High-resolution water vapor spectrum and line shape analysis in the Terahertz region David M. Slocum n , Robert H. Giles, Thomas M. Goyette Submillimeter-Wave Technology Laboratory, University of Massachusetts Lowell, Lowell, MA 01854, USA article info Article history: Received 24 November 2014 Received in revised form 26 February 2015 Accepted 1 March 2015 Available online 11 March 2015 Keywords: Water vapor Terahertz Continuum Spectroscopy Line shape abstract A coherent broadband high-resolution study of the water vapor absorption spectrum at 1.5 THz was performed. The transmittance was recorded for many different water vapor and air pressures at multiple path lengths at a resolution of 5–10 MHz. A post-processing routine was developed to filter the acquired data before being subjected to a global multispectral fitting analysis of 145 data sets. The experimental data was fit to multiple different line shapes and a line shape analysis was performed in order to determine the most accurate line shape in the Terahertz range. Five of the strongest water vapor lines in the region were identified and fit to the data. The line center frequencies, absolute intensities, self- and foreign-broadening coefficients, and self- and foreign-continuum coefficients were all experimentally determined along with their statistically determined error bars. The fitted parameters are compared to the values from the literature. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Water vapor is the main absorbing species in the atmo- sphere at Terahertz frequencies. The amount of water vapor in the air as well as the frequency of a signal will determine the propagation distance of the signal in the atmosphere. An accurate understanding of the atmospheric water vapor absorption spectrum is important for many fields including wireless communication links [1,2] and characterizing new sources in the Terahertz region [3,4]. In order to maximize the transmission distance, frequencies in the atmospheric transmission windows between the strong absorption lines are used for free space propagation. Within these windows, however, there is still excess absorption that was first noticed in the microwave region by Becker and Autler [5] and attributed to the far wings of other lines. It has since been shown that the common line shapes do not accurately predict far wing absorption of resonant spectral lines and this excess is commonly referred to as continuum absorp- tion. Current models for the continuum utilize empirical terms to represent the excess absorption [6–8]. Many authors have worked to identify the cause of continuum absorption [9–12], and recent work has sug- gested that water dimers play a significant role [13]. Current models employ empirical terms to account for continuum absorption and require a large amount of data to achieve an accurate and robust set of continuum parameters. Much work has been performed investigating the resonant water vapor spectrum which is characterized by the line positions, intensities, and broadening parameters [14–17], however continuum absorption is most identifiable in the atmo- spheric windows. Until recently the Terahertz region has received little attention for experimental investigations. Measurements have been performed at discrete frequencies [18–20], however it is difficult to extend the conclusions beyond their data sets. Broadband studies using atmo- spheric air have been performed [21–24], however these studies lack control of many key parameters and often fail to cover the whole parameter space. Other broadband investigations [25–27] have been performed using pure nitrogen or oxygen in laboratory conditions, however most Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jqsrt Journal of Quantitative Spectroscopy & Radiative Transfer http://dx.doi.org/10.1016/j.jqsrt.2015.03.006 0022-4073/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ1 978 934 1300. E-mail address: [email protected](D.M. Slocum). URL: http://www.stl.uml.edu (D.M. Slocum). Journal of Quantitative Spectroscopy & Radiative Transfer 159 (2015) 69–79
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Contents lists available at ScienceDirect
Journal of Quantitative Spectroscopy &Radiative Transfer
Journal of Quantitative Spectroscopy & Radiative Transfer 159 (2015) 69–79
http://d0022-40
n CorrE-mURL
journal homepage: www.elsevier.com/locate/jqsrt
High-resolution water vapor spectrum and line shape analysisin the Terahertz region
David M. Slocum n, Robert H. Giles, Thomas M. GoyetteSubmillimeter-Wave Technology Laboratory, University of Massachusetts Lowell, Lowell, MA 01854, USA
a r t i c l e i n f o
Article history:Received 24 November 2014Received in revised form26 February 2015Accepted 1 March 2015Available online 11 March 2015
A coherent broadband high-resolution study of the water vapor absorption spectrum at1.5 THz was performed. The transmittance was recorded for many different water vaporand air pressures at multiple path lengths at a resolution of 5–10 MHz. A post-processingroutine was developed to filter the acquired data before being subjected to a globalmultispectral fitting analysis of 145 data sets. The experimental data was fit to multipledifferent line shapes and a line shape analysis was performed in order to determine themost accurate line shape in the Terahertz range. Five of the strongest water vapor lines inthe region were identified and fit to the data. The line center frequencies, absoluteintensities, self- and foreign-broadening coefficients, and self- and foreign-continuumcoefficients were all experimentally determined along with their statistically determinederror bars. The fitted parameters are compared to the values from the literature.
