Abstract

A new method of instrument calibration and data analysis is presented for single-etalon interferometric measurements of winds, temperatures, and emission line intensities. The technique has been developed for the multichannel Fabry-Perot interferometer on the Dynamics Explorer spacecraft. A numerical representation of the instrumental transfer function is used based on a truncated Fourier series with empirically determined coefficients. The numerical form is compared with the conventional analytic form. The Fourier coefficients describing the instrument function are generated at the wavelength of a stable He–Ne laser and are translated to other wavelengths using an interpolation technique for both phase and power. A quasi-linear least-squares fitting process involving matrices provides for a rapid and accurate data reduction.

© 1984 Optical Society of America

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References

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  1. R. Chabbal, J. Rech, C.N.R.S. 24, 138 (1953).
  2. E. C. Turgeon, G. G. Shepherd, Planet. Space Sci. 9, 925 (1962).
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    [CrossRef]
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    [CrossRef] [PubMed]
  7. P. B. Hays, T. L. Killeen, B. C. Kennedy, Space Sci. Instrum. 5, 394 (1981).
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    [CrossRef] [PubMed]
  9. D. P. Sipler, M. A. Biondi, Geophys. Res. Lett. 15, 373 (1978).
    [CrossRef]
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    [CrossRef]
  11. T. L. Killeen, P. B. Hays, J. DeVos, Appl. Opt. 20, 2616 (1981).
    [CrossRef] [PubMed]

1983 (1)

1981 (2)

T. L. Killeen, P. B. Hays, J. DeVos, Appl. Opt. 20, 2616 (1981).
[CrossRef] [PubMed]

P. B. Hays, T. L. Killeen, B. C. Kennedy, Space Sci. Instrum. 5, 394 (1981).

1980 (1)

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

1978 (1)

D. P. Sipler, M. A. Biondi, Geophys. Res. Lett. 15, 373 (1978).
[CrossRef]

1971 (1)

1967 (2)

1966 (1)

1962 (1)

E. C. Turgeon, G. G. Shepherd, Planet. Space Sci. 9, 925 (1962).
[CrossRef]

1953 (1)

R. Chabbal, J. Rech, C.N.R.S. 24, 138 (1953).

Andrew, K. L.

Barlow, F. E.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

Biondi, M. A.

D. P. Sipler, M. A. Biondi, Geophys. Res. Lett. 15, 373 (1978).
[CrossRef]

Ceckowski, D. H.

Chabbal, R.

R. Chabbal, J. Rech, C.N.R.S. 24, 138 (1953).

DeVos, J.

Hays, P. B.

Hernandez, G.

Kellock, S. J.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

Kennedy, B. C.

Killeen, T. L.

Larson, H. P.

McWhirter, I.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

Rech, J.

R. Chabbal, J. Rech, C.N.R.S. 24, 138 (1953).

Rees, D.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

Roble, R. G.

Rounce, P. A.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

Shepherd, G. G.

G. G. Shepherd, J. Phys. 28, 301 (1967).
[CrossRef]

E. C. Turgeon, G. G. Shepherd, Planet. Space Sci. 9, 925 (1962).
[CrossRef]

Sipler, D. P.

D. P. Sipler, M. A. Biondi, Geophys. Res. Lett. 15, 373 (1978).
[CrossRef]

Symanow, D. A.

Turgeon, E. C.

E. C. Turgeon, G. G. Shepherd, Planet. Space Sci. 9, 925 (1962).
[CrossRef]

Appl. Opt. (5)

C.N.R.S. (1)

R. Chabbal, J. Rech, C.N.R.S. 24, 138 (1953).

Geophys. Res. Lett. (1)

D. P. Sipler, M. A. Biondi, Geophys. Res. Lett. 15, 373 (1978).
[CrossRef]

J. Phys. (1)

G. G. Shepherd, J. Phys. 28, 301 (1967).
[CrossRef]

J. Phys. E. (1)

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, J. Phys. E. 13, 763 (1980).
[CrossRef]

Planet. Space Sci. (1)

E. C. Turgeon, G. G. Shepherd, Planet. Space Sci. 9, 925 (1962).
[CrossRef]

Space Sci. Instrum. (1)

P. B. Hays, T. L. Killeen, B. C. Kennedy, Space Sci. Instrum. 5, 394 (1981).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the geometry of the optical path in a multichannel Fabry-Perot interferometer.

