Abstract

A near-infrared, two-beam interferometer has been built for astronomical observations by Fourier transform spectroscopy. Various improvements, especially a highly accurate interferometrically controlled stepping drive, have resulted in the production of laboratory spectra with 0.1-cm−1 resolution and unusually clean instrumental line shape, and spectra of Venus and Mars with about 1-cm−1 resolution.

© 1966 Optical Society of America

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  1. P. Fellgett, thesis, Cambridge1951,and J. Physique (France) 19,187 (1958).
  2. P. Jacquinot, 17e Congrès GAMS 25 (1954).
  3. P. L. Richards, J. Opt. Soc. Am. 54, 1474 (1964) gives a complete review of the situation together with the most illustrative results published so far.
    [CrossRef]
  4. J. Connes and P. Gush, J. Physique (France) 20, 915 (1959),and J. Physique (France) 21, 645 (1960).
  5. E. Archbold and H. A. Gebbie, Proc. Phys. Soc. 80, 793 (1962).
    [CrossRef]
  6. L. Mertz, Mem. Soc. Roy. Sci. de Liège 9, 120 (1964).
  7. H. C. Bowers, Appl. Opt. 3, 627 (1964);N. J. Woolf, Appl. Opt. 3, 1195 (1964);J. F. James, J. Quant. Spectry. Radiative Transfer 4, 793 (1964).
    [CrossRef]
  8. H. A. Gebbie, G. Roland, and L. Delbouille, Monthly Notices Roy. Astron. Soc. 123, 497 (1962);Astron. J. 69, 334 (1964).
  9. W. M. Sinton, J. Quant. Spectry. Radiative Transfer 2 (1964).
  10. G. Kuiper, Comm. Lun. and Plan. Lab., Univ. of Arizona1, 83 (1962).
  11. J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).
  12. Another method of estimating noise is of course to compare spectra computed from different interferograms.
  13. P. L. Richards (Ref. 3) has recently built a stepping drive for his far-infrared interferometer and has used it with very good success, for reasons which are comparable to our own. The main differences are that he does not use true integration nor interferometric control. L. Delbouille at the Institut d’Astrophysique Université de Liège, has also been independently developing a stepping drive.
  14. J. Pinard, Echantillonnage des interferogrammes en spectroscopic par transformation de Fourier—These de 3eme cycle, Uni-versité de Paris, 1963—Preliminary results were also briefly described by J. Connes at the Liège Colloquium on Infrared Astronomical Spectra, June 1963[Mem. Soc. Roy. Sci. de Liège 9, 81 (1964)].
  15. While the interferometer itself remained basically unchanged throughout the experiments, the fore optics suffered considerable modifications; only the latest version need be fully described here.
  16. This is by far the greatest part of the time, if we can believe most astronomers.
  17. The automatic guider was not available during the early part of the experiments (Mount Wilson and Kitt Peak).
  18. In fact, this system was used only for Mars at Observatoire de Saint Michel and the dimensions were then Φ=3 mm, l=100 mm. For Venus and Jupiter at Mount Wilson and Kitt Peak a different device was tried, because it could be improvised more quickly: a rapidly rotating dove prism was placed right after the coudé focus and made the whole beam rotate at 300 revolutions/sec. The results were about as good as those with the light pipe, but the system was very noisy and cumbersome; moreover, since the speed of revolution was not very stable it was difficult to avoid beats with harmonics of the chopper frequency.
  19. L. Mertz, J. Phys. (France) 19, 233 (1958).
  20. M. Cuisenier, Interferomètre de Michelson pour spectroscopie par transformation de Fourier, These de 3eme cycle, Université de Paris, 1964.
  21. We have also made a CaF2 beam splitter with Ge coating for use at longer wavelengths. Since the absorption of Ge would be too large in the visible, the quadrants corresponding to C and D are covered with a TiO layer.
  22. These were cut from a single paraboloid of 20-mm focal length and 120-mm aperture by the Atelier de l′Institut d’Optique de Paris under the direction of J. Demarcq and were found, even when used at full aperture, to give an image definition better than 0.1 mm.
  23. On the other hand, balancing does not depend on the sensitivity of the receivers and it is not necessary to match them.
  24. 198Hg with high-frequency excitation is used for D>5 cm.
  25. Sanborn Company, Waltham, Massachusetts.
  26. Prior to the speed servo, an oil damper was used to stabilize the velocity. It gave reasonably good results, but the speed was still subject to large, slow variations and had to be readjusted by hand control; also, transportation of the instrument was made difficult. On the other hand, it gave better damping of high-frequency external vibrations.
  27. Bell Telephone Company.
  28. Even airplane transmission is not error proof. The tapes sometimes went to London.
  29. Several reasons for preferring pure cosine transforms have been given earlier (Ref. 11, p. 133): Optimum signal-to-noise ratio and perfect linearity in the computed spectrum; reduction in the scanning length and the computing time.Another important reason is given by L. Delbouille, G. Roland, and H. A. Gebbie, [Mem. Soc. Roy. Sci. de Liège 9, 125 (1964)]; it is the only method which does not rectify negative portions of the spectrum. It has, however, the disadvantage that an extremely accurate value of ∊ is needed.
  30. The unapodized profile from the same interferogram shows a resolving power R0=105.
  31. For this reason apodization is never used with gratings. However, it has been shown [P. Jacquinot and B. Roizen Dossier, in Progress in Optics III, edited by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), p. 31.], that it is actually possible to improve the diffraction pattern of an extremely good grating. But the device used for the demonstration, a diamond-shaped diaphragm, would be inconvenient in any practical spectrometer or spectrograph because it needs a point source. Also, the making of an apodizing screen of the size of a large modern grating would no doubt be a delicate operation.
  32. To a physicist turned astronomer some of the environmental difficulties involved appeared rather more severe than anticipated. For instance, the usually reliable servo once refused to operate. A check of the electrical, then of the optical system, was made, and revealed the unexpected combination of a “cat’s eye” with a mouse’s nest inside. On a different occasion, the paper punch appeared to be making a slightly irregular noise; upon investigation a rattlesnake was found to be responsible.
  33. We thank W. E. Mitchell for the loan of this record which shows increased resolving power when compared with the Mc-Math–Hulbert— University of Michigan atlas.The latest improvements in the instrument are described by W. E. Mitchell and O. C. Mohler, Appl. Opt. 3, 467 (1964).
    [CrossRef]
  34. For instance, the PbS cells were then much too large, because the system had originally been designed with the hope of using it with a bigger telescope.
  35. Defined by taking the center of the half-width on special plots, using 50 spectral points per resolution width. Since the resolving power is not large enough to separate these lines completely, their profiles are slightly asymmetrical and there would be no point in giving the absolute positions.
  36. G. P. Kuiper, Mem. Soc. Roy. Sci. Liège 9, 365 (1964).
  37. Furthermore, the 1965 opposition was not a near one; the energy available in 1971 should be larger by a factor of 3.