& 2015 Elsevier Ltd. All rights reserved.
1. Introduction
Water vapor is the main absorbing species in the atmo-sphere at Terahertz frequencies. The amount of water vaporin the air as well as the frequency of a signal will determinethe propagation distance of the signal in the atmosphere.An accurate understanding of the atmospheric water vaporabsorption spectrum is important for many fields includingwireless communication links [1,2] and characterizing newsources in the Terahertz region [3,4]. In order to maximizethe transmission distance, frequencies in the atmospherictransmission windows between the strong absorption linesare used for free space propagation. Within these windows,however, there is still excess absorption that was firstnoticed in the microwave region by Becker and Autler [5]and attributed to the far wings of other lines. It has sincebeen shown that the common line shapes do not accuratelypredict far wing absorption of resonant spectral lines and
(D.M. Slocum).
this excess is commonly referred to as continuum absorp-tion. Current models for the continuum utilize empiricalterms to represent the excess absorption [6–8].
Many authors have worked to identify the cause ofcontinuum absorption [9–12], and recent work has sug-gested that water dimers play a significant role [13]. Currentmodels employ empirical terms to account for continuumabsorption and require a large amount of data to achieve anaccurate and robust set of continuum parameters. Muchwork has been performed investigating the resonant watervapor spectrumwhich is characterized by the line positions,intensities, and broadening parameters [14–17], howevercontinuum absorption is most identifiable in the atmo-spheric windows. Until recently the Terahertz region hasreceived little attention for experimental investigations.Measurements have been performed at discrete frequencies[18–20], however it is difficult to extend the conclusionsbeyond their data sets. Broadband studies using atmo-spheric air have been performed [21–24], however thesestudies lack control of many key parameters and often failto cover the whole parameter space. Other broadbandinvestigations [25–27] have been performed using purenitrogen or oxygen in laboratory conditions, however most
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broadband studies are performed at low resolution. Morestudies are necessary for a complete analysis of the watervapor continuum.
The current study expands on previous work [28–30] ofbroadband water vapor absorption measurements usingdry air as a broadening agent. Atmospheric transmissiondata in the 1.5 THz atmospheric window were taken overmultiple path lengths and pressures at a high resolution of5–10 MHz. The transmittance was fit to an absorptionspectrum with an added empirical continuum term toidentify the relevant parameters, which include directmeasurement of the line strength, center frequency, self-and foreign-broadening coefficient, and the self- andforeign-continuum coefficients. Additionally, the statisticalerror bars for all of the fit parameters are reported. Theline parameters are compared with the 2012 HITRANDatabase [31] (HITRAN) while the continuum parametersare compared with values from the literature.
2. Experimental setup
Transmission data were collected in the frequency range1.45–1.55 THz. A frequency-multiplied source from VirginiaDiodes Inc. was used to multiply up the continuous-waveLO signal from an Agilent E8257D Signal Generator by afactor of 96. A sub-harmonic mixing receiver from VirginiaDiodes Inc. was used to output the mixed signal betweenthe received radiation with the upconverted LO signal froma second Agilent E8257D Signal Generator. The phase noiseof the signal was measured to be �35 dBc at 10 kHz fromthe carrier at transmitter frequencies around 1.5 THz. The
Fig. 1. A schematic of the RF circu
transmission information from the receiver is then carriedto an IF frequency after being passed through a down-converter circuit to lower the frequency from 3.1 GHz to70 MHz. A reference signal from the downconverter is usedas a carrier frequency for a dual channel digital RF lock-inamplifier to collect the magnitude and phase of the receivedelectric field directly. Fig. 1 shows a diagram of the RFcircuitry used to downconvert the receiver IF signal.
