Abstract

We compare four types of instruments for recording monochromatic astronomical images: filters; slitless spectrographs; multislit spectrographs; and interferometers. Each of these instruments has been used on the sodium emission cloud of Io, with varying degrees of success. Multislit spectrographs and interferometers encode the signal, and it can be extracted with a noise level close to that for photon statistics. This is not normally the case for filters and slitless spectrographs. On balance, we find that a Mach-Zehnder interferometer provides the best system for imaging faint monochromatic signals on a brighter continuum background.

© 1978 Optical Society of America

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References

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  1. R. A. Brown, Y. L. Yung. “Io, Its Atmosphere and Optical Emissions,” in Jupiter, T. Gehrels, Ed. (U. Arizona Press, Tucson, 1976), p. 1102.
  2. H. D. Babcock, Astrophys. J. 57, 209 (1923).
    [CrossRef]
  3. J. Bricard, A. Kastler, Ann. Geophys. 6, 286 (1950).
  4. H. C. Van de Hulst, “Scattering in the Atmospheres of the Earth and Planets,” in The Atmospheres of the Earth and Planets, G. P. Kuiper, Ed. (U. Chicago Press, Chicago, 1952), p 49.
  5. Telescope defects and plate scale vary between telescopes. When we wish to be specific, we refer to the 1.55-m Agassiz telescope of Harvard College Observatory, with the Cassegrain focus (f/20) changed by a lens to f/9.6 and a plate scale of 13 sec of arc/mm.
  6. D. L. Matson, B. A. Goldberg, T. V. Johnson, R. W. Carlson, “Images of Io’s Sodium Cloud,” submitted to Science (1978).
    [CrossRef]
  7. R. Goody, J. Apt, Planet. Space Sci. 25, 603 (1977).
    [CrossRef]
  8. G. Münch, J. T. Bergstralh, Publ. Astron. Soc. Pac. 89, 232 (1977).
    [CrossRef]
  9. F. J. Murcray, R. M. Goody, “Pictures of the Io Sodium Cloud,” submitted to Astrophys. J. (1978).
    [CrossRef]
  10. A. M. Title, Appl. Opt. 15, 2871 (1976).
    [CrossRef] [PubMed]
  11. H. K. Palmer, Lick Obs. Bull. 2, 46 (1902).
  12. Units for D arc sec of arc/Å, and it depends upon both on the telescope and the spectrograph. D′, measured in mm/Å, depends only on the spectrograph design. If ρ is the telescope plate scale in sec of arc/mm, then D = ρD′.
  13. O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
    [CrossRef]
  14. It is only partly coincidence that the dispersion is close to the limit given by Eq. (6). The optimum design of a spectrograph for stellar observations matches seeing (1–2 sec of arc) and limiting spectral resolution (~0.05 Å). The coincidence arises because the Na D-lines have widths close to the limiting resolution.
  15. L. Mertz, Appl. Opt. 16, 812 (1977).
    [CrossRef] [PubMed]

1977 (3)

R. Goody, J. Apt, Planet. Space Sci. 25, 603 (1977).
[CrossRef]

G. Münch, J. T. Bergstralh, Publ. Astron. Soc. Pac. 89, 232 (1977).
[CrossRef]

L. Mertz, Appl. Opt. 16, 812 (1977).
[CrossRef] [PubMed]

1976 (1)

1959 (1)

O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
[CrossRef]

1950 (1)

J. Bricard, A. Kastler, Ann. Geophys. 6, 286 (1950).

1923 (1)

H. D. Babcock, Astrophys. J. 57, 209 (1923).
[CrossRef]

1902 (1)

H. K. Palmer, Lick Obs. Bull. 2, 46 (1902).

Apt, J.

R. Goody, J. Apt, Planet. Space Sci. 25, 603 (1977).
[CrossRef]

Babcock, H. D.

H. D. Babcock, Astrophys. J. 57, 209 (1923).
[CrossRef]

Bergstralh, J. T.

G. Münch, J. T. Bergstralh, Publ. Astron. Soc. Pac. 89, 232 (1977).
[CrossRef]

Bricard, J.

J. Bricard, A. Kastler, Ann. Geophys. 6, 286 (1950).

Brown, R. A.

R. A. Brown, Y. L. Yung. “Io, Its Atmosphere and Optical Emissions,” in Jupiter, T. Gehrels, Ed. (U. Arizona Press, Tucson, 1976), p. 1102.

