High-resolution water vapor spectrum and line shape analysis in the Terahertz region

Journal of Quantitative Spectroscopy & Radiative Transfer 159 (2015) 69–79

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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

a r t i c l e i n f o

abstract

Article history: Received 24 November 2014 Received in revised form 26 February 2015 Accepted 1 March 2015 Available online 11 March 2015

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.

Keywords: Water vapor Terahertz Continuum Spectroscopy Line shape

1. Introduction Water vapor is the main absorbing species in the atmosphere 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

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).

http://dx.doi.org/10.1016/j.jqsrt.2015.03.006 0022-4073/& 2015 Elsevier Ltd. All rights reserved.

this excess is commonly referred to as continuum absorption. 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 suggested 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 atmospheric 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 atmospheric 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

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broadband studies are performed at low resolution. More studies are necessary for a complete analysis of the water vapor continuum. The current study expands on previous work [28–30] of broadband water vapor absorption measurements using dry air as a broadening agent. Atmospheric transmission data in the 1.5 THz atmospheric window were taken over multiple path lengths and pressures at a high resolution of 5–10 MHz. The transmittance was fit to an absorption spectrum with an added empirical continuum term to identify the relevant parameters, which include direct measurement of the line strength, center frequency, selfand foreign-broadening coefficient, and the self- and foreign-continuum coefficients. Additionally, the statistical error bars for all of the fit parameters are reported. The line parameters are compared with the 2012 HITRAN Database [31] (HITRAN) while the continuum parameters are compared with values from the literature. 2. Experimental setup Transmission data were collected in the frequency range 1.45–1.55 THz. A frequency-multiplied source from Virginia Diodes Inc. was used to multiply up the continuous-wave LO signal from an Agilent E8257D Signal Generator by a factor of 96. A sub-harmonic mixing receiver from Virginia Diodes Inc. was used to output the mixed signal between the received radiation with the upconverted LO signal from a second Agilent E8257D Signal Generator. The phase noise of the signal was measured to be 35 dBc at 10 kHz from the carrier at transmitter frequencies around 1.5 THz. The

transmission information from the receiver is then carried to an IF frequency after being passed through a downconverter circuit to lower the frequency from 3.1 GHz to 70 MHz. A reference signal from the downconverter is used as a carrier frequency for a dual channel digital RF lock-in amplifier to collect the magnitude and phase of the received electric field directly. Fig. 1 shows a diagram of the RF circuitry used to downconvert the receiver IF signal. The setup also contains two off-axis parabolic mirrors used to collimate the radiation out of the source and to focus the radiation into the receiver. The sample was contained in a variable path-length White Cell, a detailed description of the cell can be found in Ref. [28]. Fig. 2a shows a schematic of the experimental setup and Fig. 2b shows a simplified schematic of the RF circuitry showing only frequency changing components and combining all of the frequency multipliers into a single icon. As shown in Figs. 1 and 2, the signals from the transmitter and receiver LO synthesizers are mixed and upconverted in order to build a reference for the receiver IF signal. The reference signal and receiver IF signal are then each mixed with two different IF signals differing by 70 MHz. Finally the shifted reference and receiver IF signals are mixed together to reduce the receiver IF signal to 70 MHz. Data was collected using a step scan with a separation between data points of 5 and 10 MHz for the self- and foreign-broadened data respectively. The absorption of a resonant line as well as continuum absorption depends on many parameters including the absorbing species pressure, foreign gas pressure, and pathlength. All three of these parameters were varied in this study to identify four line parameters per spectral line and

Fig. 1. A schematic of the RF circuitry in the downconverter.

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Fig. 2. (a) A schematic of the experimental setup and (b) a simplified diagram of the RF circuitry in the downconverter.

two continuum parameters from the data. A detailed description of the self-broadened data collection can be found in Ref. [30]. A similar process was employed for the foreign-broadened data collection. The cell was evacuated to below 20 mTorr and sealed. A calibration scan, with the source blocked, and a background scan were then completed. Water vapor was released into the cell to the desired pressure followed by dry air to the desired pressure. After the system reached equilibrium, a sample scan was completed and more dry air was released into the cell. This process of releasing dry air and completing scans was repeated six times for each path-length and water vapor pressure at approximately 25, 50, 100, 250, 500, and

