Abstract

An inversion algorithm capable of reconstructing the volume emission rate of thermospheric airglow features from satellite photometry has been developed. The accuracy and resolution of this technique are investigated using simulated data, and the inversions of several sets of observations taken by the Visible Airglow Experiment are presented.

© 1984 Optical Society of America

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References

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  1. P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
    [CrossRef]
  2. R. G. Roble, P. B. Hays, “A Technique for Recovering the Vertical Number Density Profile of Atmospheric Gasses from Planetary Occultation Data,” Planet. Space Sci. 20, 1727 (1972)
    [CrossRef]
  3. R. Gordon, R. Bender, G. T. Herman, “Algebraic Reconstruction Techniques (ART) and Three-Dimensional Electron Microscopy and X-ray Photography,” J. Theoret. Biol. 29, 471 (1970).
    [CrossRef]
  4. R. Gordon, G. T. Herman, “Three-Dimensional Reconstruction from Projections, a Review of Algorithms,” Int. Rev. Cytol. 38, 11 (1974).
  5. P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
    [CrossRef]
  6. R. J. Thomas, T. M. Donahue, “Analysis of OGO-6 Observations of the OI 5577 Å Tropical Nightglow,” J. Geophys. Res. 77, 3557 (1972).
    [CrossRef]
  7. B. Wasser, T. M. Donahue, “Atomic Oxygen Between 80 and 120 km: Evidence for a Latitudinal Variation in Vertical Transport near the Mesopause,” J. Geophys. Res. 84, 1297 (1979).
    [CrossRef]
  8. C. G. Fesen, P. B. Hays, “Two-Dimensional Inversion Technique for Satellite Airglow Data,” Appl. Opt. 21, 3784 (1982).
    [CrossRef] [PubMed]
  9. A. M. Cormack, “Representation of a Function by its Line Integrals with Some Radiological Applications,” J. Appl. Phys. 34, 2722 (1963).
    [CrossRef]
  10. A. M. Cormack, “Representation of a Function by its Line Integrals, with some Radiological Applications, II,” J. Appl. Phys. 35, 2906 (1964).
    [CrossRef]
  11. I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, 1983).
  12. A. Vallance Jones, Aurora (Reidel, Hingham, Mass., 1974).
    [CrossRef]
  13. V. J. Abreu, P. B. Hays, “Parallax and Atmospheric Scattering Effects on the Inversion of Satellite Auroral Observations,” Appl. Opt., 20, 2203 (1981).
    [CrossRef] [PubMed]
  14. M. H. Rees, V. J. Abreu, “Auroral Photometry from the Atmosphere Explorer Satellite,” J. Geophys. Res. 89, 317 (1984).
    [CrossRef]

1984 (1)

M. H. Rees, V. J. Abreu, “Auroral Photometry from the Atmosphere Explorer Satellite,” J. Geophys. Res. 89, 317 (1984).
[CrossRef]

1982 (1)

1981 (1)

1979 (1)

B. Wasser, T. M. Donahue, “Atomic Oxygen Between 80 and 120 km: Evidence for a Latitudinal Variation in Vertical Transport near the Mesopause,” J. Geophys. Res. 84, 1297 (1979).
[CrossRef]

1978 (1)

P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
[CrossRef]

1974 (1)

R. Gordon, G. T. Herman, “Three-Dimensional Reconstruction from Projections, a Review of Algorithms,” Int. Rev. Cytol. 38, 11 (1974).

1973 (1)

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

1972 (2)

R. G. Roble, P. B. Hays, “A Technique for Recovering the Vertical Number Density Profile of Atmospheric Gasses from Planetary Occultation Data,” Planet. Space Sci. 20, 1727 (1972)
[CrossRef]

R. J. Thomas, T. M. Donahue, “Analysis of OGO-6 Observations of the OI 5577 Å Tropical Nightglow,” J. Geophys. Res. 77, 3557 (1972).
[CrossRef]

1970 (1)

R. Gordon, R. Bender, G. T. Herman, “Algebraic Reconstruction Techniques (ART) and Three-Dimensional Electron Microscopy and X-ray Photography,” J. Theoret. Biol. 29, 471 (1970).
[CrossRef]

1964 (1)

A. M. Cormack, “Representation of a Function by its Line Integrals, with some Radiological Applications, II,” J. Appl. Phys. 35, 2906 (1964).
[CrossRef]

1963 (1)

A. M. Cormack, “Representation of a Function by its Line Integrals with Some Radiological Applications,” J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

Abreu, V. J.

