Abstract

The minimum quantities of the nine most abundant, isolated, atmospheric gases that are detectable with a refractometer are calculated. An examination of the applicability of refractometric techniques for detecting and analyzing gaseous mixtures is discussed and a comparison made against other established techniques. Traditionally, most gas analysis performed with an interferometer is in determining the dispersion or refractivity of a known sample, presented here is the inverse approach, where refractivities are measured to determine the concentrations of particular species within a gas. The method, and experimental results for determining the minimum quantities of a particular species detectable in a mixture has been explored, as well as the complications, such as the indistinguishability of dynamic polarizabilities of different gases and the subsequent demands for accurate pressure and fringe measurements of using interferometric techniques. It is shown that the concentration of a single (isolated) gas, in units of number density, can be determined to within approximately 110×1018m3, and a mixture of the three most abundant gases, N2, O2 and Ar, to within 3.4×104partsin106(ppm) when a minimum detectable fringe shift of λ/100 is assumed.

© 2009 Optical Society of America

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References

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2005

1996

1995

1994

1993

F. S. Chau, H. M. Shang, C. C. Soh, and Y. Y. Hung, “Determination of fractional fringe orders in holographic interferometry using polarization phase shifting,” Opt. Laser Technol. 25, 371-375 (1993).
[CrossRef]

1991

1990

U. Hohm and K. Kerl, “Interferometric measurements of the dipole polarizability of molecules between 300 K and 1100 K,” Mol. Phys. 69, 819-831 (1990).
[CrossRef]

1988

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

1977

1971

1969

1966

1964

1932

C. Cuthbertson and M. Cuthbertson, “The refraction and dispersion of neon and helium,” Proc. R. Soc. London Ser. A 135, 40-47 (1932).
[CrossRef]

1920

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide and methane,” Proc. R. Soc. London Ser. A 97, 152-159(1920).
[CrossRef]

1880

H. Lorentz, “Über die beziehung zwischen der fortpflanzungsgeschwindigkeit des lichtes und der körperdichte,” Ann. Phys 245, 641-665 (1880).
[CrossRef]

L. Lorenz, “Über die refractionsconstante,” Ann. Phys 247, 70-103 (1880).
[CrossRef]

Birch, K. P..

Bonne, U.

U. Bonne, G. Yogesh, T. Osamu, and Z. Hans, “Gas sensors,” in Comprehensive Microsystems (Elsevier, 2008), pp. 375-432.
[CrossRef]

Chau, F. S.

F. S. Chau, H. M. Shang, C. C. Soh, and Y. Y. Hung, “Determination of fractional fringe orders in holographic interferometry using polarization phase shifting,” Opt. Laser Technol. 25, 371-375 (1993).
[CrossRef]

Ciddor, P. E.

Cuthbertson, C.

C. Cuthbertson and M. Cuthbertson, “The refraction and dispersion of neon and helium,” Proc. R. Soc. London Ser. A 135, 40-47 (1932).
[CrossRef]

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide and methane,” Proc. R. Soc. London Ser. A 97, 152-159(1920).
[CrossRef]

Cuthbertson, M.

C. Cuthbertson and M. Cuthbertson, “The refraction and dispersion of neon and helium,” Proc. R. Soc. London Ser. A 135, 40-47 (1932).
[CrossRef]

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide and methane,” Proc. R. Soc. London Ser. A 97, 152-159(1920).
[CrossRef]

Davies, W. L.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Demmel, J. W.

J. W. Demmel, Applied Numerical Linear Algebra (Society for Industrial and Applied Mathematics, 1997).
[CrossRef]

Fisher, D. J.

Gentili, K. L.

Golub, G. H.

G. H. Golub and C. F. Van Loan, “Johns Hopkins studies in the mathematical sciences,” Matrix Computations (Johns Hopkins University, 1996).

Hahn, C. E. W.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Hans, Z.

U. Bonne, G. Yogesh, T. Osamu, and Z. Hans, “Gas sensors,” in Comprehensive Microsystems (Elsevier, 2008), pp. 375-432.
[CrossRef]

Heinisch, C.

Hohm, U.

U. Hohm and K. Kerl, “Interferometric measurements of the dipole polarizability of molecules between 300 K and 1100 K,” Mol. Phys. 69, 819-831 (1990).
[CrossRef]

Huang, S.

Hung, Y. Y.

F. S. Chau, H. M. Shang, C. C. Soh, and Y. Y. Hung, “Determination of fractional fringe orders in holographic interferometry using polarization phase shifting,” Opt. Laser Technol. 25, 371-375 (1993).
[CrossRef]

Jackson, R.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Kerl, K.

U. Hohm and K. Kerl, “Interferometric measurements of the dipole polarizability of molecules between 300 K and 1100 K,” Mol. Phys. 69, 819-831 (1990).
[CrossRef]

Khanna, B.

Kobayashi, T.

Laird, C. K.

C. K. Laird, “Chemical analysis: gas analysis,” in Instrumentation Reference Book, Third ed., W.Boyes, ed. (Butterworth Heinemann, 2002).

Lichtenberg, S.

Lorentz, H.

H. Lorentz, “Über die beziehung zwischen der fortpflanzungsgeschwindigkeit des lichtes und der körperdichte,” Ann. Phys 245, 641-665 (1880).
[CrossRef]

Lorenz, L.

L. Lorenz, “Über die refractionsconstante,” Ann. Phys 247, 70-103 (1880).
[CrossRef]

Mansfield, C. R.

McGraghan, T.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Misawa, K.

Mullins, O. C.

Old, J. G.

Osamu, T.

