Abstract

Using Fourier analysis, the periodicity of rotational coherent anti-Stokes Raman scattering spectra is shown to offer a new possibility for gas-temperature evaluation. In a simple way, this approach can be used for data reduction leading to a rapid temperature-evaluation procedure.

© 1985 Optical Society of America

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References

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  1. J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, AIAA paper 80-1542 (1980).
  2. D. V. Murphy, R. K. Chang, Opt. Lett. 6, 233 (1981).
    [CrossRef] [PubMed]
  3. J. W. Fleming, A. B. Harvey, W. T. Barnes, in Temperature: Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. V, pp. 589–594.
  4. J. B. Zheng, J. B. Snow, D. V. Murphy, A. Leipertz, R. K. Chang, R. L. Farrow, Opt. Lett. 9, 341 (1984).
    [CrossRef] [PubMed]
  5. J. J. Barrett, A. B. Harvey, J. Opt. Soc. Am. 65, 392 (1975).
    [CrossRef]
  6. J. J. Barrett, Opt. Eng. 16, 85 (1977).
  7. E. J. Burlbaw, R. L. Armstrong, Appi. Opt. 22, 2860 (1983).
    [CrossRef]
  8. W. M. Tolles, J. W. Nibler, J. R. McDonald, A. B. Harvey, Appl. Spectrosc. 31, 253 (1977).
    [CrossRef]
  9. M. A. Yuratich, Mol. Phys. 38, 625 (1979).
    [CrossRef]
  10. K. S. Jammu, G. E. St. John, H. L. Welsh, Can. J. Phys. 44, 797 (1966).
    [CrossRef]
  11. J. Bendtsen, J. Raman Spectrosc. 2, 133 (1974).
    [CrossRef]

1984

1983

E. J. Burlbaw, R. L. Armstrong, Appi. Opt. 22, 2860 (1983).
[CrossRef]

1981

1979

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[CrossRef]

1977

1975

1974

J. Bendtsen, J. Raman Spectrosc. 2, 133 (1974).
[CrossRef]

1966

K. S. Jammu, G. E. St. John, H. L. Welsh, Can. J. Phys. 44, 797 (1966).
[CrossRef]

Armstrong, R. L.

E. J. Burlbaw, R. L. Armstrong, Appi. Opt. 22, 2860 (1983).
[CrossRef]

Barnes, W. T.

J. W. Fleming, A. B. Harvey, W. T. Barnes, in Temperature: Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. V, pp. 589–594.

Barrett, J. J.

Bendtsen, J.

J. Bendtsen, J. Raman Spectrosc. 2, 133 (1974).
[CrossRef]

Burlbaw, E. J.

E. J. Burlbaw, R. L. Armstrong, Appi. Opt. 22, 2860 (1983).
[CrossRef]

Chang, R. K.

Eckbreth, A. C.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, AIAA paper 80-1542 (1980).

Farrow, R. L.

Fleming, J. W.

J. W. Fleming, A. B. Harvey, W. T. Barnes, in Temperature: Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. V, pp. 589–594.

Hall, R. J.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, AIAA paper 80-1542 (1980).

Harvey, A. B.

W. M. Tolles, J. W. Nibler, J. R. McDonald, A. B. Harvey, Appl. Spectrosc. 31, 253 (1977).
[CrossRef]

J. J. Barrett, A. B. Harvey, J. Opt. Soc. Am. 65, 392 (1975).
[CrossRef]

J. W. Fleming, A. B. Harvey, W. T. Barnes, in Temperature: Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. V, pp. 589–594.

Jammu, K. S.

K. S. Jammu, G. E. St. John, H. L. Welsh, Can. J. Phys. 44, 797 (1966).
[CrossRef]

John, G. E. St.

K. S. Jammu, G. E. St. John, H. L. Welsh, Can. J. Phys. 44, 797 (1966).
[CrossRef]

Leipertz, A.

McDonald, J. R.

Murphy, D. V.

Nibler, J. W.

Shirley, J. A.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, AIAA paper 80-1542 (1980).

Snow, J. B.

Tolles, W. M.

Verdieck, J. F.

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, AIAA paper 80-1542 (1980).

Welsh, H. L.

K. S. Jammu, G. E. St. John, H. L. Welsh, Can. J. Phys. 44, 797 (1966).
[CrossRef]

Yuratich, M. A.

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[CrossRef]

Zheng, J. B.

Appi. Opt.

E. J. Burlbaw, R. L. Armstrong, Appi. Opt. 22, 2860 (1983).
[CrossRef]

Appl. Spectrosc.

Can. J. Phys.

K. S. Jammu, G. E. St. John, H. L. Welsh, Can. J. Phys. 44, 797 (1966).
[CrossRef]

J. Opt. Soc. Am.

J. Raman Spectrosc.

J. Bendtsen, J. Raman Spectrosc. 2, 133 (1974).
[CrossRef]

Mol. Phys.

M. A. Yuratich, Mol. Phys. 38, 625 (1979).
[CrossRef]

Opt. Eng.

J. J. Barrett, Opt. Eng. 16, 85 (1977).

Opt. Lett.

Other

J. A. Shirley, R. J. Hall, J. F. Verdieck, A. C. Eckbreth, AIAA paper 80-1542 (1980).

J. W. Fleming, A. B. Harvey, W. T. Barnes, in Temperature: Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. V, pp. 589–594.

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Figures (5)

Fig. 1
Fig. 1

Calculated N2 rotational CARS spectrum for a temperature of 500 K.

Fig. 2
Fig. 2

(a) Real and (b) imaginary parts of the Fourier series of the rotational CARS spectrum in Fig. 1.

Fig. 3
Fig. 3

Temperature dependence of the real part of the Fourier spectrum, which contains all spectral information within the first 64 channels [see Fig. 2(a)]. When normalized appropriately, several of the channels can be used for temperature evaluation.

Fig. 4
Fig. 4

Envelope of the rotational CARS spectrum reconstructed from 11 channels of the Fourier spectrum (channels 65 to 76) for 7 different N2 temperatures. The envelope for 300 K is the left-most one, and that for 900 K the right-most one. Both maximum position and FWHM value of each envelope give a clear temperature indication.

Fig. 5
Fig. 5

Real part of the Fourier coefficients for A, N2 and for B, O2. The separability of both gas components becomes clear when the appropriate channel sequences are selected.

Equations (11)

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χ ( 3 ) ( x ) 2 = 1 Δ ω 2 j a j 2 ( x - x j ) 2 + γ j 2 .
S ( x ) = 0 1 K ( x - x ) χ ( 3 ) ( x ) 2 d x .
s m = 0 1 S ( x ) exp ( - i 2 π m x ) d x ,
s m = k m c m ,
c m = 0 1 χ ( 3 ) ( x ) 2 exp ( - i 2 π m x ) d x ,
c m = π j a j 2 γ j exp ( - 2 π m γ j ) exp ( - i 2 π m x j ) .
c m = π γ exp ( - 2 π m γ ) c m ,
c m = j a j 2 exp ( - i 2 π m j / M ) .
c M + m = j a j 2 exp ( - i 2 π m j / M ) exp ( - 12 π j ) ,
c M + m = c m .
c M - m = c m * .

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