Carlson, R. W.

D. L. Matson, B. A. Goldberg, T. V. Johnson, R. W. Carlson, “Images of Io’s Sodium Cloud,” submitted to Science (1978).
[CrossRef]

Coffeen, M. F.

O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
[CrossRef]

Glather, E. M.

O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
[CrossRef]

Goldberg, B. A.

D. L. Matson, B. A. Goldberg, T. V. Johnson, R. W. Carlson, “Images of Io’s Sodium Cloud,” submitted to Science (1978).
[CrossRef]

Goody, R.

R. Goody, J. Apt, Planet. Space Sci. 25, 603 (1977).
[CrossRef]

Goody, R. M.

F. J. Murcray, R. M. Goody, “Pictures of the Io Sodium Cloud,” submitted to Astrophys. J. (1978).
[CrossRef]

Johnson, T. V.

D. L. Matson, B. A. Goldberg, T. V. Johnson, R. W. Carlson, “Images of Io’s Sodium Cloud,” submitted to Science (1978).
[CrossRef]

Kastler, A.

J. Bricard, A. Kastler, Ann. Geophys. 6, 286 (1950).

Matson, D. L.

D. L. Matson, B. A. Goldberg, T. V. Johnson, R. W. Carlson, “Images of Io’s Sodium Cloud,” submitted to Science (1978).
[CrossRef]

Mertz, L.

Münch, G.

G. Münch, J. T. Bergstralh, Publ. Astron. Soc. Pac. 89, 232 (1977).
[CrossRef]

O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
[CrossRef]

Murcray, F. J.

F. J. Murcray, R. M. Goody, “Pictures of the Io Sodium Cloud,” submitted to Astrophys. J. (1978).
[CrossRef]

Palmer, H. K.

H. K. Palmer, Lick Obs. Bull. 2, 46 (1902).

Title, A. M.

Van de Hulst, H. C.

H. C. Van de Hulst, “Scattering in the Atmospheres of the Earth and Planets,” in The Atmospheres of the Earth and Planets, G. P. Kuiper, Ed. (U. Chicago Press, Chicago, 1952), p 49.

Wilson, O. C.

O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
[CrossRef]

Yung, Y. L.

R. A. Brown, Y. L. Yung. “Io, Its Atmosphere and Optical Emissions,” in Jupiter, T. Gehrels, Ed. (U. Arizona Press, Tucson, 1976), p. 1102.

Ann. Geophys. (1)

J. Bricard, A. Kastler, Ann. Geophys. 6, 286 (1950).

Appl. Opt. (2)

Astrophys. J. (1)

H. D. Babcock, Astrophys. J. 57, 209 (1923).
[CrossRef]

Astrophys. J. Suppl. Ser. (1)

O. C. Wilson, G. Münch, E. M. Glather, M. F. Coffeen, Astrophys. J. Suppl. Ser. 4, 199 (1959).
[CrossRef]

Lick Obs. Bull. (1)

H. K. Palmer, Lick Obs. Bull. 2, 46 (1902).

Planet. Space Sci. (1)

R. Goody, J. Apt, Planet. Space Sci. 25, 603 (1977).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

G. Münch, J. T. Bergstralh, Publ. Astron. Soc. Pac. 89, 232 (1977).
[CrossRef]

Other (7)

F. J. Murcray, R. M. Goody, “Pictures of the Io Sodium Cloud,” submitted to Astrophys. J. (1978).
[CrossRef]

R. A. Brown, Y. L. Yung. “Io, Its Atmosphere and Optical Emissions,” in Jupiter, T. Gehrels, Ed. (U. Arizona Press, Tucson, 1976), p. 1102.

H. C. Van de Hulst, “Scattering in the Atmospheres of the Earth and Planets,” in The Atmospheres of the Earth and Planets, G. P. Kuiper, Ed. (U. Chicago Press, Chicago, 1952), p 49.

Telescope defects and plate scale vary between telescopes. When we wish to be specific, we refer to the 1.55-m Agassiz telescope of Harvard College Observatory, with the Cassegrain focus (f/20) changed by a lens to f/9.6 and a plate scale of 13 sec of arc/mm.

D. L. Matson, B. A. Goldberg, T. V. Johnson, R. W. Carlson, “Images of Io’s Sodium Cloud,” submitted to Science (1978).
[CrossRef]

Units for D arc sec of arc/Å, and it depends upon both on the telescope and the spectrograph. D′, measured in mm/Å, depends only on the spectrograph design. If ρ is the telescope plate scale in sec of arc/mm, then D = ρD′.

