Abstract

A new method is described for inferring wavelength spectra from two-dimensional images of Fabry-Perot interference fringes. This new method addresses the practical difficulties that have been previously encountered in determining the fringe image’s center, magnification, and distortions accurately enough to fully exploit the spectral resolution provided by the etalon. The method proceeds in two steps. First, the instrument’s mapping of image position to interference order is characterized by use of images of a scene illuminated uniformly by a highly monochromatic laser. Then this information is applied to resample two-dimensional images of unknown radiation sources down to sets of one or more one-dimensional wavelength spectra. Discrete cross-correlation techniques are used at both stages of analysis.

© 2002 Optical Society of America

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References

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  1. G. G. Shepherd, C. W. Lake, J. R. Miller, L. L. Cogger, “A spatial spectral scanning technique for the Fabry-Perot spectrometer,” Appl. Opt. 4, 267–272 (1965).
    [CrossRef]
  2. G. G. Sivjee, T. J. Hallinan, G. R. Swenson, “Fabry-Perot-interferometer imaging system for thermospheric temperature and wind measurements,” Appl. Opt. 19, 2206–2209 (1980).
    [CrossRef] [PubMed]
  3. T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Symanow, D. H. Ceckowski, “Image plane detector for the dynamics explorer Fabry-Perot interferometer,” Appl. Opt. 22, 3503–3513 (1983).
    [CrossRef] [PubMed]
  4. R. Sekar, S. Gurubaran, R. Sridharan, “All sky imaging Fabry-Perot spectrometer for optical investigation of the upper atmosphere,” Indian J. Radio Space Phys. 22, 197–204 (1993).
  5. M. A. Biondi, D. P. Sipler, M. E. Zipf, J. L. Baumgardner, “All-sky Doppler interferometer for thermospheric dynamics studies,” Appl. Opt. 34, 1646–1654 (1995).
    [CrossRef] [PubMed]
  6. H. Nakajima, S. Okano, H. Fukunishi, T. Ono, “Observations of thermospheric wind velocities and temperatures by the use of a Fabry-Perot Doppler imaging system at Syowa Station, Antarctica,” Appl. Opt. 34, 8382–8395 (1995).
    [CrossRef] [PubMed]
  7. K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, T. Ogawa, “Three-channel imaging Fabry-Perot interferometer for measurement of midlatitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
    [CrossRef]
  8. J. Bland, R. B. Tully, “The Hawaii imaging Fabry-Perot interferometer (HIFI),” Astron. J. 98, 723–735 (1989).
    [CrossRef]
  9. M. Conde, R. W. Smith, “Phase compensation of a separation scanned, all-sky imaging Fabry-Perot spectrometer for auroral studies,” Appl. Opt. 36, 5441–5450 (1997).
    [CrossRef] [PubMed]
  10. M. Born, E. Wolf, Principles of Optics: electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford, 1980), Vol. 1.
  11. P. A. Wilksch, “Instrument function of the Fabry-Perot spectrometer,” Appl. Opt. 24, 1502–1511 (1985).
    [CrossRef] [PubMed]
  12. G. Hernandez, O. A. Mills, J. L. Smith, “TESS: a high-luminosity high-resolution twin-étalon scanning spectrometer,” Appl. Opt. 20, 3687–3688 (1981).
    [CrossRef] [PubMed]

2001 (1)

1997 (1)

1995 (2)

1993 (1)

R. Sekar, S. Gurubaran, R. Sridharan, “All sky imaging Fabry-Perot spectrometer for optical investigation of the upper atmosphere,” Indian J. Radio Space Phys. 22, 197–204 (1993).

1989 (1)

J. Bland, R. B. Tully, “The Hawaii imaging Fabry-Perot interferometer (HIFI),” Astron. J. 98, 723–735 (1989).
[CrossRef]

1985 (1)

1983 (1)

1981 (1)

1980 (1)

1965 (1)

Baumgardner, J. L.

Biondi, M. A.

Bland, J.

J. Bland, R. B. Tully, “The Hawaii imaging Fabry-Perot interferometer (HIFI),” Astron. J. 98, 723–735 (1989).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics: electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford, 1980), Vol. 1.

Ceckowski, D. H.

Cogger, L. L.

Conde, M.

Ejiri, M. K.

Fukunishi, H.

Gurubaran, S.

R. Sekar, S. Gurubaran, R. Sridharan, “All sky imaging Fabry-Perot spectrometer for optical investigation of the upper atmosphere,” Indian J. Radio Space Phys. 22, 197–204 (1993).

Hallinan, T. J.

Hays, P. B.

Hernandez, G.

Kadota, T.

Katoh, Y.

Kennedy, B. C.

Killeen, T. L.

Lake, C. W.

Miller, J. R.

Mills, O. A.

Nakajima, H.

Ogawa, T.

Okano, S.

Ono, T.

Otsuka, Y.

Sekar, R.

R. Sekar, S. Gurubaran, R. Sridharan, “All sky imaging Fabry-Perot spectrometer for optical investigation of the upper atmosphere,” Indian J. Radio Space Phys. 22, 197–204 (1993).

Shepherd, G. G.

Shiokawa, K.

Sipler, D. P.

Sivjee, G. G.

Smith, J. L.

Smith, R. W.

Sridharan, R.

R. Sekar, S. Gurubaran, R. Sridharan, “All sky imaging Fabry-Perot spectrometer for optical investigation of the upper atmosphere,” Indian J. Radio Space Phys. 22, 197–204 (1993).

