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A Phase-Based Metrology System for Measuring Trace-Gas Concentration
J.H. Rentz, J.A. Gargas, and C.R. Schwarze
Optra, Inc.
461 Boston St.
Topsfield, MA 01983-1290
phone: (978) 887-6600 fax: (978) 887-0022
Project Summary
I. Introduction
Recent advances in tunable laser diodes and their availability at multiple wavelengths in the near-IR has
opened a new era of spectroscopic gas concentration measurement techniques. By adjusting temperature
and injection current, the laser diode can be tuned to the wavelength of a molecular resonance of interest,
and the absorption can be measured and used to obtain concentration. The injection current can also be
modulated, allowing for synchronous detection schemes such as wavelength and frequency modulated
spectroscopy (WMS and FMS) which effectively bypass the large 1/f noise component of the laser diode.14
In this paper, a new WMS technique is presented which measures phase due to the anomalous dispersion
around a resonance for trace gas detection.
II. Theory
This technique uses a polarization sensitive Mach-Zehnder interferometer to measure a phase signal which
is proportional to the slope of the anomalous dispersion profile. One arm of the interferometer contains a
sample cell filled with the gas under study and the other arm a vacuum reference cell as shown in Figure 1.
Figure 1.
The laser is dithered about the line center with an amplitude equal to the full-width at half-max (FWHM)
of the transition. Light which traverses the sample gas cell develops a phase shift relative to the vacuum
reference cell due to the anomalous dispersion in the gas; the resulting optical signals at the detectors are
given by
P
(1)
PA ,B = 0 ( 1 ± k1 f Sin( 2πσL( ∆n ))
2
1
where Po is the laser diode power, k1f is a constant gain term associated with harmonic detection, σ is the
wavenumber, L is the path length, and ∆n is the refractive index difference due to the anomalous
dispersion. The phase is extracted by normalizing the difference signal by the sum signal,
V
(2)
Vφ = A − B = k1 f Sin( 2πσL( ∆n )).
VA + B
Equation 2 also shows that this technique eliminates laser relative intensity noise (RIN). The refractive
index difference, ∆n, for an input frequency modulation equal to the FWHM is
αo
(3)
∆n =
.
4πσ o
For ppm and ppb concentrations, the magnitude of the phase becomes
αL
(4)
Vφ = k1 f o .
2
Equation 4 demonstrates the direct dependence of phase on absorption and, thus, concentration.
Figure 2 depicts the relationship between slope of the anomalous dispersion and phase modulation
amplitude. The input frequency modulation, ∆ω, generates an output phase modulation, Vφ, which is
proportional to the slope of the anomalous dispersion. It is also clear from Figure 2 that this phase-based
method produces a significantly larger signal than absorption techniques for small modulation amplitudes.
This difference is because the slope of the absorption profile goes to zero near line center while the slope
of the anomalous dispersion profile is at its maximum at line center.
Figure 2.
III. Experimental Results
Measurements have been made using this technique for water vapor at 1392.5 nm. Water vapor cells were
made containing two different known concentrations. A low concentration cell was filled with dry
nitrogen of a known water quantity and pumped down to the Doppler region. A high concentration cell
was filled with 100% RH air and pumped down to the same pressure. A computer model was used to
overlay the data and extract a concentration measurement. Figure 3 shows the profile obtained at the first
harmonic of the input modulation frequency for the high concentration cell. The profile generated is
actually the first derivative of the anomalous dispersion curve as dictated by the Kramers-Kronig relations;
the profile seen at the second harmonic is the second derivative, which also resembles the original
anomalous dispersion curve.5 The measured concentration was 3.25*1015 molecules/cm3 with a theoretical
concentration of 9.8*1014 molecules/cm3. The discrepancy can be attributed to the sealing process of the
cells extracting excess water from the cell walls. The low concentration profile is shown in Figure 4. The
measured concentration was 6.5*1014 molecules/cm3 with a theoretical concentration of 2.4*1013
molecules/cm3. Again, uncertainty in the control measurement can be attributed to the sealing process.
The asymmetry in the low concentration profile is the result of a slight path difference in the two arms of
2
the interferometer which exhibits itself as a bias away from the resonance. This bias was small, however,
in comparison to the measurement signal.
Further work demonstrating this measurement technique is in progress utilizing variable pressure cells with
a hygrometer, a pressure transducer, and a vacuum pump. The goal is to eliminate the uncertainty due to
the sealing process through real time monitoring of the cell’s humidity and pressure. This work will allow
for multiple measurement at various concentrations in the Doppler-, Voigt-, and Pressure-broadened
regimes.
Figure 3.
Figure 4.
High-Concentration Sample Cell Data
0.16
0.7
0.14
0.6
0.12
Magnitude of 1st Harmonic Signal (V)
Magnitude of 1st Harmonic Signal (V)
0.8
Low -Concentration Sample Cell Data
measured data
model
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
measured data
model
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
-0.2
-0.04
-0.3
-0.06
-0.08
-0.4
-2000
-1000
0
1000
2000
-2000
Frequency from Resonance (MHz)
-1000
0
1000
2000
Frequency from Resonance (MHz)
IV. Summary
A new and innovative method for trace gas detection has been presented using the slope of the anomalous
dispersion curve around a resonance to determine concentration. This method has proven superior to
straight absorption techniques in that the measurement signal is independent of laser relative intensity noise
as well as intensity modulation. This phase-based technique also results in a significantly larger signal that
absorption-based methods for small modulation amplitudes.
References
1
Reid, J. and Labrie, D., “Second-Harmonic Detection with Tunable Diode Lasers - Comparison of
Experiment and Theory”, Appl. Phys. B, 26, pp 203-10 (1981).
2
Carlisle, C. and Cooper, D., “Tunable-Diode-Laser Frequency-Modulation Spectroscopy Using
Balanced Homodyne Detection”, Opt. Lett., Vol 14, No 23, pp. 1306-08 (1989).
3
Goldstein, N. and Adler-Golden, S., “Long-Atmospheric-Path Measurements of Near-Visible Absorption
Lines of O2 Isotopes and H2O with a Prototype AlGaAs Laser Transceiver System”, Appl. Opt.,
Vol 32, No 30, pp. 5849-55 (1993).
4
Hovde, D. and Parsons, C., “Wavelength Modulation Detection of Water Vapor with a Vertical Cavity
Surface-Emitting Laser”, Appl. Opt., Vol 36, No 6, pp. 1135-38 (1997).
5
Yariv, A., Quantum Electronics, 3rd Edition, John Wiley & Sons, NY. (1989).
3