Fig. 2
Fig. 2

Pressure scan calibration for the multichannel FPI on Dynamics Explorer. The measured transfer function obtained by scanning the instrument using light from a frequency-stabilized He–Ne laser is plotted with pressure (dry nitrogen) and wavelength.

Fig. 3
Fig. 3

Power spectrum from the Fourier decomposition of the DE-FPI instrument calibration for channels 1 and 10. Also shown is an analytic power spectrum for comparison. See text for details.

Fig. 4
Fig. 4

Illustration of the wavelength translation technique for the instrument transfer function. The power spectrum, excluding reflectivity damping terms, is plotted as a function of n1 and m2, where m and n are integers, λ1 is the primary wavelength of the calibration, and λ2 is the secondary wavelength at which the translated coefficients are required. See text for further details.

Fig. 5
Fig. 5

Contour maps showing systematic error incurred through the use of the matrix technique described in the text for (a) a wind measurement and (b) a temperature measurement. Errors are plotted as functions of the accuracy of the guessed input values (Vo,To) used in calculating the matrix. The accuracies are given by VVo and TTo, where V and T are the correct values. the DE-FPI instrument for a typical shown were calculated using measurement of wind and temperature in the earth’s theremosphere (see text).

Fig. 6
Fig. 6

Typical spectrogram obtained at 6300 Å in the earth’s nightglow using the multichannel FPI on Dynamics Explorer. Each channel samples a spectral interval of 0.015 Å. The secondary peak seen in channels 10–12 corresponds to detection of the adjacent order of interference. Spectrogram analysis detailed in Table I.

Tables (1)

Tables Icon

Table I Spectrogram Analysis Comparison

Equations (37)

