Abstract

The field-compensation principle, which has been applied to interferometric spectroscopy independently by P. Connes and by L. Mertz, allows the useful solid angle accepted by an interferometer to be increased by an amount that can be very large. This paper is concerned with a particular application of this principle using the Michelson interferometer. Although the technique is difficult to utilize where a wide range of path differences is required, the interferometer takes an extremely simple form when constructed for a narrow range of path difference about a fixed central path difference. While such an instrument has a limited use in spectroscopy, there is one type of measurement which it is admirably suited to perform: the determination of the width of a single isolated atomic line whose analytical shape is known. A description is given of the theory and construction of a wide-angle Michelson interferometer now being used for the measurement of Doppler temperatures from the width of the 5577 Å atomic oxygen line in the nightglow and aurora. This line is known to be accurately gaussian in shape, and is well-isolated from other lines, making it an ideal subject for this instrument.

© 1966 Optical Society of America

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References

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  1. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
    [Crossref]
  2. R. Chabbal, Thèses, Université de Paris, 1958.
  3. J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 873 (1963).
  4. G. G. Shepherd, C. W. Lake, J. R. Miller, and L. L. Cogger, Appl. Opt. 4, 267 (1965).
    [Crossref]
  5. P. Fellgett, J. Phys. Radium 19, 237 (1958).
    [Crossref]
  6. J. Connes, J. Phys. Radium 19, 197 (1958).
    [Crossref]
  7. H. A. Gebbie, J. Phys. Radium 19, 230 (1958).
    [Crossref]
  8. J. Connes and H. Gush, J. Phys. Radium 20, 915 (1959).
    [Crossref]
  9. P. Connes, J. Phys. Radium 19, 215 (1958).
    [Crossref]
  10. A. Girard, Appl. Opt. 2, 79 (1963).
    [Crossref]
  11. B. A. Tinsley, J. Opt. Soc. Am. 55, 599A (1965).
  12. P. Jacquinot, Rep. Progr. Phys. 23, 267 (1960).
    [Crossref]
  13. D. M. Hunten, Ann. Geophys. 17, 249 (1961).
  14. J. A. Nilson and G. G. Shepherd, Planetary Space Sci. 5, 299 (1961).
    [Crossref]
  15. E. C. Turgeon and G. G. Shepherd, Planetary Space Sci. 9, 295 (1962).
    [Crossref]
  16. A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planetary Space Sci. 13, 551 (1965).
    [Crossref]
  17. G. Hansen, Optik 12, 5 (1955).
  18. G. Hansen and W. Kinder, Optik 15, 560 (1958).
  19. The authors are indebted to Dr. W. H. Steel for drawing these references to their attention.
  20. P. Connes, Rev. Opt. 35, 37 (1956).
  21. L. Mertz, preprints of papers presented at the Fifth Meeting and Conference of the I. C. O., Stockholm, Aug. 1959. Ed.: E. Ingelstam.
  22. P. Connes, J. Phys. Radium 19, 262 (1958).
    [Crossref]
  23. A. A. Michelson, Studies in Optics, (University of Chicago Press, Chicago, 1927).
  24. Of course, for a grating spectrometer, the angle φ determines only the slit width; the slit length must also be considered in comparing the two instruments.
  25. The assembly was fabricated by Hilger and Watts, Inc.
  26. R. L. Hilliard and G. G. Shepherd, Planetary Space Sci. (to be published, 1966).

1965 (3)

G. G. Shepherd, C. W. Lake, J. R. Miller, and L. L. Cogger, Appl. Opt. 4, 267 (1965).
[Crossref]

B. A. Tinsley, J. Opt. Soc. Am. 55, 599A (1965).

A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planetary Space Sci. 13, 551 (1965).
[Crossref]

1963 (2)

1962 (1)

E. C. Turgeon and G. G. Shepherd, Planetary Space Sci. 9, 295 (1962).
[Crossref]

1961 (2)

D. M. Hunten, Ann. Geophys. 17, 249 (1961).

J. A. Nilson and G. G. Shepherd, Planetary Space Sci. 5, 299 (1961).
[Crossref]

1960 (1)

P. Jacquinot, Rep. Progr. Phys. 23, 267 (1960).
[Crossref]

1959 (1)

J. Connes and H. Gush, J. Phys. Radium 20, 915 (1959).
[Crossref]

1958 (6)

P. Connes, J. Phys. Radium 19, 215 (1958).
[Crossref]

P. Fellgett, J. Phys. Radium 19, 237 (1958).
[Crossref]

J. Connes, J. Phys. Radium 19, 197 (1958).
[Crossref]

H. A. Gebbie, J. Phys. Radium 19, 230 (1958).
[Crossref]

G. Hansen and W. Kinder, Optik 15, 560 (1958).

P. Connes, J. Phys. Radium 19, 262 (1958).
[Crossref]

1956 (1)

P. Connes, Rev. Opt. 35, 37 (1956).

1955 (1)

G. Hansen, Optik 12, 5 (1955).

1954 (1)

Bens, A. R.