750 Torr of total pressure. A total of 7 path lengths and 3 water 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 a thermocouple and varied from 24.2–25.9 1C between data sets. The pressure within the cell was monitored using one of two capacitance manometers from MKS Industries. One sensor was used for high-pressure measurements with the total pressure in the range 10–1000 Torr and a 0.1 Torr increment while the low-pressure measurements were performed using a sensor with a pressure range of 0–10 Torr and a 1 mTorr increment. The humidity in the cell was measured directly using a Honeywell HIH-4000 humidity

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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 to self- (air-) broadening.

sensor located in the cell, which was calibrated using saturated salt solutions. The given uncertainties of the measurement gauges were 1 1C, 0.25%, and 3.5% for the thermocouple, pressure gauge, and relative humidity sensor respectively. 3. Data Data was collected under a variety of conditions including both self- and air-broadened spectra at multiple pressures for multiple path lengths. The data scans took 25 and 12 min for self- and foreign-broadening respectively. A plot showing the different measurement conditions can be seen in Fig. 3. The open markers refer to self-broadened data while the closed markers refer to air-broadened data. As can be seen in the figure, a large portion of the parameter space was covered in this study. The large variation in the measurement conditions allowed for an accurate fitting of the water vapor absorption line and continuum parameters. 4. Data processing Interfering signals were present in the raw data that manifest as low frequency base line fluctuations as a result of ambient sources, electronic noise in the RF circuitry, and reflections within the experimental setup. Post-processing data techniques were applied to the collected data to remove the scintillations caused by the interfering signals and recover the transmittance of the setup. The post-processing routine included a calibration scan, leakage signal removal, digital filtering, a range gate, and distortion correction. The first post-processing technique applied to the data was the subtraction of the complex valued calibration scan, completed with the source blocked, to remove any signals not being produced directly from the source. Second, the leakage signal was removed from the data by subtracting the mean value of the complex valued data set from itself to

remove any signal with stationary phase caused by electronic leakage through the RF downconverter circuit. This subtraction amounts to the removal of the signal located at the zeroth bin in Fourier distance space. Next the data was transformed into distance space using a Fast Fourier Transform where a digital notch filter was applied to remove any interfering signals within 1 m of the main peak. After the digital filtering, a Gaussian window centered on the main signal was applied to the data in Fourier distance space as a range gate to remove any remaining interfering signals that had not traveled the appropriate distance through the setup. Tests were performed to identify the main signal peak in Fourier distance space. Measurements of an empty cell at multiple path lengths were taken and the moving peak between scans corresponds to the main signal. Both the notch filter and range gate reduce the base line fluctuations in the spectrum caused by the interfering signals. After the window was applied, the data was transformed back into frequency space and the magnitude of the complex data was taken. The magnitude was then normalized by dividing by the background scan, completed with an empty cell, after being post-processed according to the routine outlined above. This normalized data was then squared to arrive at the transmittance. Finally, a correction was applied to the transmittance to account for any distortions acquired from the range gating [30]. Eqs. (1) present the steps performed in the post-processing routine Calibration:

jðzÞ ¼ aðzÞ  cðzÞ

Leakage Removal: Filtering:

kðzÞ ¼ jðzÞ  μ


 mðzÞ ¼ S ℱ kðzÞ

Range Gate: pðzÞ ¼ ðwðxÞ n ℜ½mðzÞ; ℑ½mðzÞÞ Magnitude:


 qðxÞ ¼ ℱ  1 pðzÞ 

ð1aÞ ð1bÞ ð1cÞ ð1dÞ ð1eÞ

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73

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) and after (red) applying the range gating routine. (b) Experimental transmittance for a propagation length of 8 m and a pressure of 2.57 Torr. The transmittance before (red) and after (black) correcting for the range gate distortion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Normalization:

nðxÞ ¼

qðxÞ bðxÞ

ð1fÞ

Transmittance:

t ðxÞ ¼

n2 ðxÞ dðxÞ

ð1gÞ

In Eqs. (1), a(z) is the acquired complex raw data, c(z) is the acquired complex calibration data completed with the source blocked, μ is the average value of the function j(z), w(x) is the applied range gate window, b(x) is the magnitude of the post-processed background data completed with an empty cell, n(x) is the normalized magnitude of the post-processed data, t(x) is the transmittance, d(x) is the calculated distortion spectrum, S[] is the filtering function, j(z) is the calibrated data, k(z) is j(z) minus the leakage signal, m(z) is the filtered Fourier Transform of k(z), p(z) is the range gate of m(z), and q(x) is the magnitude of the inverse Fourier Transform of p(z). The distortion acquired from the range gating is strongest in the absorption lines and weakest in the atmospheric windows. As can be seen in Fig. 4, there is significant distortion in the peaks of the absorption lines which must be accounted for in order to obtain an accurate fitting of the line parameters. Since the distortion function is separable from the absorption spectrum line shape, the distortion can be removed using the convolution theorem of Fourier Transforms, Eqs. (2) and (3) Z hðxÞ ¼ lðxÞdðxÞ ¼ ðf n g ÞðxÞ ¼ f ðyÞg ðx yÞdy ð2Þ


 ℱ hðxÞ ¼ ℱ f ðxÞ ℱ g ðxÞ

ð3Þ

The absorption spectrum line shape can then be found by dividing the inverse Fourier Transform of Eq. (3) by d(x) to get Eq. (4)
   hðxÞ ℱ  1 ℱ f ðxÞ ℱ½g ðxÞ lðxÞ ¼ ¼ ð4Þ dðxÞ dðxÞ

In Eqs. (2)–(4) h(x) is the output from the range gate, l(x) is the absorption spectrum line shape, f(x) is the input to the
 range gate, and ℱ g ðxÞ is the applied range gate window. The distortion function was defined by dividing an ideal line shape calculated with the parameters in HITRAN into the result of the same line shape after passing through the range gate mathematics, d(x)¼h(x)/l(x). After the fitting routine was completed, the retrieved line parameters were then used to redefine the ideal line shape function and distortion function. The new transmittance data from the redefinition was then subjected to the fitting routine. This process of redefining the distortion function and fitting the resulting transmittance was performed iteratively until convergence of the fitted parameters was achieved. 5. Discussion Molecular absorption of incident radiation follows the Beer–Lambert Law:
 ð5Þ τðνÞ ¼ exp  lðαl ðνÞ þ αc ðνÞÞ In Eq. (5) τ is the transmittance, l is the propagation distance, ν is the frequency, αl is the resonant line absorption coefficient, and αc is the continuum contribution to the absorption coefficient. The resonant absorption coefficient is calculated as a sum over each individual absorption line using a suitable line shape factor [32] X αl ðνÞ ¼ N H2O Sk F ðν; νk Þ ð6Þ k

The present study investigated five different line shapes: the Van Vleck-Weisskopf with a ν2 prefactor (VVW2), the Van Vleck-Weisskopf with a ν1 prefactor (VVW1), the Full Lorentz (FL), the Simple Lorentz (SL), and the Gross (GR). Each line shape employed a 750 GHz cut off setting the contribution of a 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 the line shapes are given in Eq. (7) !   1 ν 2 Δνk Δνk VVW2 F ðν; νk Þ ¼ þ π νk ðν  νk Þ2 þ Δν2k ðν þ νk Þ2 þ Δν2k ð7aÞ VVW1

F ðν; νk Þ ¼



ν π νk 1



Δνk Δνk þ ðν  νk Þ2 þ Δν2k ðν þ νk Þ2 þ Δν2k

!

ð7bÞ F ðν; νk Þ ¼

FL



ν π νk 1



Δνk Δνk  ðν  νk Þ2 þ Δν2k ðν þ νk Þ2 þ Δν2k

!

ð7cÞ F ðν; νk Þ ¼

SL

F ðν; νk Þ ¼

GR



ν π νk 1

1



Δνk ðν  νk Þ2 þ Δν2k

! ð7dÞ

4ν2 Δνk

ð7eÞ

π ðν2  ν2k Þ2 þ 4ν2 Δν2k

The continuum contribution to the absorption coefficient is modeled by Eq. (8) [6], which is an approximation using empirically determined values to best reproduce the continuum in a narrow frequency range

αc ðνÞ ¼ ν2 P s P s C s θns þ P f C f θnf ð8Þ Finally the temperature of the sample is accounted for through Eqs. (9) and (10)    1 1 hc 5=2  E″ ð9Þ Sk ðT Þ ¼ Sk ðT 0 Þθ exp  T T0 k