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I ( λ ) = R 0 0 Y ( λ ) ψ ( λ - λ r ) d λ ,
N i = A o Ω i t Q i T o i · 10 6 4 π 0 T F ( λ ) ψ ( λ , θ i ) Y ( λ ) d λ + B i ,
θ i = tan - 1 [ 1 f o ( r i 2 + r i + 1 2 2 ) 1 / 2 ] ,
Y ( λ ) = R o exp - ( λ - λ l Δ λ T ) T π Δ λ T + R λ | o .
Δ λ T = ( 2 k T m ) ½ λ t c .
ψ ( λ , θ i ) = 1 - R 1 + R { 1 + 2 n = 1 R n sinc ( n N S ) · sinc ( n N A i ) · exp ( - n 2 D 2 4 ) · cos [ 2 π n μ ( λ - λ r Δ λ 0 ) cos θ i ] }
A FSR = π f o 2 λ d o
0 T F ( λ ) d λ = Δ λ F ¯ ,
N i = C o i t [ Δ λ F ¯ R λ | o ( 1 - R 1 + R ) + T F o ( λ l ) × R o ( 1 + 2 n = 1 R n sinc ( n N s ) sinc ( n N A i ) × exp { - n 2 [ D 2 + G 2 ( T ) ] } · cos [ 2 π n μ ( λ l - λ r Δ λ o ) cos θ i ] ) ] + B i ,
G ( T ) = π c 2 k T m λ l Δ λ o = π Δ λ T Δ λ o .
M = λ l Δ λ o = 2 μ d o λ l = M o + y ( o ) ,
cos [ 2 π n μ ( λ l - λ r ) Δ λ o cos θ i ] = cos { 2 π n [ M o + y ( o ) - i N A i + M o v c ] } = cos { 2 π n [ y ( o ) - y i + M o v c ] } ,
ψ i ( λ ) = a o i + n = 1 [ a n i cos 2 π n Δ λ o ( λ - λ r + ϕ i ) + b n i sin 2 π n Δ λ o ( λ - λ r + ϕ i ) ] ,
N i = C o 1 t ( Δ λ F ¯ R λ | o a o i ( 1 - R 1 + R ) + T F o ( λ l ) × R o { a o i + n = 1 [ a n i cos 2 π n Δ λ o ( λ l - λ r + ϕ i ) + b n i sin 2 π n Δ λ o ( λ l - λ r + ϕ i ) ] exp [ - n 2 G 2 ( T ) ] } ) + B i
2 π n μ Δ λ o ( λ l ) cos θ i = 4 π n μ o d o λ o ( 1 + δ μ μ o + δ d d o - δ λ λ o - θ i 2 2 + ) ,
a o 1 = 1.0             b o 1 = 0.0 , a n i = 2 R n sinc ( n N S ) sinc ( n N A i ) exp - ( n 2 D 2 ) · cos 4 π μ o d o n λ o ( 1 - θ i 2 2 ) , b n i = 2 R n sinc ( n N s ) sinc ( n N A i ) exp - ( n 2 D 2 ) · sin 4 π μ o d o n λ o ( 1 - θ i 2 2 ) .
a o = 1 2 Δ P FSR j = 1 N tot - 1 ( P j + 1 - P j ) ( f j + 1 + f j ) , a n = 1 π n j = 1 N tot - 1 { f j + 1 sin ( 2 π n P j + 1 Δ P FSR ) - f j sin ( 2 π n P j Δ P FSR ) - f j + 1 - f j n ( P j + 1 - P j ) Δ P FSR 2 π [ 2 cos ( 2 π n P j Δ P FSR ) sin 2 ( n π Δ j Δ P FSR ) + sin ( 2 π n P j Δ P FSR ) sin ( 2 π n Δ j Δ P FSR ) ] } . b n = 1 π n j = 1 N tot - 1 { f j cos ( 2 π n P j Δ P FSR ) - f j + 1 cos ( 2 π n P j + 1 Δ P FSR ) + f j + 1 - f j n ( P j + 1 - P j ) Δ P FSR 2 π [ cos ( 2 π n P j Δ P FSR ) sin 2 ( π n Δ j Δ P FSR ) - 2 sin ( 2 π n P j Δ P FSR ) · sin 2 ( π n Δ j Δ P FSR ) ] } ,
a n i = a n sin ϕ i + b n cos ϕ i , b n i = a n cos ϕ i + b n sin ϕ i ,
C o i ( λ ) = N i cal a o i Δ λ F ¯ R λ | cal t cal · 1 + R 1 - R ,
R λ | cal
a n i ( λ ) = 2 R n ( λ ) sinc ( n λ C 1 ) sinc ( n λ C 2 ) exp - [ ( n λ ) 2 C 3 ] × cos [ n λ C 4 ( 1 - θ i 2 2 ) ]
Φ n i ( n λ ) = tan - 1 ( b n i a n i ) , P n i ( n λ ) = { [ a n i R n ( λ ) ] 2 + [ b n i R n ( λ ) ] 2 } 1 / 2 ,
P m i ( λ 2 ) = ( P n + 1 - P n i ) ( m λ 2 - n λ 1 ) ( n + 1 λ 1 ) + P n i .
N i = C o 1 T F o R o t n = 0 16 { a n i exp [ - n 2 G 2 ( T ) ] cos n ( X + 2 π M o v c ) + b n i exp [ - n 2 G 2 ( T ) ] sin n ( X + 2 π M o v c ) } + a o i B B G + B i ,
X = 2 π ( λ o - λ r + ϕ i ) Δ λ o
B B G = C o 1 t Δ λ F ¯ R λ | o ( 1 - R 1 + R ) .
N i ( v o + v , T o + Δ T ) - B i = C o 1 T F o R o t { F i ( o ) ( v o , T o ) + v F i ( 1 ) ( v o , T o ) } + Δ T F i ( 2 ) ( v o , T o ) } + B B G a o i ,
F i ( o ) = n = 0 16 [ a n i exp [ - n 2 G 2 ( T o ) ] cos n ( X + 2 π M o v o c ) + b n i exp [ - n 2 G 2 ( T o ) ] sin n ( X + 2 π M o v o c ) ] ,
F i ( 1 ) = - 2 π M o c n = 0 16 { n a n i exp [ - n 2 G 2 ( T o ) ] sin n ( X + 2 π M o v o c ) - n b n i exp [ - n 2 G 2 ( T o ) ] cos n ( X + 2 π M o v o c ) } ,
F i ( 2 ) = - G 2 ( T o ) T o n = 0 16 { n 2 a n i exp [ - n 2 G 2 ( T o ) ] cos n ( X + 2 π M o v o c ) + n 2 b n i exp [ - n 2 G 2 ( T o ) ] sin n ( X + 2 π M o v o c ) } .
x 1 = C o 1 T F o R o t x 2 = v x 1 , x 3 = Δ T x 1 , x 4 = B B G , }
N i = N i - B i = k = 1 4 A i k x k             i = 1 N c H .
A i k = F i ( k - 1 ) ( v o , T o )             1 k 3 ,
A i k = a o i             for k = 4.
x = ( A T A ) - 1 A T N ,
δ x k 2 = i = 1 N c H ( C k i ) 2 N i .
v , T , R o , and R λ | o

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