The setup also contains two off-axis parabolic mirrorsused to collimate the radiation out of the source and to focusthe radiation into the receiver. The sample was contained ina variable path-length White Cell, a detailed description ofthe cell can be found in Ref. [28]. Fig. 2a shows a schematic ofthe experimental setup and Fig. 2b shows a simplifiedschematic of the RF circuitry showing only frequency chan-ging components and combining all of the frequency multi-pliers into a single icon. As shown in Figs. 1 and 2, the signalsfrom the transmitter and receiver LO synthesizers are mixedand upconverted in order to build a reference for the receiverIF signal. The reference signal and receiver IF signal are theneach mixed with two different IF signals differing by 70 MHz.Finally the shifted reference and receiver IF signals are mixedtogether to reduce the receiver IF signal to 70 MHz. Data wascollected using a step scan with a separation between datapoints of 5 and 10 MHz for the self- and foreign-broadeneddata respectively.
The absorption of a resonant line as well as continuumabsorption depends on many parameters including theabsorbing species pressure, foreign gas pressure, and path-length. All three of these parameters were varied in thisstudy to identify four line parameters per spectral line and
itry in the downconverter.
Fig. 2. (a) A schematic of the experimental setup and (b) a simplified diagram of the RF circuitry in the downconverter.
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two continuum parameters from the data. A detaileddescription of the self-broadened data collection can befound in Ref. [30]. A similar process was employed for theforeign-broadened data collection. The cell was evacuatedto below 20 mTorr and sealed. A calibration scan, with thesource blocked, and a background scan were then com-pleted. Water vapor was released into the cell to thedesired pressure followed by dry air to the desiredpressure. After the system reached equilibrium, a samplescan was completed and more dry air was released into thecell. This process of releasing dry air and completing scanswas repeated six times for each path-length and watervapor pressure at approximately 25, 50, 100, 250, 500, and
750 Torr of total pressure. A total of 7 path lengths and 3water vapor pressures were investigated: 2, 3, 4, 5, 6, 7,and 8 m and approximately 4, 11, and 16 Torr.
The temperature of the system was monitored using athermocouple and varied from 24.2–25.9 1C between datasets. The pressure within the cell was monitored using one oftwo capacitance manometers from MKS Industries. Onesensor was used for high-pressure measurements with thetotal pressure in the range 10–1000 Torr and a 0.1 Torrincrement while the low-pressure measurements were per-formed using a sensor with a pressure range of 0–10 Torrand a 1 mTorr increment. The humidity in the cell wasmeasured directly using a Honeywell HIH-4000 humidity
Fig. 3. A plot of the data collected during the study. The different shaped markers refer to different path lengths while the open (closed) markers refer toself- (air-) broadening.
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sensor located in the cell, which was calibrated usingsaturated salt solutions. The given uncertainties of themeasurement gauges were 1 1C, 0.25%, and 3.5% for thethermocouple, pressure gauge, and relative humidity sensorrespectively.
3. Data
Data was collected under a variety of conditions includ-ing both self- and air-broadened spectra at multiple pres-sures for multiple path lengths. The data scans took 25 and12 min for self- and foreign-broadening respectively. A plotshowing the different measurement conditions can be seenin Fig. 3. The open markers refer to self-broadened datawhile the closed markers refer to air-broadened data. Ascan be seen in the figure, a large portion of the parameterspace was covered in this study. The large variation in themeasurement conditions allowed for an accurate fitting ofthe water vapor absorption line and continuum parameters.
4. Data processing
Interfering signals were present in the raw data thatmanifest as low frequency base line fluctuations as a result ofambient sources, electronic noise in the RF circuitry, andreflections within the experimental setup. Post-processingdata techniques were applied to the collected data to removethe scintillations caused by the interfering signals andrecover the transmittance of the setup. The post-processingroutine included a calibration scan, leakage signal removal,digital filtering, a range gate, and distortion correction.