Δνk ðTÞ ¼ γ sk P s θms þ γ f k P f θmf

ð10Þ

In Eqs. (6)–(10), F(ν,νk) is the line shape factor, NH2O is the number density of water molecules, Δνk is the half width at half max, γsk and γfk are the self and foreign line broadening constants, 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 the line strength, νk is the line center frequency, Cs and Cf are the self- and foreign-continuum coefficients, ns and nf are the continuum temperature exponents, ms and mf are the broadening temperature exponents, E″ is the lower state energy, and h, c, and k are Planck’s constant, the speed of light, and Boltzmann’s constant respectively. The values for E″ and mf used in the study were taken from HITRAN while the value for ms was a constant value of 1 for every transition [33]. There has been some discussion in the literature as to which line shape is the most appropriate to use when fitting absorption lines. Hill [34] has shown that in the microwave frequency region the Van Vleck-Weisskopf line shape is the most accurate in the line centers, but states that the choice is less critical at higher frequencies. The factor Δνk/νk determines the difference between the line shapes and is two orders of magnitude smaller in the Terahertz frequency region compared with the 22.235 GHz line used by Hill. All five line shapes in Eq. (7) were used to fit the experimental transmittance data to Eq. (5) in order to determine how the choice of line shape affects the spectrum and fitting in the Terahertz range. The transmittance of each data set collected was found by applying the post-processing routine outlined in Section 4. The transmittance was then fit to Eq. (5) using the definitions of Eqs. (6)–(10). The Levenberg–Marquardt non-linear least squares fitting technique was utilized with the line strength, center frequency, self- and foreignbroadening coefficients, and the self- and foreigncontinuum coefficients as fitting parameters and the contribution from other lines in the region as constants.

Table 1 A table of the line fitting parameters from the study and corresponding HITRAN values. The units are in MHz for frequency, m2 MHz for line strength, MHz/ Torr for the line broadening parameters, and m  1/MHz2/Torr2 for the continuum coefficients.

ν1 S1 γs1 γf1 ν2 S2 γs2 γf2 ν3 S3 γs3 γf3 ν4 S4 γs4 γf4 ν5 S5 γs5 γf5 Cs Cf a

VVW2

VVW1

FL

SL

GR

HITRANa

1,473,557.7 (40) 1.765 (48)  10  23 17.51 (76) 3.701 (335) 1,491,930.0 (8) 1.246 (6)  10  22 19.69 (16) 3.318 (56) 1,494,061.7 (11) 8.205 (54)  10  23 18.31 (20) 3.285 (73) 1,507,243.3 (31) 2.202 (50)  10  23 16.34 (59) 4.332 (326) 1,541,965.7 (3) 4.614 (4)  10  21 17.75 (4) 3.340 (6) 1.073 (4)  10  17 8.361 (21)  10  19

1,473,556.9 (43) 2.010 (51)  10  23 19.92 (80) 4.191 (355) 1,491,930.0 (8) 1.247 (6)  10  22 19.69 (16) 3.333 (56) 1,494,061.7 (10) 8.188 (54)  10  23 18.25 (20) 3.311 (73) 1,507,243.9 (31) 2.096 (50)  10  23 15.51 (58) 4.646 (357) 1,541,965.8 (3) 4.540 (4)  10  21 18.06 (4) 3.271 (6) 1.049 (4)  10  17 8.014 (21)  10  19

1,473,556.9 (43) 2.012 (51)  10  23 19.94 (81) 4.192 (355) 1,491,930.0 (8) 1.247 (6)  10  22 19.69 (16) 3.334 (56) 1,494,061.7 (10) 8.187 (54)  10  23 18.24 (20) 3.311 (73) 1,507,243.9 (31) 2.096 (50)  10  23 15.50 (58) 4.647 (357) 1,541,965.8 (3) 4.539 (4)  10  21 18.07 (4) 3.271 (6) 1.057 (4)  10  17 8.167 (21)  10  19

1,473,556.9 (43) 2.014 (51)  10  23 19.96 (81) 4.195 (355) 1,491,930.0 (8) 1.247 (6)  10  22 19.69 (16) 3.334 (56) 1,494,061.7 (10) 8.187 (54)  10  23 18.24 (20) 3.311 (73) 1,507,243.9 (31) 2.095 (50)  10  23 15.50 (58) 4.650 (358) 1,541,965.8 (3) 4.539 (4)  10  21 18.07 (4) 3.271 (6) 1.065 (4)  10  17 8.322 (21)  10  19