M. H. Rees, V. J. Abreu, “Auroral Photometry from the Atmosphere Explorer Satellite,” J. Geophys. Res. 89, 317 (1984).
[CrossRef]

V. J. Abreu, P. B. Hays, “Parallax and Atmospheric Scattering Effects on the Inversion of Satellite Auroral Observations,” Appl. Opt., 20, 2203 (1981).
[CrossRef] [PubMed]

Bender, R.

R. Gordon, R. Bender, G. T. Herman, “Algebraic Reconstruction Techniques (ART) and Three-Dimensional Electron Microscopy and X-ray Photography,” J. Theoret. Biol. 29, 471 (1970).
[CrossRef]

Carignan, G.

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

Cormack, A. M.

A. M. Cormack, “Representation of a Function by its Line Integrals, with some Radiological Applications, II,” J. Appl. Phys. 35, 2906 (1964).
[CrossRef]

A. M. Cormack, “Representation of a Function by its Line Integrals with Some Radiological Applications,” J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

Donahue, T. M.

B. Wasser, T. M. Donahue, “Atomic Oxygen Between 80 and 120 km: Evidence for a Latitudinal Variation in Vertical Transport near the Mesopause,” J. Geophys. Res. 84, 1297 (1979).
[CrossRef]

R. J. Thomas, T. M. Donahue, “Analysis of OGO-6 Observations of the OI 5577 Å Tropical Nightglow,” J. Geophys. Res. 77, 3557 (1972).
[CrossRef]

Fesen, C. G.

Gordon, R.

R. Gordon, G. T. Herman, “Three-Dimensional Reconstruction from Projections, a Review of Algorithms,” Int. Rev. Cytol. 38, 11 (1974).

R. Gordon, R. Bender, G. T. Herman, “Algebraic Reconstruction Techniques (ART) and Three-Dimensional Electron Microscopy and X-ray Photography,” J. Theoret. Biol. 29, 471 (1970).
[CrossRef]

Gradshteyn, I.

I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, 1983).

Hays, P. B.

C. G. Fesen, P. B. Hays, “Two-Dimensional Inversion Technique for Satellite Airglow Data,” Appl. Opt. 21, 3784 (1982).
[CrossRef] [PubMed]

V. J. Abreu, P. B. Hays, “Parallax and Atmospheric Scattering Effects on the Inversion of Satellite Auroral Observations,” Appl. Opt., 20, 2203 (1981).
[CrossRef] [PubMed]

P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
[CrossRef]

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

R. G. Roble, P. B. Hays, “A Technique for Recovering the Vertical Number Density Profile of Atmospheric Gasses from Planetary Occultation Data,” Planet. Space Sci. 20, 1727 (1972)
[CrossRef]

Herman, G. T.

R. Gordon, G. T. Herman, “Three-Dimensional Reconstruction from Projections, a Review of Algorithms,” Int. Rev. Cytol. 38, 11 (1974).

R. Gordon, R. Bender, G. T. Herman, “Algebraic Reconstruction Techniques (ART) and Three-Dimensional Electron Microscopy and X-ray Photography,” J. Theoret. Biol. 29, 471 (1970).
[CrossRef]

Kennedy, B. C.

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

Rees, M. H.

M. H. Rees, V. J. Abreu, “Auroral Photometry from the Atmosphere Explorer Satellite,” J. Geophys. Res. 89, 317 (1984).
[CrossRef]

Roble, R. G.

P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
[CrossRef]

R. G. Roble, P. B. Hays, “A Technique for Recovering the Vertical Number Density Profile of Atmospheric Gasses from Planetary Occultation Data,” Planet. Space Sci. 20, 1727 (1972)
[CrossRef]

Rusch, D. W.

P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
[CrossRef]

Ryzhik, I.

I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, 1983).

Shepherd, G. G.

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

Thomas, R. J.

R. J. Thomas, T. M. Donahue, “Analysis of OGO-6 Observations of the OI 5577 Å Tropical Nightglow,” J. Geophys. Res. 77, 3557 (1972).
[CrossRef]

Vallance Jones, A.

A. Vallance Jones, Aurora (Reidel, Hingham, Mass., 1974).
[CrossRef]

Walker, J. C. G.

P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
[CrossRef]

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

Wasser, B.

B. Wasser, T. M. Donahue, “Atomic Oxygen Between 80 and 120 km: Evidence for a Latitudinal Variation in Vertical Transport near the Mesopause,” J. Geophys. Res. 84, 1297 (1979).
[CrossRef]

Appl. Opt. (2)

Int. Rev. Cytol. (1)

R. Gordon, G. T. Herman, “Three-Dimensional Reconstruction from Projections, a Review of Algorithms,” Int. Rev. Cytol. 38, 11 (1974).

