Abstract

To insure that long-term determinations of Doppler width and shift—derived from observations of atmospheric emissions—are internally consistent and reliable, we have developed a method to both continuously and nonintrusively determine and monitor the instrumental constants of the Fabry–Perot spectrometer making the observations. We have used this method at our isolated field experiment at South Pole, Antarctica, because the instrument is only accessible to us for a few days every year. Here we report both the method and the Fabry–Perot stability results for the past 22 years of operation. The method involves the description of real Fabry–Perot instrumental constants as a small departure from those of an ideal Fabry–Perot. In general, this model is applicable for most observations. However, experimentally, there are times when the small-departure model is not applicable, thus indicating how to best reduce the observations into physical quantities for the utmost consistency in the geophysical results.

© 2011 Optical Society of America

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References

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  1. C. Fabry and H. Buisson, “Variation de la surface optique avec la longueur d’onde dans la réflexion sur les couches métalliques minces,” J. Phys. 7, 417–429 (1908).
    [CrossRef]
  2. P. Giacomo, “Méthode directe de mesure des caractéristiques d’un systéme interférentiel de Fabry–Perot,” Compt. Rend. 235, 1627–1629 (1952).
  3. W. R. Bennett, “Deconvolution of spectral lines by Fourier analysis,” Appl. Opt. 17, 3344–3345 (1978).
    [CrossRef] [PubMed]
  4. S. Mar, M. A. Gigosos, and J. M. Moreno, “Deconvolution of spectral lines: an improved method,” Appl. Opt. 18, 2914–2916 (1979).
    [CrossRef] [PubMed]
  5. T. E. Schnackenberg, “Measurement of a Fabry–Perot interferometer reflectivity,” Master’s thesis (University of Washington, 2006).
  6. G. Hernandez and O. A. Mills, “Feedback stabilized Fabry–Perot interferometer,” Appl. Opt. 12, 126–130 (1973).
    [CrossRef] [PubMed]
  7. P. Jacquinot and C. Dufour, “Conditions optiques d’emploi des cellules photo-électriques dans les spectrographes et les interféromètres,” J. Res. CRNS 6, 91–103 (1948).
  8. G. Hernandez, Fabry–Perot Interferometers (Cambridge University, 1986).
  9. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).
  10. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980).
  11. G. Hernandez, “Analytical description of a Fabry–Perot spectrometer. 3. Off-axis behavior and interference filters,” Appl. Opt. 18, 3364–3365 (1979).
    [CrossRef] [PubMed]
  12. J. F. Conner, R. W. Smith, and G. Hernandez, “Techniques for deriving Doppler temperatures from multiple-line Fabry–Perot profiles: an analysis,” Appl. Opt. 32, 4437–4444 (1993).
    [CrossRef] [PubMed]

1993 (1)

1979 (2)

1978 (1)

1973 (1)

1952 (1)

P. Giacomo, “Méthode directe de mesure des caractéristiques d’un systéme interférentiel de Fabry–Perot,” Compt. Rend. 235, 1627–1629 (1952).

1948 (1)

P. Jacquinot and C. Dufour, “Conditions optiques d’emploi des cellules photo-électriques dans les spectrographes et les interféromètres,” J. Res. CRNS 6, 91–103 (1948).

1908 (1)

C. Fabry and H. Buisson, “Variation de la surface optique avec la longueur d’onde dans la réflexion sur les couches métalliques minces,” J. Phys. 7, 417–429 (1908).
[CrossRef]

Bennett, W. R.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

Buisson, H.

C. Fabry and H. Buisson, “Variation de la surface optique avec la longueur d’onde dans la réflexion sur les couches métalliques minces,” J. Phys. 7, 417–429 (1908).
[CrossRef]

Conner, J. F.

Dufour, C.

P. Jacquinot and C. Dufour, “Conditions optiques d’emploi des cellules photo-électriques dans les spectrographes et les interféromètres,” J. Res. CRNS 6, 91–103 (1948).

Fabry, C.