1,473,556.9 (43) 2.014 (51)  10  23 19.97 (81) 4.195 (355) 1,491,930.0 (8) 1.247 (6)  10  22 19.68 (16) 3.335 (56) 1,494,061.7 (10) 8.186 (54)  10  23 18.24 (20) 3.312 (74) 1,507,243.9 (31) 2.094 (50)  10  23 15.49 (58) 4.652 (358) 1,541,965.8 (3) 4.538 (4)  10  21 18.07 (4) 3.270 (6) 1.065 (4)  10  17 8.327 (21)  10  19

1,473,570.5 1.843  10–23 16.3 3.50 1,491,926.9 1.265  10–22 17.5 3.72 1,494,056.8 8.262  10–23 18.0 3.83 1,507,261.0 2.459  10–23 17.3 3.82 1,541,967.1 4.593  10–21 17.6 3.36 – –

The HITRAN values were converted from their given units into those used in the current study.

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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 overlaid in black. The legend gives the partial pressures in Torr of water vapor and air respectively in the ordered pair.

A global multispectral fit was employed to fit all 145 data sets simultaneously to achieve the most robust parameter set. Using this fitting routine, 4 parameters per line for 5 separate lines and 2 continuum parameters were identified for a total of 22 parameters for each line shape. The fitted parameters along with one standard deviation from the statistical fitting can be seen in Table 1 for the five different line shapes considered in the study. Also displayed in the table are the corresponding values from HITRAN converted to the units used for the present study. As can be seen in Table 1, the fitting for all five line shapes yields nearly identical results for the 1492 and 1494 GHz lines. The fitted parameters for the other lines showed small but statistically significant differences. The discrepancies for these parameters varied from 1–14% with the largest discrepancies occurring for the weakest transition. The cause of the deviation between different line profiles for these transitions and not the 1492 and 1494 GHz transitions may be due to the small intensity of the 1474 and 1507 GHz lines and the lower SNR of the 1542 GHz line. As can be seen in Fig. 5, the 1474 and 1507 GHz lines are only observable in the lowest pressure data sets and even then are only slightly out of the noise while the 1542 GHz line is subjected to more noise than the other transitions. The continuum parameters also 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 line asymmetry parameter R from Hill’s analysis [34] was calculated for each line shape

R¼





α νk þ Δνk  α νk  Δνk

αðνk þ Δνk Þ þ αðνk  Δνk Þ 2



ð11Þ

There was a variation in the asymmetry parameter of up to a factor of 4 for the varying line shapes. However, the magnitude of the asymmetry parameter is two orders of magnitude lower for the five lines investigated as compared to Hill’s test line at 22.235 GHz. The values obtained for the asymmetry parameter yields a difference of less than 1% between the absorption values at symmetrical points around the line center compared to the average of the two points. A 1% difference in the absorption coefficient translates to a maximum difference in the transmittance of less than 0.5%. This change in the transmittance was not measurable in the current study therefore any difference between the line shapes is insignificant for the present work and supports the assertion that the choice of line shape is not a critical one in the Terahertz range. In addition, the mean square error for the fitting varied by only 0.12% between the different line shapes with a minimum value of 0.00210 for the VVW2 profile. Although previous authors have attributed significance to the difference in line shape and the effect on the measured parameters [25], we find no significant difference in the global fit of this study. Although not a critical choice, the VVW2 line shape had the lowest MSE and provided the best fit to the experimental data, in agreement with Hill’s results. Given these results, the remainder of the discussion will focus on the VVW2 line shape. After the line shape analysis was completed, the fitting routine was run multiple times for different experimental conditions. The water vapor pressure, temperature, and air pressure were all varied by the stated gauge uncertainties to get an understanding of how this might affect the retrieved parameters. These adjustments had little affect on the line parameters, 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 a larger or smaller amount of water vapor will result in a Table 2 Details of the fitting procedure for transmittance data. Points fit