U. Bonne, G. Yogesh, T. Osamu, and Z. Hans, “Gas sensors,” in Comprehensive Microsystems (Elsevier, 2008), pp. 375-432.
[CrossRef]

Palayiwa, E.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Peck, E. R.

Petrov, V.

Petter, J.

Rabbito, P.

Schroeder, R. J.

Shadbolt, P.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Shang, H. M.

F. S. Chau, H. M. Shang, C. C. Soh, and Y. Y. Hung, “Determination of fractional fringe orders in holographic interferometry using polarization phase shifting,” Opt. Laser Technol. 25, 371-375 (1993).
[CrossRef]

Soh, C. C.

F. S. Chau, H. M. Shang, C. C. Soh, and Y. Y. Hung, “Determination of fractional fringe orders in holographic interferometry using polarization phase shifting,” Opt. Laser Technol. 25, 371-375 (1993).
[CrossRef]

Sugg, B. R.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Tschudi, T.

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, “Johns Hopkins studies in the mathematical sciences,” Matrix Computations (Johns Hopkins University, 1996).

Verdin, A.

A. Verdin, Gas Analysis Instrumentation (MacMillan, 1973).

Weller, S. J.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

Yogesh, G.

U. Bonne, G. Yogesh, T. Osamu, and Z. Hans, “Gas sensors,” in Comprehensive Microsystems (Elsevier, 2008), pp. 375-432.
[CrossRef]

Ann. Phys

H. Lorentz, “Über die beziehung zwischen der fortpflanzungsgeschwindigkeit des lichtes und der körperdichte,” Ann. Phys 245, 641-665 (1880).
[CrossRef]

L. Lorenz, “Über die refractionsconstante,” Ann. Phys 247, 70-103 (1880).
[CrossRef]

Appl. Opt.

B. J. Anaesth.

B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. McGraghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, “An automated interferometer for the analysis of anaesthetic gas mixtures,” B. J. Anaesth. 61, 484-491(1988).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Mol. Phys.

U. Hohm and K. Kerl, “Interferometric measurements of the dipole polarizability of molecules between 300 K and 1100 K,” Mol. Phys. 69, 819-831 (1990).
[CrossRef]

Opt. Laser Technol.

F. S. Chau, H. M. Shang, C. C. Soh, and Y. Y. Hung, “Determination of fractional fringe orders in holographic interferometry using polarization phase shifting,” Opt. Laser Technol. 25, 371-375 (1993).
[CrossRef]

Opt. Lett.

Proc. R. Soc. London Ser. A

C. Cuthbertson and M. Cuthbertson, “The refraction and dispersion of neon and helium,” Proc. R. Soc. London Ser. A 135, 40-47 (1932).
[CrossRef]

Proc. R. Soc. London Ser. A

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide and methane,” Proc. R. Soc. London Ser. A 97, 152-159(1920).
[CrossRef]

Other

G. H. Golub and C. F. Van Loan, “Johns Hopkins studies in the mathematical sciences,” Matrix Computations (Johns Hopkins University, 1996).

While still useful here, this applies only to perturbation theory for the least squares problem. Our system is a perturbation to a constrained and bounded least-squares problem, and no such references for estimates on uncertainty in x could be found relating to this special system.

J. W. Demmel, Applied Numerical Linear Algebra (Society for Industrial and Applied Mathematics, 1997).
[CrossRef]

NASA, “Advanced environmental monitoring and control,” http://aemc.jpl.nasa.gov/activities/mms.cfm.

A. Verdin, Gas Analysis Instrumentation (MacMillan, 1973).

C. K. Laird, “Chemical analysis: gas analysis,” in Instrumentation Reference Book, Third ed., W.Boyes, ed. (Butterworth Heinemann, 2002).

U. Bonne, G. Yogesh, T. Osamu, and Z. Hans, “Gas sensors,” in Comprehensive Microsystems (Elsevier, 2008), pp. 375-432.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Sagnac interferometer.

Fig. 2
Fig. 2

Output of the interferometer at wavelengths (a) 532, (b) 543.5, and (c)  594 nm . The horizontal axis represents time.

Fig. 3
Fig. 3

Output of the interferometer at wavelengths (d) 612, (e) 632.8, and (f)  780 nm . The horizontal axis represents time.

Fig. 4
Fig. 4

Ratio of n to P as a function of wavelength with quadratic trendline.

Tables (5)

Tables Icon

Table 1 Dynamic Polarizability of Selected Atmospheric Gases a

Tables Icon

Table 2 Minimum Number Density to Elicit Interferometric Detection at λ = 555 nm , τ = 100 , and L = 0.5 m

Tables Icon

Table 3 Ratio of Refractive Index to Pressure at Various Wavelengths

Tables Icon

Table 4 Quantities of Ar, O 2 , and N 2 Detected via Refractometry a

Tables Icon

Table 5 Average Quantities of Ar, O 2 , and N 2 over 1000 Repetitions a

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

n min = λ τ L + 1 ,
n 2 1 n 2 + 2 = 4 π 3 N α ( λ ) ,
N ( λ , L ) = λ 2 π α ( λ ) τ L .
n ( λ ) 1 + 2 π P N A R T j x j α ( λ ) j Z j ,
2 π N A R T A . x = B ,
C n σ max σ min ,
n = m λ L .
δ m = 1 2 π arccos ( V p p 2 ξ V p p ) ,
( n P ) i = λ L Δ P ,
n P ( λ ) 2.9405 7.6371 × 10 4 λ + 4.8819 × 10 7 λ 2 .
Δ Ar = 0.092 , Δ N 2 = 0.11 , Δ O 2 = 0.17.
1 3 Δ Ar 2 + Δ N 2 2 + Δ O 2 2 = 2.22 % 2 % .
δ x x C n ( δ B B ) .

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