J. Appl. Phys. (2)

A. M. Cormack, “Representation of a Function by its Line Integrals with Some Radiological Applications,” J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

A. M. Cormack, “Representation of a Function by its Line Integrals, with some Radiological Applications, II,” J. Appl. Phys. 35, 2906 (1964).
[CrossRef]

J. Geophys. Res. (3)

R. J. Thomas, T. M. Donahue, “Analysis of OGO-6 Observations of the OI 5577 Å Tropical Nightglow,” J. Geophys. Res. 77, 3557 (1972).
[CrossRef]

B. Wasser, T. M. Donahue, “Atomic Oxygen Between 80 and 120 km: Evidence for a Latitudinal Variation in Vertical Transport near the Mesopause,” J. Geophys. Res. 84, 1297 (1979).
[CrossRef]

M. H. Rees, V. J. Abreu, “Auroral Photometry from the Atmosphere Explorer Satellite,” J. Geophys. Res. 89, 317 (1984).
[CrossRef]

J. Theoret. Biol. (1)

R. Gordon, R. Bender, G. T. Herman, “Algebraic Reconstruction Techniques (ART) and Three-Dimensional Electron Microscopy and X-ray Photography,” J. Theoret. Biol. 29, 471 (1970).
[CrossRef]

Planet. Space Sci. (1)

R. G. Roble, P. B. Hays, “A Technique for Recovering the Vertical Number Density Profile of Atmospheric Gasses from Planetary Occultation Data,” Planet. Space Sci. 20, 1727 (1972)
[CrossRef]

Radio Sci. (1)

P. B. Hays, G. Carignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, “The Visible Airglow Experiment on Atmospheric Explorer,” Radio Sci. 8, 369 (1973).
[CrossRef]

Rev. Geophys. Space Phys. (1)

P. B. Hays, D. W. Rusch, R. G. Roble, J. C. G. Walker, “The OI (6300A) Airglow,” Rev. Geophys. Space Phys. 16, 225 (1978).
[CrossRef]

Other (2)

I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, 1983).

A. Vallance Jones, Aurora (Reidel, Hingham, Mass., 1974).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Limb scans taken by a spinning satellite. Every fourth line of sight of VAE channel 1 is shown.

Fig. 2
Fig. 2

Geometry of the Cormack inversion. Every line integral f is the sum of all g(r,θ) along a path specified by distance p and angle ϕ.

Fig. 3
Fig. 3

(a) Imaginary airglow feature. Units are arbitrary but may be thought of as tens of photons cm−3 sec−1. (b) Column brightness observed by the instrument as a function of p and ϕ. Units are arbitrary but may be thought of as log10 rayleighs. (c) Estimate recovered by the inversion.

Fig. 4
Fig. 4

Estimate recovered when noise and field of view broadening were added to the simulation.

Fig. 5
Fig. 5

4278-Å emission from the 1NG band system of N 2 +. (a) The interpolated data are plotted logarithmically. (b) The estimated volume emission rate from the Cormack inversion is plotted linearly.

Fig. 6
Fig. 6

Altitude profile taken through the peak of the aurora seen in Fig. 5.

Fig. 7
Fig. 7

6300-Å emission of atomic oxygen arising from the (3P–1D) transition.

Fig. 8
Fig. 8

5577-Å emission from the (1D–1S) transition of atomic oxygen. The dayglow seen coming in from the right in (a) was excluded in performing the inversion displayed in (b).

Equations (6)

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G n ( r ) = - 1 π d d r r r F n ( p ) T n ( p / r ) d p p ( p 2 - r 2 ) 1 / 2 ,
G n ( r ) = - 1 π r d d p F n ( p ) T n ( p / r ) d p ( p 2 - r 2 ) 1 / 2 .
g ( r ) = - 1 π r d d p f ( p ) d p ( p 2 - r 2 ) 1 / 2
- π G n ( r ) = 2 A r r 1 r 2 x T n ( x ) d x ( x 2 - 1 ) 1 / 2 + B r 1 r 2 T n ( x ) d x ( x 2 - 1 ) 1 / 2 .
I m , n = r 1 r 2 x m T n ( x ) d x ( x 2 - 1 ) 1 / 2 .
I m , 0 = x m - 1 ( x 2 - 1 ) 1 / 2 m + m - 1 m I m - 2 , 0

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