to determine the best-fit temperature.

Here time-resolved LIBS methods are used in thestudy of postbreakdown phenomena in air. Follow-ing a 1064-nm Nd:YAG breakdown the OH radical isproduced transiently. The OH emissions dominate

the recorded spectra in the wavelength range of 305–322 nm, �40–300 �s after the laser pulse. The OHpopulations in the different rotation–vibration levelsdepend on chemical dynamics and are redistributedin the rotation–vibration levels after the production.The energy transfer rate between different energylevels depends on pressure and gas composition.Typically a rotation-energy transfer rate of OH oc-curs of the order of nanoseconds, and a vibration-energy transfer rate of OH occurs of the order ofmicroseconds, as discussed in articles on rotation-energy transfer and vibration-energy transfer.18–21

Therefore the rotational temperature can be consid-ered as the temperature of the surrounding gases.The temperature obtained from different vibrationstates might deviate from the temperature of the sur-rounding gas.

2. Experimental Details

Laser-induced optical breakdown in nominal STPlaboratory air was generated by focusing 1064-nmlaser radiation of 3.5-ns pulse width. Irradiances oftypically 10 TW�cm2 were reached in the focal vol-ume. A Coherent Infinity 40–100 Nd:YAG laserwas operated at a frequency of 10 or 100 Hz. Thespectra were dispersed with a 0.64-m Jobin–Yvonspectrometer and recorded with an intensified arraydetector. The gate widths were 10 �s for data re-corded between 20 and 50 �s after optical breakdown,20 �s for data recorded at 60- and 80-�s delays, and50 �s for time delays of 100–300 �s. Wavelengthcalibrations were performed with standard lightsources, and the sensitivity correction was accom-plished with a deuterium lamp. The detector’s datawere corrected for a dark-noise contribution.

Figure 1 illustrates shadowgraphs for an experi-mental arrangement similar to the one used in mea-suring the spectra. The shadowgraphs wererecorded by use of a standard video camera and byuse of a 308-nm back-light radiation source �XeCl

excimer laser, 10-ns pulse width�. The individualbreakdown events were recorded on tape; subse-quently the images �36 mm � 48 mm� were digitizedby use of image-capture software. The selected im-ages were captured for time delays of as many as 100�s after the laser spark generation. The imagesshow the development in time of the optical-breakdown kernel as well as the development in timeof the shock wave, which shows propagation speeds of�1 km�s early in the microplasma decay or for timedelays of a few microseconds. Note the reflectedshock wave that propagates back through the break-down region and the apparent fluid physics phenom-ena of the vortex generation �see, for example, the100-�s time-delay image�.22

3. OH Emission Spectra

The spectral emission from the air-breakdownplasma comprises contributions from the OH mole-cule and other species in a given wavelength region:

Stotal � SOH � Sbackground. (1)

The background emission Sbackground contains radia-tion other than OH. This background emission maybe greater than the OH emissions as evidenced inspectroscopic studies at early time delays from break-down.

The spectral distribution of the OH emission signalat a temperature T can be written as

SOH � Kε

Aε��exp��ε�kB T� , (2)

where Aε�� is the spontaneous emission associatedwith energy level ε at wavelength . Aε�� is as-sumed to be a Gaussian function with amplitude andcentral wavelength taken from the line-strength file.K is a constant that represents the detection effi-ciency, and kB is the Boltzmann constant. The OHemission is collected from the breakdown region dur-

Fig. 1. Shadowgraph images for 300-mJ breakdown pulses. The back-light source was operated at a repetition rate of 80 Hz. Theimages show records of subsequent optical breakdown events in air.

20 October 2003 � Vol. 42, No. 30 � APPLIED OPTICS 5987

ing the gate-open time of the intensified detector.The measured signal,

SOH � K� ε

Aε��exp��ε�kBT� f �T�dT, (3)

contains the temperature distribution, and� f�T�dT � 1. In our investigation the temperaturedistribution f�T� was assumed to not change signif-icantly. Note that the determined temperature isaveraged over the gate-open time and over thebreakdown region that was imaged onto the spec-trometer entrance slit.