C. Fabry and H. Buisson, “Variation de la surface optique avec la longueur d’onde dans la réflexion sur les couches métalliques minces,” J. Phys. 7, 417–429 (1908).
[CrossRef]

Giacomo, P.

P. Giacomo, “Méthode directe de mesure des caractéristiques d’un systéme interférentiel de Fabry–Perot,” Compt. Rend. 235, 1627–1629 (1952).

Gigosos, M. A.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980).

Hernandez, G.

Jacquinot, P.

P. Jacquinot and C. Dufour, “Conditions optiques d’emploi des cellules photo-électriques dans les spectrographes et les interféromètres,” J. Res. CRNS 6, 91–103 (1948).

Mar, S.

Mills, O. A.

Moreno, J. M.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980).

Schnackenberg, T. E.

T. E. Schnackenberg, “Measurement of a Fabry–Perot interferometer reflectivity,” Master’s thesis (University of Washington, 2006).

Smith, R. W.

Appl. Opt. (5)

Compt. Rend. (1)

P. Giacomo, “Méthode directe de mesure des caractéristiques d’un systéme interférentiel de Fabry–Perot,” Compt. Rend. 235, 1627–1629 (1952).

J. Phys. (1)

C. Fabry and H. Buisson, “Variation de la surface optique avec la longueur d’onde dans la réflexion sur les couches métalliques minces,” J. Phys. 7, 417–429 (1908).
[CrossRef]

J. Res. CRNS (1)

P. Jacquinot and C. Dufour, “Conditions optiques d’emploi des cellules photo-électriques dans les spectrographes et les interféromètres,” J. Res. CRNS 6, 91–103 (1948).

Other (4)

G. Hernandez, Fabry–Perot Interferometers (Cambridge University, 1986).

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980).

T. E. Schnackenberg, “Measurement of a Fabry–Perot interferometer reflectivity,” Master’s thesis (University of Washington, 2006).

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Figures (3)

Fig. 1
Fig. 1

Spectrum of the He–Ne laser, consisting of the coherent addition of sixty 8 s scans. The scan encompasses about 2.8 orders of the etalon.

Fig. 2
Fig. 2

Fourier series decomposition of the laser measurement of Fig. 1. The top panel shows the logarithm of the absolute value of the coefficients c n , while the lower panel shows the linear values of these coefficients. Because of the large range in the scale, only the coefficients near the zero crossings are shown for the lower panel. In both cases, the zero crossings associated with the aperture are well defined, making it possible to precisely determine the aperture.

Fig. 3
Fig. 3

Results of the determination of reflectivity (top), aperture size (middle), and apparent temperature (bottom) of a FPS. The graph shows a small and slow change in the reflectivity over the 22-year period as well as the two sizes of aperture used. It also shows a decrease in the apparent temperature past 1992, as we began to understand and utilize the diagnostic capabilities of the present method.

Equations (9)

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Y i = a + b n = 1 N c n cos [ 2 π n ( x i x 0 ) / X ] ,
c n = R n exp ( n 2 G g 2 ) sinc ( 2 n d f * ) sinc ( 2 n f * ) exp ( n 2 G s 2 ) .
ln | c n | = n ln R n 2 G g 2 + ln | sinc ( 2 n d f * ) | + ln | sinc ( 2 n f * ) | n 2 G s 2 .
ln | c n | = n ln R + ln | sinc ( 2 n d f * ) | + ln | sinc ( 2 n f * ) | n 2 ( G s 2 + G g 2 ) .
ln sinc ( x ) = ln sin ( π x ) ln ( π x ) = ( π x ) 2 / 6 ( π x ) 4 / 180 ( π x ) 6 / 2835 , 0 x < 1 .
ln | c n | = n ln R + ln | sinc ( 2 n f * ) | n 2 ( G s 2 + G g 2 + H d f * 2 ) ,
ln | c n | = n ln R + ln | sinc ( 2 n f * ) | n 2 G τ 2 .
ln | c n | = n ln R n 2 γ τ + ln | sinc ( 2 n f * ) | .
c n = R n exp ( n 2 γ τ ) sinc ( 2 n f * ) .

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