The first post-processing technique applied to the datawas the subtraction of the complex valued calibration scan,completed with the source blocked, to remove any signalsnot being produced directly from the source. Second, theleakage signal was removed from the data by subtracting themean value of the complex valued data set from itself to
remove any signal with stationary phase caused by electronicleakage through the RF downconverter circuit. This subtrac-tion amounts to the removal of the signal located at thezeroth bin in Fourier distance space. Next the data wastransformed into distance space using a Fast Fourier Trans-form where a digital notch filter was applied to remove anyinterfering signals within 1 m of the main peak. After thedigital filtering, a Gaussian window centered on the mainsignal was applied to the data in Fourier distance space as arange gate to remove any remaining interfering signals thathad not traveled the appropriate distance through the setup.Tests were performed to identify the main signal peak inFourier distance space. Measurements of an empty cell atmultiple path lengths were taken and the moving peakbetween scans corresponds to the main signal. Both thenotch filter and range gate reduce the base line fluctuationsin the spectrum caused by the interfering signals. After thewindow was applied, the data was transformed back intofrequency space and the magnitude of the complex data wastaken. The magnitude was then normalized by dividing bythe background scan, completed with an empty cell, afterbeing post-processed according to the routine outlinedabove. This normalized data was then squared to arrive atthe transmittance. Finally, a correction was applied to thetransmittance to account for any distortions acquired fromthe range gating [30]. Eqs. (1) present the steps performed inthe post-processing routine
Calibration: j zð Þ ¼ a zð Þ�c zð Þ ð1aÞ
Leakage Removal: k zð Þ ¼ j zð Þ�μ ð1bÞ
Filtering: m zð Þ ¼ S ℱ k zð Þ� �� � ð1cÞ
Range Gate: p zð Þ ¼ w xð Þ nℜ½m zð Þ�;ℑ½m zð Þ�ð Þ ð1dÞ
Magnitude: q xð Þ ¼ ℱ�1 p zð Þ� ��� �� ð1eÞ
Fig. 4. (a) Simulated transmittance for a propagation length of 8 m and a pressure of 2 Torr of water vapor. The simulated transmittance before (black) andafter (red) applying the range gating routine. (b) Experimental transmittance for a propagation length of 8 m and a pressure of 2.57 Torr. The transmittancebefore (red) and after (black) correcting for the range gate distortion. (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)
D.M. Slocum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 159 (2015) 69–79 73
Normalization: n xð Þ ¼ q xð Þb xð Þ ð1fÞ
Transmittance: t xð Þ ¼ n2 xð Þd xð Þ ð1gÞ
In Eqs. (1), a(z) is the acquired complex raw data, c(z) is theacquired complex calibration data completed with the sourceblocked, μ is the average value of the function j(z),w(x) is theapplied range gate window, b(x) is the magnitude of thepost-processed background data completed with an emptycell, n(x) is the normalized magnitude of the post-processeddata, t(x) is the transmittance, d(x) is the calculated distortionspectrum, S[] is the filtering function, j(z) is the calibrateddata, k(z) is j(z) minus the leakage signal, m(z) is the filteredFourier Transform of k(z), p(z) is the range gate of m(z), andq(x) is the magnitude of the inverse Fourier Transform of p(z).
The distortion acquired from the range gating is stron-gest in the absorption lines and weakest in the atmo-spheric windows. As can be seen in Fig. 4, there issignificant distortion in the peaks of the absorption lineswhich must be accounted for in order to obtain anaccurate fitting of the line parameters. Since the distortionfunction is separable from the absorption spectrum lineshape, the distortion can be removed using the convolu-tion theorem of Fourier Transforms, Eqs. (2) and (3)
h xð Þ ¼ l xð Þd xð Þ ¼ f n gð Þ xð Þ ¼Z
f yð Þg x�yð Þdy ð2Þ
ℱ hðxÞ� �¼ℱ f xð Þ� �ℱ g xð Þ� � ð3Þ
The absorption spectrum line shape can then be found bydividing the inverse Fourier Transform of Eq. (3) by d(x) toget Eq. (4)
l xð Þ ¼ h xð Þd xð Þ ¼
ℱ�1 ℱ f xð Þ� �ℱ g xð Þ½ �� �
d xð Þ ð4Þ
In Eqs. (2)–(4) h(x) is the output from the range gate, l(x) isthe absorption spectrum line shape, f(x) is the input to therange gate, and ℱ g xð Þ� �
is the applied range gate window.The distortion function was defined by dividing an ideal
line shape calculated with the parameters in HITRAN into theresult of the same line shape after passing through the rangegate mathematics, d(x)¼h(x)/l(x). After the fitting routinewas completed, the retrieved line parameters were thenused to redefine the ideal line shape function and distortionfunction. The new transmittance data from the redefinitionwas then subjected to the fitting routine. This process ofredefining the distortion function and fitting the resultingtransmittance was performed iteratively until convergence ofthe fitted parameters was achieved.