In the near-UV wavelength region of nominally300–325 nm the emission spectra are composed ofoverlapping electronic transitions of primarily NO,N2, and OH and to a lesser degree of O2 and atomicspecies. The emitted radiation also contains infor-mation about species number densities. The contri-butions to the emission spectrum from other speciescan be computed with the NEQAIR program by set-ting the OH concentration to zero. The results ofcomputing these contributions show the expectedwavelength dependency. However, we typicallyused an uniform contribution from all other species inthe analysis instead of NEQAIR-predicted spectra.The uncertainties of the wavelength positions in theNEQAIR code that was available to us could causesystematic errors. The line positions in theNEQAIR code are typically accurate within 1 cm�1,yet improvements in the OH line positions to an ac-curacy of better than 0.015 cm�1 for the 0–0 band ofOH, and of better than 0.05 cm�1 for the 1–1 and 2–2bands, were reported by Levin et al.23 For compar-ison the line-strength accuracy is typically betterthan 0.01 cm�1 for the wavelength regime of interestin this work, i.e., between 305 and 322 nm. An ap-plication of exclusively the NEQAIR code for theanalysis of the 32-cm�1 resolution breakdown spectrawould be desirable; however, not only accurate wave-length positions for OH but also for all other radiat-ing species would be required. Nevertheless theNEQAIR code has been instrumental for us in esti-mating the contributions from other species, namely,Sbackground, and accordingly in determining the num-ber densities of OH.

4. Results

The measured spectra were analyzed in the range of305–312 and 305–322 nm. Only the OH 0–0 band ispresent in the range of 305–312 nm, the 1–1 bandappears near 312 nm, and the 2–2 band appears near318 nm. The temperature obtained by fitting in therange of 305–322 nm differs slightly from the tem-perature obtained by fitting in the range of 305–312nm. Contributions from the 1–1 and 2–2 bands aresmall compared with the 0–0-band contributions tothe merit function for a 305–322-nm fitting. Evi-dence of thermodynamic nonequilibrium could not befound because OH molecular bands other than 0–0are too weak for accurate results to be obtained.

Figure 2 shows the emission spectra that were re-corded at a time delay of 30 �s after the optical-breakdown event in air. The spectral resolution was32 cm�1. Figure 2 also shows the least-squaresdata-reduction results. The experimental spectrumwas analyzed by use of the NEQAIR code3–5 whencomputed mole fractions of the plasma conditionswere used.6,7 A temperature of T � 5800 K wasinferred from this superposition spectrum. Predom-inantly the N2 Second Positive system is seen in thespectral emissions at a time delay of 10 �s; OH emis-sions can be recognized at time delays of 20–30 �s.Contributions from the band structure of the N2 Sec-ond Positive system is reduced at a time delay of 40�s. Subsequently emissions from the plasma decayare primarily due to the A2�7X2II UV system of OHin the wavelength region of 305–322 nm.

Figure 3 illustrates the recorded and fitted emis-sion spectrum for a time delay of 60 �s after laser-induced optical breakdown. The contributions tothe measured signals are mainly due to OH emis-sions. However, Fig. 3 also shows that other speciescontribute at a level of �20% of the maximum mea-sured signal. These additional signals are best de-scribed as background in the analysis of an OHemission spectrum. A temperature of T � 4000 K isinferred.

Figure 4 shows time-resolved emission spectra ofpredominantly OH. This spectrum was recorded ata time delay of 100 �s. Figure 4 also shows the

Fig. 2. Measured and with the NEQAIR program fitted emissionspectrum at a time delay of 30 �s after a laser-induced opticalbreakdown in air: circles, measured; curve, fitted.

Fig. 3. Measured and with the BESP program fitted emissionspectrum at a time delay of 60 �s: circles, measured; curve, fitted.

