Abstract

Fourier spectroscopy has enjoyed considerable success in the measurement of sources that are stationary with respect to time. A technique for the study of time-varying spectral features, by use of Fourier spectroscopy, is presented. With this technique, the multiplex advantage is retained and the available measurement time is utilized efficiently. The technique consists of obtaining a series of interferograms, separated sequentially in time, according to the time-resolution capability of the detection system. The interferogram signal is recorded over a time interval, Δt, corresponding to a particular time tj, in the evolution of the source. The entire series of interferograms is obtained in a single scan of a Michelson interferometer. The S/N may be improved by continued exposure at the same optical path difference, corresponding to the same tj in the evolution of the source. The time-sequenced interferograms are transformed to obtain the recovered spectra at successive time intervals. As a demonstration of the technique, the spectral evolution of a N2/O2 gas mixture subjected to high-energy-electron irradiation is given in 50 µs intervals. The spectra clearly show the change in time of the fundamental sequence of NO (X2Π, Δν = 1), and the (001 → 000) vibration–rotation bands of N2O and NO2.

© 1975 Optical Society of America

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References

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  1. P. Fellgett, thesis (University of Cambridge, 1951).
  2. P. Jacquinot and C. Doufour, J. Rech. du C. N. R. S. 6, 91 (1948).
  3. G. Guelachvili, dissertation, Doctor of Science, Physics (University of Paris, South, 1972).
  4. R. E. Murphy and H. Sakai, Aspen International Conference on Fourier Spectroscopy (Aspen, Colo., 1970); p. 301.
  5. R. Hanel, M. Forman, T. Meilleur, R. Westcott, and J. Pritchard, Appl. Opt. 8, 2059 (1969).
    [Crossref] [PubMed]
  6. J. Connes and P. Connes, J. Opt. Soc. Am. 56, 896 (1966).
    [Crossref]
  7. J. O. Lephardt and G. Vilcins, J. Opt. Soc. Am. 64, 1363A (1974).
  8. G. Davidson and R. R. O’Neil, Air Force Cambridge Research Laboratories Report, No. AFCRL-64-466 (1964).
  9. A. Cohn and G. Caledonia, J. Appl. Phys. 41, 3767 (1970).
    [Crossref]
  10. M. Forman, J. Opt. Soc. Am. 56, 908 (1966).

1974 (1)

J. O. Lephardt and G. Vilcins, J. Opt. Soc. Am. 64, 1363A (1974).

1970 (1)

A. Cohn and G. Caledonia, J. Appl. Phys. 41, 3767 (1970).
[Crossref]

1969 (1)

1966 (2)

J. Connes and P. Connes, J. Opt. Soc. Am. 56, 896 (1966).
[Crossref]

M. Forman, J. Opt. Soc. Am. 56, 908 (1966).

1948 (1)

P. Jacquinot and C. Doufour, J. Rech. du C. N. R. S. 6, 91 (1948).

Caledonia, G.

A. Cohn and G. Caledonia, J. Appl. Phys. 41, 3767 (1970).
[Crossref]

Cohn, A.

A. Cohn and G. Caledonia, J. Appl. Phys. 41, 3767 (1970).
[Crossref]

Connes, J.

Connes, P.

Davidson, G.

G. Davidson and R. R. O’Neil, Air Force Cambridge Research Laboratories Report, No. AFCRL-64-466 (1964).

Doufour, C.

P. Jacquinot and C. Doufour, J. Rech. du C. N. R. S. 6, 91 (1948).

Fellgett, P.

P. Fellgett, thesis (University of Cambridge, 1951).

Forman, M.

Guelachvili, G.

G. Guelachvili, dissertation, Doctor of Science, Physics (University of Paris, South, 1972).

Hanel, R.

Jacquinot, P.

P. Jacquinot and C. Doufour, J. Rech. du C. N. R. S. 6, 91 (1948).

Lephardt, J. O.

J. O. Lephardt and G. Vilcins, J. Opt. Soc. Am. 64, 1363A (1974).

Meilleur, T.

Murphy, R. E.

R. E. Murphy and H. Sakai, Aspen International Conference on Fourier Spectroscopy (Aspen, Colo., 1970); p. 301.

O’Neil, R. R.

G. Davidson and R. R. O’Neil, Air Force Cambridge Research Laboratories Report, No. AFCRL-64-466 (1964).

Pritchard, J.