1,359,480

Data sets fit Path lengths fit H2O pressures fit Air pressures fit MSE

145 2–8 m 1.94–16.37 Torr 0–746.2 Torr 0.00210

smaller or larger continuum term to account for the observed absorption in the windows between lines. Displayed in Table 2 are the relevant details of the final fitting. Fig. 5 shows a plot of the transmittance across the full frequency range under foreign-broadening conditions while Fig. 6 shows a portion of the spectrum with two water vapor absorption lines under both self- and foreignbroadening conditions. As can be seen in the figures, the fitting is able to accurately fit the many different conditions present in the study. The fitting routine is also able to simultaneously fit the differing resonant and continuum absorption sections of the spectrum. Fig. 7 shows a portion of the spectrum with no resonant absorption lines where the continuum absorption is proportionally strongest. The fitting routine was able to accurately fit these two sections

Fig. 6. (a) Shows plots of the transmittance through 5 m of mixtures containing 16 Torr of water vapor and varying air pressures of 10–730 Torr in color with the fits overlaid in black. (b) Shows plots of the transmittance through 8 m of varying water vapor pressures of 2–15 Torr with no added air in color and fits overlaid in black. The legend gives the partial pressures in Torr of water vapor and air respectively in the ordered pair.

Fig. 7. (a) Shows plots of the transmittance through 6 m of mixtures containing 16 Torr of water vapor and varying air pressures of 10–730 Torr in color with the fits overlaid in black. (b) Shows plots of the transmittance through 5 m of varying water vapor pressures of 2–15 Torr with no added air in color and fits overlaid in black. The legend gives the partial pressures in Torr of water vapor and air respectively in the ordered pair.

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Table 3 A comparison of the experimentally determined line parameters with those available in HITRAN. The absolute and percent discrepancies are displayed in the 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 broadening coefficients. Current study ν1 S1 γs1 γf1 ν2 S2 γs2 γf2 ν3 S3 γs3 γf3 ν4 S4 γs4 γf4 ν5 S5 γs5 γf5 a b c

1,473,553.9(40) 1.764(47)  10  23 17.43(75) 3.689(333) 1,491,931.2(9) 1.251(6)  10  22 19.99(16) 3.285(55) 1,494,062.3(10) 8.174(53)  10  23 18.14(20) 3.272(72) 1,507,234.7(31) 2.206(50)  10  23 16.30(59) 4.423(332) 1,541,965.4(3) 4.614(4)  10  21 17.75(4) 3.340(6)

HITRAN

Discrepancy

1,473,570.5 1.843  10–23 16.3 3.50 1,491,926.9 1.265  10–22 17.5 3.72 1,494,056.8 8.262  10–23 18.0 3.83 1,507,261.0 2.459  10–23 17.3 3.82 1,541,967.1 4.593  10–21 17.6 3.36

16.6 7.900  10–25  .13  0.189  4.3 1.400  10–24  2.49 0.435  5.5 8.800  10–25  0.14 0.558 26.3 2.530  10–24 1.00  0.603 1.7  2.100  10–23  0.15 0.020

Discrepancy (%) 3

1.13  10 4.29 6.93 5.40 2.88  10  4 1.11 14.23 11.69 3.68  10  4 1.07 0.78 14.57 1.74  10  3 10.29 5.78 15.79 1.10  10  4 0.46 0.85 0.60

HITRAN source Calculated [35] Calculated [14] Unpublisheda Calculated [36] [37] Communicationb Adaptedc Adaptedc Calculated [35] Calculated [14] Unpublisheda Calculated [36] [37] Communicationb Adaptedc Adaptedc Calculated [35] Calculated [14] Calculated [38] Calculated [39]

HITRAN reference as R.R. Gamache unpublished data (2000). HITRAN reference as private communication with John C. Pearson (2000). HITRAN reference as use of HD16O measured values assuming no vibrational dependence from R.A. Toth.

Table 4 A 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 airbroadened continuum coefficients. Kuhn et al.a [18]

Current study Cs Cf a

8

2.622 (9)  10 2.043 (5)  10  9

8

8.88 (16)  10 2.52 (9)  10  9

Podobedov et al. [26,27] 8

3.83  10 1.60  10  9

Koshelev et al.a [19] 8

7.96 (9)  10 2.875 (35)  10  9

Yang et al. [25] 9.50  10  8 1.69  10  9

Values for nitrogen-broadening and not air-broadening.