A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planetary Space Sci. 13, 551 (1965).
[Crossref]

Chabbal, R.

Cogger, L. L.

A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planetary Space Sci. 13, 551 (1965).
[Crossref]

G. G. Shepherd, C. W. Lake, J. R. Miller, and L. L. Cogger, Appl. Opt. 4, 267 (1965).
[Crossref]

Connes, J.

J. Connes and H. Gush, J. Phys. Radium 20, 915 (1959).
[Crossref]

J. Connes, J. Phys. Radium 19, 197 (1958).
[Crossref]

Connes, P.

P. Connes, J. Phys. Radium 19, 215 (1958).
[Crossref]

P. Connes, J. Phys. Radium 19, 262 (1958).
[Crossref]

P. Connes, Rev. Opt. 35, 37 (1956).

Fellgett, P.

P. Fellgett, J. Phys. Radium 19, 237 (1958).
[Crossref]

Gebbie, H. A.

H. A. Gebbie, J. Phys. Radium 19, 230 (1958).
[Crossref]

Girard, A.

Gush, H.

J. Connes and H. Gush, J. Phys. Radium 20, 915 (1959).
[Crossref]

Hansen, G.

G. Hansen and W. Kinder, Optik 15, 560 (1958).

G. Hansen, Optik 12, 5 (1955).

Hilliard, R. L.

R. L. Hilliard and G. G. Shepherd, Planetary Space Sci. (to be published, 1966).

Hunten, D. M.

D. M. Hunten, Ann. Geophys. 17, 249 (1961).

Jacquinot, P.

P. Jacquinot, Rep. Progr. Phys. 23, 267 (1960).
[Crossref]

P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
[Crossref]

Kinder, W.

G. Hansen and W. Kinder, Optik 15, 560 (1958).

Lake, C. W.

Mack, J. E.

McNutt, D. P.

Mertz, L.

L. Mertz, preprints of papers presented at the Fifth Meeting and Conference of the I. C. O., Stockholm, Aug. 1959. Ed.: E. Ingelstam.

Michelson, A. A.

A. A. Michelson, Studies in Optics, (University of Chicago Press, Chicago, 1927).

Miller, J. R.

Nilson, J. A.

J. A. Nilson and G. G. Shepherd, Planetary Space Sci. 5, 299 (1961).
[Crossref]

Roesler, F. L.

Shepherd, G. G.

G. G. Shepherd, C. W. Lake, J. R. Miller, and L. L. Cogger, Appl. Opt. 4, 267 (1965).
[Crossref]

A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planetary Space Sci. 13, 551 (1965).
[Crossref]

E. C. Turgeon and G. G. Shepherd, Planetary Space Sci. 9, 295 (1962).
[Crossref]

J. A. Nilson and G. G. Shepherd, Planetary Space Sci. 5, 299 (1961).
[Crossref]

R. L. Hilliard and G. G. Shepherd, Planetary Space Sci. (to be published, 1966).

Tinsley, B. A.

B. A. Tinsley, J. Opt. Soc. Am. 55, 599A (1965).

Turgeon, E. C.

E. C. Turgeon and G. G. Shepherd, Planetary Space Sci. 9, 295 (1962).
[Crossref]

Ann. Geophys. (1)

D. M. Hunten, Ann. Geophys. 17, 249 (1961).

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
[Crossref]

B. A. Tinsley, J. Opt. Soc. Am. 55, 599A (1965).

J. Phys. Radium (6)

P. Connes, J. Phys. Radium 19, 262 (1958).
[Crossref]

P. Fellgett, J. Phys. Radium 19, 237 (1958).
[Crossref]

J. Connes, J. Phys. Radium 19, 197 (1958).
[Crossref]

H. A. Gebbie, J. Phys. Radium 19, 230 (1958).
[Crossref]

J. Connes and H. Gush, J. Phys. Radium 20, 915 (1959).
[Crossref]

P. Connes, J. Phys. Radium 19, 215 (1958).
[Crossref]

Optik (2)

G. Hansen, Optik 12, 5 (1955).

G. Hansen and W. Kinder, Optik 15, 560 (1958).

Planetary Space Sci. (3)

J. A. Nilson and G. G. Shepherd, Planetary Space Sci. 5, 299 (1961).
[Crossref]

E. C. Turgeon and G. G. Shepherd, Planetary Space Sci. 9, 295 (1962).
[Crossref]

A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planetary Space Sci. 13, 551 (1965).
[Crossref]

Rep. Progr. Phys. (1)

P. Jacquinot, Rep. Progr. Phys. 23, 267 (1960).
[Crossref]

Rev. Opt. (1)

P. Connes, Rev. Opt. 35, 37 (1956).

Other (7)

L. Mertz, preprints of papers presented at the Fifth Meeting and Conference of the I. C. O., Stockholm, Aug. 1959. Ed.: E. Ingelstam.

The authors are indebted to Dr. W. H. Steel for drawing these references to their attention.