Sakai, H.

R. E. Murphy and H. Sakai, Aspen International Conference on Fourier Spectroscopy (Aspen, Colo., 1970); p. 301.

Vilcins, G.

J. O. Lephardt and G. Vilcins, J. Opt. Soc. Am. 64, 1363A (1974).

Westcott, R.

Appl. Opt. (1)

J. Appl. Phys. (1)

A. Cohn and G. Caledonia, J. Appl. Phys. 41, 3767 (1970).
[Crossref]

J. Opt. Soc. Am. (3)

M. Forman, J. Opt. Soc. Am. 56, 908 (1966).

J. Connes and P. Connes, J. Opt. Soc. Am. 56, 896 (1966).
[Crossref]

J. O. Lephardt and G. Vilcins, J. Opt. Soc. Am. 64, 1363A (1974).

J. Rech. du C. N. R. S. (1)

P. Jacquinot and C. Doufour, J. Rech. du C. N. R. S. 6, 91 (1948).

Other (4)

G. Guelachvili, dissertation, Doctor of Science, Physics (University of Paris, South, 1972).

R. E. Murphy and H. Sakai, Aspen International Conference on Fourier Spectroscopy (Aspen, Colo., 1970); p. 301.

G. Davidson and R. R. O’Neil, Air Force Cambridge Research Laboratories Report, No. AFCRL-64-466 (1964).

P. Fellgett, thesis (University of Cambridge, 1951).

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Figures (6)

FIG. 1
FIG. 1

A schematic diagram of data recording (above the dashed line) and playback (below). The infrared source is excited by 32 kV electron irradiation of a nitrogen–oxygen gas mixture. The interferogram signal and reference signal are processed by time gates to produce time-sequenced signals as the interferometer optical path difference is varied.

FIG. 2
FIG. 2

The upper oscilloscope trace shows the interferogram signal produced by a single electron pulse at an optical path difference of 0.01 cm. The electron–gun trigger pulse triggers the oscilloscope and corresponds to the time t0. The interferogram-signal sample pulse at tj and background reference signal sample pulse at tb are shown below the signal trace. The duration of the sample time gates is 50 µs. The lower oscilloscope trace shows the interferogram signal at an optical path difference of 0. 01 cm averaged over 50 pulses of electron irradiation of the N2/O2 gas mixture.

FIG. 3
FIG. 3

Time–sequenced interferograms of the source taken at 1, 2, 3, 4, and 5 ms after initial perturbation by electron impact. Each interferogram consists of 1 ms samples that have been integrated for 1 s. The electron irradiation was terminated at 3.1 ms.

FIG. 4
FIG. 4

Recovered spectra, giving relative intensity vs wave number vs time at 500 µs intervals over a time span of 11 ms, showing excitation of NO, N2O, and NO2. The time scale is represented as progressing perpendicularly into the plane of the page. The earliest spectrum corresponds to 250 jus after initial electron bombardment of the N2/O2 gas mixture. Spectra are not corrected for the relative spectral response of the interferometer.

FIG. 5
FIG. 5

Recovered spectra, giving relative intensity vs wave number vs time at 500 µs intervals over a time span of 11 ms, showing relaxation of NO, N2O, and NO2. These are the same spectra as are shown in Fig. 4, but with the time scale reversed, so as to show the back side of the spectra.

FIG. 6
FIG. 6

Relative intensity vs wave number vs time at 50 µs intervals over a time span of 1.2 ms, showing the detailed relaxation of the NO (Δυ = 1) vibration–rotation bands. This corresponds to the same spectra as shown in Fig. 5, but with increased time resolution. The over-all system time response is 60 µs so that successive spectra are not completely independent

Equations (7)

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

F ( t ) = f ( t ) g ( t t ) d t ,
F ( t ) = t 1 / 4 f max t + 1 / 4 f max f ( t ) d t .
F ( x , t ) = [ 0 B ( σ , t ) cos ( 2 π σ x ) d σ ] g ( t t ) d t ,
B ( σ , t j ) = F ( x , t j ) cos ( 2 π σ x ) d x .
F ( x , t j ) = 0 B ( σ , t j ) cos ( 2 π σ x ) d σ ,
B ( σ , t j ) = x 0 = 0 x N = X F ( x , t j ) cos ( 2 π σ x ) d x ,
δ σ = 1 / 2 X .