5. Discussion
Molecular absorption of incident radiation follows theBeer–Lambert Law:
τ νð Þ ¼ exp � l αl νð Þþαc νð Þð Þ� � ð5ÞIn Eq. (5) τ is the transmittance, l is the propagationdistance, ν is the frequency, αl is the resonant lineabsorption coefficient, and αc is the continuum contribu-tion to the absorption coefficient. The resonant absorptioncoefficient is calculated as a sum over each individualabsorption line using a suitable line shape factor [32]
αl νð Þ ¼NH2O
Xk
SkF ν;νkð Þ ð6Þ
The present study investigated five different line shapes: theVan Vleck-Weisskopf with a ν2 prefactor (VVW2), the VanVleck-Weisskopf with a ν1 prefactor (VVW1), the Full Lorentz(FL), the Simple Lorentz (SL), and the Gross (GR). Each lineshape employed a 750 GHz cut off setting the contribution ofa line more than 750 GHz away from the center frequency to
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be 0, F(|ν�νk|4750 GHz,νk)¼0. The functional form of theline shapes are given in Eq. (7)
VVW2 F ν;νkð Þ ¼ 1π
ννk
� �2 Δνkν�νkð Þ2þΔν2k
þ ΔνkðνþνkÞ2þΔν2k
!
ð7aÞ
VVW1 F ν;νkð Þ ¼ 1π
ννk
� � Δνkðν�νkÞ2þΔν2k
þ Δνkνþνkð Þ2þΔν2k
!
ð7bÞ
FL F ν;νkð Þ ¼ 1π
ννk
� � Δνkðν�νkÞ2þΔν2k
� ΔνkðνþνkÞ2þΔν2k
!
ð7cÞ
SL F ν;νkð Þ ¼ 1π
ννk
� �Δνk
ðν�νkÞ2þΔν2k
!ð7dÞ
GR F ν;νkð Þ ¼ 1π
4ν2Δνkðν2�ν2k Þ2þ4ν2Δν2k
ð7eÞ
The continuum contribution to the absorption coefficient ismodeled by Eq. (8) [6], which is an approximation usingempirically determined values to best reproduce the con-tinuum in a narrow frequency range
αc νð Þ ¼ ν2Ps PsCsθns þPf Cfθ
nf ð8Þ
Finally the temperature of the sample is accounted forthrough Eqs. (9) and (10)
Sk Tð Þ ¼ Sk T0ð Þθ5=2exp � 1T� 1T0
� �hckE″
� �ð9Þ
ΔνkðTÞ ¼ γskPsθms þγf kPfθ
mf ð10Þ
Table 1A table of the line fitting parameters from the study and corresponding HITRAN vTorr for the line broadening parameters, and m�1/MHz2/Torr2 for the continuu
a The HITRAN values were converted from their given units into those used
In Eqs. (6)–(10), F(ν,νk) is the line shape factor, NH2O is thenumber density of water molecules, Δνk is the half width athalf max, γsk and γfk are the self and foreign line broadeningconstants, Ps and Pf are the self and foreign gas pressures, θ is(To/T) where To is 300 K and T is the temperature, Sk is theline strength, νk is the line center frequency, Cs and Cf are theself- and foreign-continuum coefficients, ns and nf are thecontinuum temperature exponents,ms andmf are the broad-ening temperature exponents, E″ is the lower state energy,and h, c, and k are Planck’s constant, the speed of light, andBoltzmann’s constant respectively. The values for E″ and mf
used in the study were taken from HITRAN while the valuefor ms was a constant value of 1 for every transition [33].