R. Chabbal, Thèses, Université de Paris, 1958.

A. A. Michelson, Studies in Optics, (University of Chicago Press, Chicago, 1927).

Of course, for a grating spectrometer, the angle φ determines only the slit width; the slit length must also be considered in comparing the two instruments.

The assembly was fabricated by Hilger and Watts, Inc.

R. L. Hilliard and G. G. Shepherd, Planetary Space Sci. (to be published, 1966).

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Figures (8)

Fig. 1
Fig. 1

The conventional Michelson interferometer. Position 1 of M1′ is for zero path difference, and the emergent rays are collinear. Position 2 corresponds to a nonzero path difference, and the emergent rays have a relative displacement.

Fig. 2
Fig. 2

Wide-angle Michelson interferometer. The front-surfaced mirror M2 has been replaced by a back-surfaced slab of refractive index n. The dotted line indicates the apparent path of the ray in the slab as reflected from the vertical image of M2. Although there is a nonzero path difference, the emergent rays are collinear.

Fig. 3
Fig. 3

Showing the geometry of the reflection in the slab in detail. The path in glass is indicated by the solid line, and the superimposed path in air is shown as the dotted line.

Fig. 4
Fig. 4

Showing the effect of a finite aperture on the WAMI. The geometry is shown in the inset. The spiral is the locus of the tip of a vector representing the intensity and phase of the fringes transmitted by the aperture. Moving up the spiral corresponds to opening up the aperture. The aperture half-angle φm is shown in radians by the open arrows. The change in path difference from the center of the aperture to its edge is indicated, in wavelengths, by the solid arrows. The spiral is drawn for a path difference of 5.0 cm and a wavelength of 5577 Å

Fig. 5
Fig. 5

Showing how the aperture visibility parameter Va changes with aperture half-angle φm for various values of e = t′ − t/n. e is the displacement from the normal incidence QZP condition. The path difference is 5 cm. The curve marked MI is for a conventional Michelson interferometer.

Fig. 6
Fig. 6

The same data as in Fig. 5, plotted to show the variation of Va with e for various φm.

Fig. 7
Fig. 7

Showing the configuration of the optics used for the constructed instrument.

Fig. 8
Fig. 8

Some sample recordings obtained with the WAMI. The upper trace indicates the source radiance as obtained by the monitor photometer. (a) A scan across an auroral form, (b) nightglow, and (c) rapidly fluctuating aurora.

Equations (28)

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B σ B 0 exp [ - ( σ - σ 0 ) 2 4 ln 2 / w 2 ] ,
w = ( 7.16 × 10 - 7 ) σ 0 ( T / M ) , 1 2
V = exp [ - Q T Δ 2 ] ,
Q = ( ( 7.16 ) 2 × 10 - 14 / 4 ln 2 ) ( π 2 σ 0 2 / M ) .
Q = 3.66 × 10 - 5 ° K - 1 cm - 2 .
Δ 0 ( QZP ) = 2 ( n t - t / n ) .
Δ = 2 n a - 2 b - s .
a = t / cos φ n ,             b = t / cos φ ,
s = 2 sin φ ( t tan φ n - t tan φ ) .
Δ = 2 ( t n cos φ n - t cos φ ) .
Δ - Δ 0 = A φ + B φ 2 + C φ 3 + D φ 4 + E φ 5 +
t = t / n + e .
cos φ n = ( 1 / n ) [ n 2 - φ 2 + φ 4 / 3 ] 1 2 .
( Δ - Δ 0 ) WAMI = e φ 2 + ( t / 4 n 2 ) ( n - 1 / n ) φ 4 .
( Δ - Δ 0 ) WAMI = e φ 2 + Δ 0 φ 4 / 8 n 2 .
( Δ 0 - Δ ) MI = Δ 0 φ 2 / 2 - Δ 0 φ 4 / 24.
( Δ - Δ 0 ) WAMI Δ 0 φ 4 / 8 n 2 .
φ d φ = n [ 1 / 2 ( Δ - Δ 0 ) Δ 0 ] 1 2 d Δ .
φ d φ = n ( δ / 2 N δ 0 ) 1 2 .
A exp ( i α ) = 1 + 1 - 1 2 exp ( i δ ) + 2 - 1 2 exp ( i 2 δ ) + M - 1 2 exp ( i M δ ) .
w Δ W = 2 ( ln 2 ) 1 2 / π 0.5.
R WAMI = σ π Δ W / 2 ( ln 2 ) 1 2 2 σ Δ W .
R M I = 2 σ Δ M .
F = S Ω τ B ,
( φ M 2 ) WAMI / ( φ M 2 ) MI = [ 2 n 2 Δ 0 / ( Δ - Δ 0 ) ] 1 2 ,
( φ M 2 ) WAMI / ( φ M 2 ) MI = 2 n ( R ) 1 2 .
V obs = V a V i e - Q T Δ 2
d Δ / d λ = 2 t d n / d λ .