5988 APPLIED OPTICS � Vol. 42, No. 30 � 20 October 2003

least-squares data-reduction results that were ob-tained by use of line-strength files for OH.

Figure 5 shows the results for the spectroscopictemperature versus time delay. The error bars forthe inferred spectroscopic temperature are large fortime delays smaller than 50 �s, and they are moder-ately small for time delays greater than 100 �s. Fig-ure 5 also shows the Monte Carlo simulation resultsfor an error magnitude of 20% �x � 0.2� as summa-rized in Section 5. For time delays of more than 150

�s, or for temperatures of �3000 K, the backgroundcontributions are of the order of 1% or less of theintegrated emission. Consequently the tempera-ture is exclusively found from the OH spectral emis-sions. The inferred spectroscopic temperaturesrepresent temporal averages over the intensifiergate-open time. As indicated, 80-�s time-delay datawere recorded by using a gate width of 20 �s. Thetemperatures also represent spatial averages. Com-parison with the shadowgraph images �see Fig. 1�indicates that future, spatially resolved measure-ments would be desirable for further investigation ofkernel �or interaction regime� characteristics.

Computed number densities were used in the cal-culation of an emissions spectrum.7 Table 1 showsthe results for the thermodynamic equilibrium spe-cies number densities. Figure 6 shows the OH molefraction and number density versus temperature.The data points for the fitted temperatures from thetime-resolved spectra are indicated. The estimatederror in determining the spectroscopic temperatureresults in OH number densities that are accuratewithin a factor of �2.

5. Monte Carlo Simulation

Monte Carlo simulations are invoked for investigat-ing the accuracy of the inferred temperature. For

Fig. 4. Measured and with the BESP program fitted emissionspectrum at a time delay of 100 �s: circles, measured; curve,fitted.

Fig. 5. Spectroscopic temperature and its variance versus timedelay from optical breakdown, induced by use of Coherent Infinity40–100 Nd:YAG 1064-nm radiation of 3.5-ns pulse width, focusedto a typical peak intensity in air of 1013 W�cm2: squares, triangles,spectroscopic temperatures obtained with BESP; circles, MonteCarlo simulations.

Table 1. Equilibrium Atomic and Molecular Number Densities �cm�3� versus Temperature �103 K�

T 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

OH 1.3 � 1016 2.6 � 1016 1.8 � 1016 5.8 � 1015 1.5 � 1015 4.2 � 1014 1.4 � 1014 4.9 � 1013

Ar 2.9 � 1016 2.3 � 1016 1.9 � 1016 1.5 � 1016 1.3 � 1016 1.2 � 1016 1.0 � 1016 9.0 � 1015

N 7.9 � 1011 3.1 � 1013 4.0 � 1014 2.7 � 1015 1.2 � 1016 4.0 � 1016 1.0 � 1017 2.2 � 1017

O 1.9 � 1016 1.2 � 1017 3.3 � 1017 4.9 � 1017 5.3 � 1017 5.0 � 1017 4.5 � 1017 4.0 � 1017

e� – – 1.0 � 1012 6.2 � 1012 2.4 � 1013 6.5 � 1013 1.4 � 1014 2.6 � 1014

N2 2.4 � 1018 1.9 � 1018 1.5 � 1018 1.2 � 1018 1.1 � 1018 9.5 � 1017 8.0 � 1017 6.4 � 1017

O2 5.8 � 1017 4.0 � 1017 2.0 � 1017 5.7 � 1016 1.3 � 1016 3.3 � 1015 9.4 � 1014 3.2 � 1014

CO 7.1 � 1014 3.4 � 1015 5.0 � 1015 4.7 � 1015 4.3 � 1015 3.8 � 1015 3.3 � 1015 2.8 � 1015

NO 6.3 � 1016 9.7 � 1016 1.0 � 1017 7.4 � 1016 4.4 � 1016 2.6 � 1016 1.6 � 1016 9.4 � 1015

NO� – – 1.0 � 1012 6.2 � 1012 2.4 � 1013 6.5 � 1013 1.4 � 1014 2.6 � 1014

NAira 3.1 � 1018 2.6 � 1018 2.2 � 1018 1.9 � 1018 1.7 � 1018 1.6 � 1018 1.4 � 1018 1.3 � 1018

aNAir denotes the number density of air for all species at the indicated temperature.