Swenson, G. R.

Symanow, D. A.

Tully, R. B.

J. Bland, R. B. Tully, “The Hawaii imaging Fabry-Perot interferometer (HIFI),” Astron. J. 98, 723–735 (1989).
[CrossRef]

Wilksch, P. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics: electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford, 1980), Vol. 1.

Zipf, M. E.

Appl. Opt. (9)

G. G. Shepherd, C. W. Lake, J. R. Miller, L. L. Cogger, “A spatial spectral scanning technique for the Fabry-Perot spectrometer,” Appl. Opt. 4, 267–272 (1965).
[CrossRef]

G. G. Sivjee, T. J. Hallinan, G. R. Swenson, “Fabry-Perot-interferometer imaging system for thermospheric temperature and wind measurements,” Appl. Opt. 19, 2206–2209 (1980).
[CrossRef] [PubMed]

T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Symanow, D. H. Ceckowski, “Image plane detector for the dynamics explorer Fabry-Perot interferometer,” Appl. Opt. 22, 3503–3513 (1983).
[CrossRef] [PubMed]

M. A. Biondi, D. P. Sipler, M. E. Zipf, J. L. Baumgardner, “All-sky Doppler interferometer for thermospheric dynamics studies,” Appl. Opt. 34, 1646–1654 (1995).
[CrossRef] [PubMed]

H. Nakajima, S. Okano, H. Fukunishi, T. Ono, “Observations of thermospheric wind velocities and temperatures by the use of a Fabry-Perot Doppler imaging system at Syowa Station, Antarctica,” Appl. Opt. 34, 8382–8395 (1995).
[CrossRef] [PubMed]

K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, T. Ogawa, “Three-channel imaging Fabry-Perot interferometer for measurement of midlatitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
[CrossRef]

M. Conde, R. W. Smith, “Phase compensation of a separation scanned, all-sky imaging Fabry-Perot spectrometer for auroral studies,” Appl. Opt. 36, 5441–5450 (1997).
[CrossRef] [PubMed]

P. A. Wilksch, “Instrument function of the Fabry-Perot spectrometer,” Appl. Opt. 24, 1502–1511 (1985).
[CrossRef] [PubMed]

G. Hernandez, O. A. Mills, J. L. Smith, “TESS: a high-luminosity high-resolution twin-étalon scanning spectrometer,” Appl. Opt. 20, 3687–3688 (1981).
[CrossRef] [PubMed]

Astron. J. (1)

J. Bland, R. B. Tully, “The Hawaii imaging Fabry-Perot interferometer (HIFI),” Astron. J. 98, 723–735 (1989).
[CrossRef]

Indian J. Radio Space Phys. (1)

R. Sekar, S. Gurubaran, R. Sridharan, “All sky imaging Fabry-Perot spectrometer for optical investigation of the upper atmosphere,” Indian J. Radio Space Phys. 22, 197–204 (1993).

Other (1)

M. Born, E. Wolf, Principles of Optics: electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford, 1980), Vol. 1.

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration showing the major components of the imaging spectrometer instruments that are discussed here. Also shown is the geometry of the quantities x, y, and θ. The azimuthal angle ϕ is omitted for simplicity; m does not depend on this angle.

Fig. 2
Fig. 2

These panels show model fringes A M [m(x, y)] depicted in blue, superimposed over observed laser calibration fringes B c (x, y), depicted in orange. The four panels (clockwise from top left) show the effects of incorrect choices for model parameters y 0, γ x , β y , and ε, respectively. The intensity scale is arbitrary.

Fig. 3
Fig. 3

Variation of goodness of fit, κ, between the observed fringes B c (x, y) and the model fringes A M [m(x, y)], as a function of the fractional part of the value of the m 0 model parameter. The vertical dashed line indicates the value chosen by the fitting program as the best estimate of m 0 for this iteration.

Fig. 4
Fig. 4

Fringes of the λ630.0-nm airglow and auroral emission taken from Inuvik, Canada, on 9 February 2001, at 1148 UT.

Fig. 5
Fig. 5

Spectrum derived from Fig. 3 by use of Eq. (11). The wavelength interval spans one free spectral range (Δλ), corresponding to ∼10 pm for this etalon.

Fig. 6
Fig. 6

Difference between fitting functions of the forms given by expression (6) and Eq. (7) to calibration fringes B c (x, y), as explained in the text.

Equations (15)

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Am=τ1+4R/1-R2sin2πm,
m=2μt cosθλ+ϕrλπ,
Δλ=λ22μt.
mx, ym0-Lθ2x, yμtλ,
θ=Lθx, y=αx-x02+y-y021/2,
mx, ym0-βx-x02+y-y02,
u=x-x0+γx|x-x0|, v=y-y0+γy|y-y0|.
ψx, y=βxu2+βyv2+βxyuv.
mx, y=m0-ψx, y+εψ2x, y,
χ2=x=1Nxy=1NyAMmx, y-Bcx, yBcx, y2.
κ=x=1Nxy=1NyAM¯mx, y×Bc¯x, y,
Bx, y=δAΩ 0 Ax, y, λSix, y, λdλ,
mx, y, λo=mx, y, λcλcλo,
Ax, y, λo=Amx, y, λcλcλo.
Bλo=x=1Nxy=1NyAx, y, λo×Bx, yx=1Nxy=1Ny Ax, y, λo

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