as well as the full bandwidth of the transceiver simultaneously with a single parameter set. The data was also passed through the fitting routine with additional fitting parameters. The additional fitting parameters were the self-induced pressure shift δs and the airinduced pressure shift δf. These parameters were statistically undetermined when included in the fitting routine and were therefore not included in the final fitting. Despite being statistically undetermined, using the δf from HITRAN as a constant improved the fit. The results of the fitting including the HITRAN foreign pressure induced shifts can be seen in Tables 3 and 4. Table 3 shows a comparison between the fitted line parameters and the values from HITRAN. As can be seen in the table, some of the experimentally determined parameters are in good agreement with the HITRAN values while others are not. The values for the 1542 GHz transition are in good agreement with the HITRAN values. This was the strongest observed transition, which makes observations and calculations of the parameters simpler. For the 1492 and 1494 GHz transitions, the next two strongest transitions, the intensities are in good agreement along with the selfbroadening coefficient for the 1494 GHz transition. The foreign-broadening coefficient of the 1494 GHz transition however is not in good agreement with the HITRAN value,

differing by 15%. This discrepancy could be due to uncertainties within the model used to calculate the HITRAN value. There is also a large discrepancy between the broadening coefficients for the 1492 GHz transition. However, this can be explained as the HITRAN values are calculated from values of another isotopologue, HD16O, assuming no vibrational dependence. There is also a relatively large discrepancy between the frequency 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 weakest transitions, showed poor agreement with all of the observed HITRAN parameters. As previously stated, these two transitions were of very small intensity that were barely outside of the noise of the system. The transitions were also only observable in a small number of the lowest pressure data sets. The fitting routine also identified the self- and foreigncontinuum coefficients. Displayed in Table 4 are the continuum parameters determined from the present work along with some values from the literature, with all values converted to units commonly used in the literature. Direct comparison of continuum parameters is only meaningful if they were determined using the same line shape and frequency region, as is the case for the present work and that of Podobedov et al. [26,27]. As can be seen in the table,

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the value of the self-continuum coefficient from the present study is smaller than the other values in the literature. This is not surprising as the line shapes used in the other studies have a lower contribution to the absorption coefficient in the far wings of the spectral lines. In contrast, the value of the foreign-continuum coefficient from the present study is in the middle of the spread of values from the literature. The two studies with larger values were performed using pure nitrogen gas as the broadening agent while the current study used dry air. Podobedov et al. [27] measured the oxygen-broadened continuum coefficient to be smaller than the nitrogen-broadened continuum coefficient. Using a linear interpolation of these two values for an airbroadened continuum coefficient would yield a smaller value than the pure nitrogen value. As can be seen in Table 4, the results of this work are in closest agreement with the work of Podobedov et al. [26,27], whose study was similar enough to the present work to warrant a direct comparison. The differences in the continuum parameters between these two sets may be due to the larger frequency range studied in Refs. [26,27], 0.3–2.7 THz, compared with the present study, 1.45–1.55 THz. The most common procedure for the determination of the continuum coefficients is a fit of the residual between an experimental spectrum and a calculated one. This procedure requires the calculation of a theoretical spectrum based on line parameters from a database. The present work utilizes a different approach for the determination of the continuum coefficients. The coefficients are determined from a global multispectral fit that includes fitting the line parameters. This method no longer relies on the line parameters from a database for the lines included in the fit. The data was also fit holding all line parameters to their HITRAN values, only fitting the continuum coefficients, in order to compare continuum coefficients determined using the same method as the literature. This fitting resulted in values of 2.648(8)  10  8 and 2.048(5)  10  9 dB/km/ (hPa GHz)2 for the self- and foreign-continuum coefficients respectively. Comparing these values to those determined with the fitted line parameters shows a difference of 2.38% and 0.266% for the self- and foreign-continuum coefficients respectively. This small change in continuum coefficients is not completely surprising as the global fitting method still relies on the line parameters from a database for all the lines that are not included in the fit. 6. Conclusions High-resolution broadband water vapor absorption measurements were presented under a variety of conditions created by varying the water vapor pressure, air pressure, and path length. The data were analyzed using a global multispectral fitting and line shape analysis. The fitting routine identified the line strength, center frequency, and self and foreign line broadening constants each for five lines as well as the self- and foreign-continuum coefficients. Five different line shapes were tested in the analysis in order to determine the effect of line shape on the fit parameters. The line shape analysis was unable to find any significant differences between the five different line shapes analyzed for the present work. At much lower

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