Fig. 6. Mole fraction of the OH molecule as a function of temper-ature. The number densities are indicated on the right: solidcircles, inferred temperature and OH number density at specifiedtime delays.

20 October 2003 � Vol. 42, No. 30 � APPLIED OPTICS 5989

the process of Monte Carlo simulation, new sets ofsynthetic data are generated by adding a randomnumber to each measured data point:

yj � yj � x � ymean � R�� , (4)

where yj is measured data and ymean is the meanvalue of �yj�. R�� is a generator function for the ran-dom number with a normal probability distribution; xis a constant factor and may be estimated from thedifferences between the measured and the fitteddata; x amounts to typically 0.1–0.15. A least-squares merit function is used to determine the pa-rameters of �i� temperature, �ii� background, and �iii�linewidth for each synthetic data set. The averages,variances, and correlations are found from an ensem-ble of the parameters calculated by repeating MonteCarlo simulations and fitting.

Figure 7 shows bar charts of the computed temper-ature distribution for different error magnitudes x.Figure 7 also shows the averages and variances ob-tained from the Monte Carlo simulations. The en-velopes shown are Gaussian distributions with thesame averages and variances as shown. However,the temperature distribution appears more like aPoisson distribution than a Gaussian distribution.The computed correlations in the Monte Carlo simu-lations show that the temperature strongly dependson the background level and is not sensitive to thelinewidth, which in turn validates our initial choice ofuniform background subtraction and choice of Gauss-ian line profile.

The background emissions are negligible for tem-peratures lower than 3500 K, and fluctuations are theprimary source of errors. Monte Carlo simulationswere performed for the spectrum recorded at a 100-�stime delay �in the range of 305–322 nm� for studyingthe differences in two kinds of errors, namely, �i�uniform errors due to background or the presence ofother species and �ii� errors due to the usual mea-surement fluctuations, which are assumed propor-tional to the measured intensity. The results of thesimulations show that the average temperatures arealmost equal. The temperature variance due to thefluctuation errors is slightly larger than the variancedue to uniform errors. This is because more errors

are attributed to lower energy levels and fewer errorsto higher energy levels, and lower energy levels yielda greater variance while higher energy levels yieldless variance.

6. Conclusions

The spectroscopic temperature measurement in thespectral region of 305–322 nm when OH emissionspectra are used shows that an analysis of overlap-ping spectra is required. Applications of theNEQAIR program and the BESP allowed us to per-form a detailed analysis of OH spectra followinglaser-induced optical breakdown. The assumptionis reasonable for the existence of thermodynamicequilibrium in the measured OH spectra subsequentto the optical breakdown of air. The backgroundemissions present in the OH spectra show a strongcorrelation with temperature, while the line profileshows hardly any correlation with temperature.The variance of the spectroscopic temperature is pro-portional to the intensity variations in the measuredspectra.

The authors thank Y.-L. Chen, I. G. Dors, J.Drakes, D. R. Keefer, J. W. L. Lewis, W. Qin, andD. H. Plemmons for interest and contributions. C.Parriger thanks the Optical Society of America fortravel support to attend the LIBS2002 conference.This work is in part supported by the National Sci-ence Foundation grant CTS-9512489, in part by agrant of High Performance Computer �HPC� timefrom the Department of Defense HPC Center, theArnold Engineering Development Center �AEDC� atArnold Air Force Base, on the Origin 2000 computer,in part by the University of Tennessee Space Insti-tute �UTSI� and UTSI’s Center for Laser Applica-tions, and a UTSI graduate research assistantship.

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