There has been some discussion in the literature as towhich line shape is the most appropriate to use when fittingabsorption lines. Hill [34] has shown that in the microwavefrequency region the Van Vleck-Weisskopf line shape is themost accurate in the line centers, but states that the choice isless critical at higher frequencies. The factor Δνk/νk deter-mines the difference between the line shapes and is twoorders of magnitude smaller in the Terahertz frequencyregion compared with the 22.235 GHz line used by Hill. Allfive line shapes in Eq. (7) were used to fit the experimentaltransmittance data to Eq. (5) in order to determine how thechoice of line shape affects the spectrum and fitting in theTerahertz range.
The transmittance of each data set collected was foundby applying the post-processing routine outlined inSection 4. The transmittance was then fit to Eq. (5) usingthe definitions of Eqs. (6)–(10). The Levenberg–Marquardtnon-linear least squares fitting technique was utilized withthe line strength, center frequency, self- and foreign-broadening coefficients, and the self- and foreign-continuum coefficients as fitting parameters and thecontribution from other lines in the region as constants.
alues. The units are in MHz for frequency, m2 MHz for line strength, MHz/m coefficients.
Fig. 5. The transmittance through 4 m of mixtures containing 11 Torr of water vapor and varying air pressures of 15–740 Torr in color with the fits overlaidin black. The legend gives the partial pressures in Torr of water vapor and air respectively in the ordered pair.
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A global multispectral fit was employed to fit all 145 datasets simultaneously to achieve the most robust parameterset. Using this fitting routine, 4 parameters per line for 5separate lines and 2 continuum parameters were identi-fied for a total of 22 parameters for each line shape. Thefitted parameters along with one standard deviation fromthe statistical fitting can be seen in Table 1 for the fivedifferent line shapes considered in the study. Also dis-played in the table are the corresponding values fromHITRAN converted to the units used for the present study.
As can be seen in Table 1, the fitting for all five line shapesyields nearly identical results for the 1492 and 1494 GHzlines. The fitted parameters for the other lines showed smallbut statistically significant differences. The discrepancies forthese parameters varied from 1–14% with the largest dis-crepancies occurring for the weakest transition. The cause ofthe deviation between different line profiles for thesetransitions and not the 1492 and 1494 GHz transitions maybe due to the small intensity of the 1474 and 1507 GHz linesand the lower SNR of the 1542 GHz line. As can be seen inFig. 5, the 1474 and 1507 GHz lines are only observable in thelowest pressure data sets and even then are only slightly outof the noise while the 1542 GHz line is subjected to morenoise than the other transitions. The continuum parametersalso showed small but statistically significant differences,which are even present in the very similar line shapes VVW1,FL, and SL. To quantifiably compare the line shapes the lineasymmetry parameter R from Hill’s analysis [34] was calcu-lated for each line shape
R¼ α νkþΔνk �α νk�Δνk
α νk þΔνkð Þþα νk �Δνkð Þ
2
� ð11Þ
There was a variation in the asymmetry parameter of up toa factor of 4 for the varying line shapes. However, themagnitude of the asymmetry parameter is two orders ofmagnitude lower for the five lines investigated as comparedto Hill’s test line at 22.235 GHz. The values obtained for theasymmetry parameter yields a difference of less than 1%between the absorption values at symmetrical pointsaround the line center compared to the average of thetwo points. A 1% difference in the absorption coefficienttranslates to a maximum difference in the transmittance ofless than 0.5%. This change in the transmittance was notmeasurable in the current study therefore any differencebetween the line shapes is insignificant for the presentwork and supports the assertion that the choice of lineshape is not a critical one in the Terahertz range. Inaddition, the mean square error for the fitting varied byonly 0.12% between the different line shapes with a mini-mum value of 0.00210 for the VVW2 profile. Althoughprevious authors have attributed significance to the differ-ence in line shape and the effect on the measured para-meters [25], we find no significant difference in the globalfit of this study. Although not a critical choice, the VVW2line shape had the lowest MSE and provided the best fit tothe experimental data, in agreement with Hill’s results.Given these results, the remainder of the discussion willfocus on the VVW2 line shape.
