Abstract

A technique for the inversion of satellite auroral brightness observations is developed, which takes into account the backscattering of light from the snow-covered ground and atmospheric scattering. The theory includes parallax effects. Parallax arises when a point in the aurora is observed from different angles against a background with a variable brightness. It is shown that observations from a spinning satellite at any given angle from nadir are sufficient to recover the auroral form.

© 1981 Optical Society of America

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References

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  1. P. B. Hays, C. D. Anger, Appl. Opt. 17, 1898 (1978).
    [CrossRef] [PubMed]
  2. P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
    [CrossRef]
  3. V. V. Sobolev, Treatise on Radiative Transfer (Van Nostrand, Princeton, N. J., 1963).
  4. W. R. Kuhn, U. Michigan Department of Atmospheric and Oceanic Sciences; private communication (1980).
  5. L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km,” Report AFCRL-68-0153, AFCRL, Bedford, Mass. (1968).
  6. M. H. Rees, U. Alaska Geophysical Institute; private communication (1980).

1978 (1)

1973 (1)

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Anger, C. D.

Elterman, L.

L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km,” Report AFCRL-68-0153, AFCRL, Bedford, Mass. (1968).

Garignan, G. R.

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Hays, P. B.

P. B. Hays, C. D. Anger, Appl. Opt. 17, 1898 (1978).
[CrossRef] [PubMed]

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Kennedy, B. C.

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Kuhn, W. R.

W. R. Kuhn, U. Michigan Department of Atmospheric and Oceanic Sciences; private communication (1980).

Rees, M. H.

M. H. Rees, U. Alaska Geophysical Institute; private communication (1980).

Shepherd, G. G.

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Sobolev, V. V.

V. V. Sobolev, Treatise on Radiative Transfer (Van Nostrand, Princeton, N. J., 1963).

Walker, J. C. G.

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Appl. Opt. (1)

Radio Sci. (1)

P. B. Hays, G. R. Garignan, B. C. Kennedy, G. G. Shepherd, J. C. G. Walker, Radio Sci. 8, 369 (1973).
[CrossRef]

Other (4)

V. V. Sobolev, Treatise on Radiative Transfer (Van Nostrand, Princeton, N. J., 1963).

W. R. Kuhn, U. Michigan Department of Atmospheric and Oceanic Sciences; private communication (1980).

L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km,” Report AFCRL-68-0153, AFCRL, Bedford, Mass. (1968).

M. H. Rees, U. Alaska Geophysical Institute; private communication (1980).

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Figures (10)

Fig. 1
Fig. 1

Three-dimensional geometry.

Fig. 2
Fig. 2

Two-dimensional geometry.

Fig. 3
Fig. 3

One-dimensional weighting function for θ equal to −30, 0, 30, and 60°, respectively.

Fig. 4
Fig. 4

Inverse weighting functions for (a) zero optical depth and (b) optical depth equal to 0.250.

Fig. 5
Fig. 5

Auroral source and satellite observations at −30, 0, 30, 60°. Measured values have been interpolated using a quadratic form.

Fig. 6
Fig. 6

Ratio of the measured brightness with an optical depth equal to 0.250 to the measured brightness in the case of no scattering for (—) 0.2-μm particles and (- - -) 5-μm particles.

Fig. 7
Fig. 7

Recovery of the source function when the parallax correction is not included in the theory. Scattering effects were not included in this simulation.

Fig. 8
Fig. 8

Curve labeled τ = 0 shows the auroral form recovered with the appropriate weighting function for zero optical depth. Curves labeled τ = 0.250 show the recovered source function from simulated measurements with optical depth equal to 0.250. Inverse weighting functions used were those for an optical depth of zero.

Fig. 9
Fig. 9

Auroral brightnesses recovered from VAE observations in 10° bins centered at 0 and ±30°. Data at both wavelengths were obtained simultaneously by channel 1 (3371 Å) and channel 2 (4278 Å), respectively. Inversion was effected independently for each angle assuming zero optical depth and the auroral altitude at 110 km.

Fig. 10
Fig. 10

Auroral brightnesses obtained by averaging the inverted data at 0, ±10, ±20, and ±30°.

Equations (11)

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B s ( r g , η ) = z π B a ( r a ) σ ( λ , α , η , ζ , ϕ 0 ) R 3 d r a
σ ( λ , α , η , ζ , ϕ 0 ) = ( C 3 F η ) [ 1 exp ( τ 0 / η ) ] + ( 3 X 1 ) F τ 0 × exp ( τ 0 / η ) + 1 4 [ χ ( γ ) 3 ζ 2 ] + X 1 η ζ ] { 1 exp [ τ 0 ( 1 η + 1 ζ ) ] } 1 η + ζ + α [ I ¯ + 2 H ¯ + exp ( τ 0 / ζ ) ] exp ( τ 0 / η ) ,
C = 1 2 ( 1 + 3 2 ζ ) 2 F , F = 1 2 [ ( 1 α ) R 0 ( τ 0 , ζ ) 4 + ( 3 X 1 ) ( 1 α ) τ 0 ] , R 0 ( τ 0 , ζ ) = 1 + 3 2 ζ + ( 1 3 2 ζ ) exp ( τ 0 / ζ ) , X 1 ( λ ) = 3 2 0 π χ ( γ , λ ) cos γ sin γ d γ , I ¯ ( τ ) τ = 0 = C 3 4 ζ , H ¯ ( τ ) τ = 0 = F 1 4 , cos γ = η ζ + ( 1 η 2 ) ( 1 ζ 2 ) cos ( ϕ ϕ 0 ) ;
B m ( r , θ ) = B a ( r ) + B a ( r a ) W 2 ( | r g r a | , θ ) d r a ,
W 2 ( | r g r a | , θ ) = z π σ ( λ , α , η , R , ϕ 0 ) R 3 .
B ̂ m ( f , θ ) = B ̂ a ( f ) + B ̂ a ( f ) W 2 ( f , θ ) exp [ 2 π i f · c ( θ ) ] ,
B a ( r ) = B m ( r , θ ) B m ( r , θ ) W 2 1 ( | r r | , θ ) d r ,
W 2 1 = F 1 { W 2 ( f , θ ) exp [ 2 π i f · c ( θ ) ] 1 + W 2 ( f , θ ) exp [ 2 π i f · c ( θ ) ] } ,
B a ( y ) = B m ( y , θ ) B m ( y , θ ) W 1 1 ( | y y | , θ ) d y ,
W 1 1 = F 1 { W 1 ( f y , θ ) exp [ 2 π i f y c ( θ ) ] 1 + W 1 ( f y , θ ) exp [ 2 π i f y c ( θ ) ] } ,
W 1 ( | y g y a | , θ ) = z π σ ( λ , α , η , z R ) tan 1 x a y a dx a R 3 ,

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