It is only partly coincidence that the dispersion is close to the limit given by Eq. (6). The optimum design of a spectrograph for stellar observations matches seeing (1–2 sec of arc) and limiting spectral resolution (~0.05 Å). The coincidence arises because the Na D-lines have widths close to the limiting resolution.

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the illumination near Jupiter and Io. The unbroken lines are contours of scattered light intensity as measured on the 1.55-m Agassiz telescope for a bandpass of 1 Å. The dashed lines show approximate positions of the 500-rayleigh and 5-krayleigh contours of the sodium emission. This figure is drawn with near maximum elongation and therefore near maximum sodium emission intensity.1 For smaller elongations the observational problem is increasingly more severe.

Fig. 2
Fig. 2

A section of Fig. 1, radially outward from Jupiter passing 10 sec of arc below Io, as viewed with the four instruments. The solid line in each graph is the intensity observed, i.e., the sum of signal and background. The dashed line, if present, is the background contribution alone. All are drawn for a 10-Å bandpass, except as otherwise indicated. (a) The performance of two different filters, one with 10-Å and the other 1-Å bandpass. The difficulty in extracting the signal in the 10-Å case is apparent. (b) The performance of the slitless spectrograph, using a dispersion of 5 sec of arc/Å and an entrance aperture of 100 sec of arc. The primary effect is the flattening of the hump caused by scattered light from Io. The over-all background level is slightly higher than for (a) because of mixing of intense scattered light from nearer to Jupiter. Part (c) is for a multislit spectrograph with the same dispersion and aperture as for (b). The slit spacing is 2 sec of arc. The reduction in background is due to the loss of half of the light on the slits. The advantage of (c) over (b) is clear. (d) The effect of a Mach-Zehnder interferometer and a 10-Å filter. The reduction in background is due to the use of only one channel of the interferometer. The distinction between signal and background is again obvious.

Fig. 3
Fig. 3

Modulation produced by a multislit spectrograph as a function of the ratio of linewidth to slit spacing. The curves differ in number of slits. Our multislit has fifty slits in a field of 100 sec of arc. Calculations are for a Gaussian line profile of unit amplitude; similar results are obtained for other profiles. The Mach-Zehnder interferometer gives similar curves.

Fig. 4
Fig. 4

The Io sodium cloud as recorded with our multislit spectrograph. The original plate is reproduced in the upper half, the lighter regions being more heavily exposed. Io is behind the square mask at the center. (The anamorphism of the spectrograph elongates the square.) The lower half of the figure shows the same exposure after processing. The contour lines are of equal intensity in the D2-line, at 500-rayleigh intervals, with 1000-rayleighs intervals accented.

Fig. 5
Fig. 5

Schematic optical layout of a Mach-Zehnder interferometer. Fringes are produced at the plane of intersection of the two beams. The angle of intersection determines the spacing of the fringes; the line of intersection determines the orientation. The glass plate widens the acceptance angle of the instrument.

Tables (1)

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Table I Modulation and Background for Imaging Systems

Equations (16)

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d L = D d λ .
N = L / ( d L ) > N 0 ,
D < [ L / ( N 0 d λ ) ] .
Δ λ sp = E / D .
Δ λ sp > N 0 d λ .
D Δ λ f 2 L .
2 d λ D > g 0 .
D < [ L / ( 2 N 0 d λ ) ] .
Δ λ sp = E / 2 D ,
I ( x , y , λ ) = S ( x , y , λ ) + B ( x , y , λ ) ,
S ( x , y , λ ) = S 1 ( x , y ) δ ( λ λ D 1 ) + S 2 ( x , y ) δ ( λ λ D 2 ) , B ( x , y , λ ) = B ( x , y ) ,
Q = A Ω T { M [ S ( x , y ) ] + R [ B ( x , y ) ] } ,
Q s = A Ω T S ( x , y ) , Q b = A Ω T B ( x , y ) Δ λ .
S N = A Ω T S ( x , y ) [ A Ω T B ( x , y ) Δ λ ] 1 / 2 = ( A Ω T ) 1 / 2 S ( B Δ λ ) 1 / 2 .
Q b = A Ω T B eff Δ λ .
S N = C 2 1 / 2 ( A Ω T ) 1 / 2 S ( x , y ) [ B eff ( x , y ) Δ λ ] 1 / 2 .

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