After the line shape analysis was completed, the fittingroutine was run multiple times for different experimentalconditions. The water vapor pressure, temperature, and airpressure were all varied by the stated gauge uncertainties toget an understanding of how this might affect the retrievedparameters. These adjustments had little affect on the lineparameters, varying by at most 3.7% for the intensity and
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broadening parameters and 370 kHz for the positions.However, the continuum parameters varied by up to 20%with the varying conditions. This is not surprising as alarger or smaller amount of water vapor will result in a
Table 2Details of the fitting procedure for transmittance data.
Points fit 1,359,480
Data sets fit 145Path lengths fit 2–8 mH2O pressures fit 1.94–16.37 TorrAir pressures fit 0–746.2 TorrMSE 0.00210
Fig. 6. (a) Shows plots of the transmittance through 5 m of mixtures containingwith the fits overlaid in black. (b) Shows plots of the transmittance through 8 mand fits overlaid in black. The legend gives the partial pressures in Torr of wate
Fig. 7. (a) Shows plots of the transmittance through 6 m of mixtures containingwith the fits overlaid in black. (b) Shows plots of the transmittance through 5 mand fits overlaid in black. The legend gives the partial pressures in Torr of wate
smaller or larger continuum term to account for theobserved absorption in the windows between lines. Dis-played in Table 2 are the relevant details of the final fitting.Fig. 5 shows a plot of the transmittance across the fullfrequency range under foreign-broadening conditions whileFig. 6 shows a portion of the spectrum with two watervapor absorption lines under both self- and foreign-broadening conditions. As can be seen in the figures, thefitting is able to accurately fit the many different conditionspresent in the study. The fitting routine is also able tosimultaneously fit the differing resonant and continuumabsorption sections of the spectrum. Fig. 7 shows a portionof the spectrum with no resonant absorption lines wherethe continuum absorption is proportionally strongest. Thefitting routine was able to accurately fit these two sections
16 Torr of water vapor and varying air pressures of 10–730 Torr in colorof varying water vapor pressures of 2–15 Torr with no added air in colorr vapor and air respectively in the ordered pair.
16 Torr of water vapor and varying air pressures of 10–730 Torr in colorof varying water vapor pressures of 2–15 Torr with no added air in colorr vapor and air respectively in the ordered pair.
Table 3A comparison of the experimentally determined line parameters with those available in HITRAN. The absolute and percent discrepancies are displayed inthe table along with the source of the HITRAN data. The units are in MHz for frequencies, m2MHz for line strengths, and MHz/Torr for line broadeningcoefficients.
Current study HITRAN Discrepancy Discrepancy (%) HITRAN source
a HITRAN reference as R.R. Gamache unpublished data (2000).b HITRAN reference as private communication with John C. Pearson (2000).c HITRAN reference as use of HD16O measured values assuming no vibrational dependence from R.A. Toth.
Table 4A table of the continuum fitting parameters along with selected values from the literature. The units are in dB/km/(hPa GHz)2 for both the self- and air-broadened continuum coefficients.
Current study Kuhn et al.a [18] Podobedov et al. [26,27] Koshelev et al.a [19] Yang et al. [25]
a Values for nitrogen-broadening and not air-broadening.
D.M. Slocum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 159 (2015) 69–79 77
as well as the full bandwidth of the transceiver simulta-neously with a single parameter set.
The data was also passed through the fitting routine withadditional fitting parameters. The additional fitting para-meters were the self-induced pressure shift δs and the air-induced pressure shift δf. These parameters were statisticallyundetermined when included in the fitting routine and weretherefore not included in the final fitting. Despite beingstatistically undetermined, using the δf from HITRAN as aconstant improved the fit. The results of the fitting includingthe HITRAN foreign pressure induced shifts can be seen inTables 3 and 4. Table 3 shows a comparison between the fittedline parameters and the values from HITRAN. As can be seenin the table, some of the experimentally determined para-meters are in good agreement with the HITRAN values whileothers are not. The values for the 1542 GHz transition are ingood agreement with the HITRAN values. This was thestrongest observed transition, which makes observationsand calculations of the parameters simpler. For the 1492 and1494 GHz transitions, the next two strongest transitions, theintensities are in good agreement along with the self-broadening coefficient for the 1494 GHz transition. Theforeign-broadening coefficient of the 1494 GHz transitionhowever is not in good agreement with the HITRAN value,
differing by 15%. This discrepancy could be due to uncertain-ties within the model used to calculate the HITRAN value.There is also a large discrepancy between the broadeningcoefficients for the 1492 GHz transition. However, this can beexplained as the HITRAN values are calculated from values ofanother isotopologue, HD16O, assuming no vibrational depen-dence. There is also a relatively large discrepancy between thefrequency positions in the 1492 and 1494 GHz transitions.This may be due to lower intensities of these transitions.Finally the 1474 and 1507 GHz transitions, the two weakesttransitions, showed poor agreement with all of the observedHITRAN parameters. As previously stated, these two transi-tions were of very small intensity that were barely outside ofthe noise of the system. The transitions were also onlyobservable in a small number of the lowest pressure data sets.
The fitting routine also identified the self- and foreign-continuum coefficients. Displayed in Table 4 are the con-tinuum parameters determined from the present workalong with some values from the literature, with all valuesconverted to units commonly used in the literature. Directcomparison of continuum parameters is only meaningful ifthey were determined using the same line shape andfrequency region, as is the case for the present work andthat of Podobedov et al. [26,27]. As can be seen in the table,
D.M. Slocum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 159 (2015) 69–7978
the value of the self-continuum coefficient from the presentstudy is smaller than the other values in the literature. Thisis not surprising as the line shapes used in the other studieshave a lower contribution to the absorption coefficient inthe far wings of the spectral lines. In contrast, the value ofthe foreign-continuum coefficient from the present study isin the middle of the spread of values from the literature.The two studies with larger values were performed usingpure nitrogen gas as the broadening agent while the currentstudy used dry air. Podobedov et al. [27] measured theoxygen-broadened continuum coefficient to be smaller thanthe nitrogen-broadened continuum coefficient. Using alinear interpolation of these two values for an air-broadened continuum coefficient would yield a smallervalue than the pure nitrogen value. As can be seen inTable 4, the results of this work are in closest agreementwith the work of Podobedov et al. [26,27], whose study wassimilar enough to the present work to warrant a directcomparison. The differences in the continuum parametersbetween these two sets may be due to the larger frequencyrange studied in Refs. [26,27], 0.3–2.7 THz, compared withthe present study, 1.45–1.55 THz.
The most common procedure for the determination ofthe continuum coefficients is a fit of the residual betweenan experimental spectrum and a calculated one. Thisprocedure requires the calculation of a theoretical spectrumbased on line parameters from a database. The presentwork utilizes a different approach for the determination ofthe continuum coefficients. The coefficients are determinedfrom a global multispectral fit that includes fitting the lineparameters. This method no longer relies on the lineparameters from a database for the lines included in thefit. The data was also fit holding all line parameters to theirHITRAN values, only fitting the continuum coefficients, inorder to compare continuum coefficients determined usingthe same method as the literature. This fitting resulted invalues of 2.648(8)�10�8 and 2.048(5)�10�9 dB/km/(hPa GHz)2 for the self- and foreign-continuum coefficientsrespectively. Comparing these values to those determinedwith the fitted line parameters shows a difference of 2.38%and 0.266% for the self- and foreign-continuum coefficientsrespectively. This small change in continuum coefficients isnot completely surprising as the global fitting method stillrelies on the line parameters from a database for all thelines that are not included in the fit.
6. Conclusions
High-resolution broadband water vapor absorptionmeasurements were presented under a variety of condi-tions created by varying the water vapor pressure, airpressure, and path length. The data were analyzed using aglobal multispectral fitting and line shape analysis. Thefitting routine identified the line strength, center frequency,and self and foreign line broadening constants each for fivelines as well as the self- and foreign-continuum coefficients.Five different line shapes were tested in the analysis inorder to determine the effect of line shape on the fitparameters. The line shape analysis was unable to findany significant differences between the five different lineshapes analyzed for the present work. At much lower
frequencies the Van Vleck-Weisskopf line shape has beenshown to be the most accurate, but in the Terahertz regionthe choice of line shape is much less significant.
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