1964 (7)

L. Mertz, Mem. Soc. Roy. Sci. de Liège 9, 120 (1964).

W. M. Sinton, J. Quant. Spectry. Radiative Transfer 2 (1964).

Several reasons for preferring pure cosine transforms have been given earlier (Ref. 11, p. 133): Optimum signal-to-noise ratio and perfect linearity in the computed spectrum; reduction in the scanning length and the computing time.Another important reason is given by L. Delbouille, G. Roland, and H. A. Gebbie, [Mem. Soc. Roy. Sci. de Liège 9, 125 (1964)]; it is the only method which does not rectify negative portions of the spectrum. It has, however, the disadvantage that an extremely accurate value of ∊ is needed.

G. P. Kuiper, Mem. Soc. Roy. Sci. Liège 9, 365 (1964).

We thank W. E. Mitchell for the loan of this record which shows increased resolving power when compared with the Mc-Math–Hulbert— University of Michigan atlas.The latest improvements in the instrument are described by W. E. Mitchell and O. C. Mohler, Appl. Opt. 3, 467 (1964).
[CrossRef]

H. C. Bowers, Appl. Opt. 3, 627 (1964);N. J. Woolf, Appl. Opt. 3, 1195 (1964);J. F. James, J. Quant. Spectry. Radiative Transfer 4, 793 (1964).
[CrossRef]

P. L. Richards, J. Opt. Soc. Am. 54, 1474 (1964) gives a complete review of the situation together with the most illustrative results published so far.
[CrossRef]

1962 (2)

H. A. Gebbie, G. Roland, and L. Delbouille, Monthly Notices Roy. Astron. Soc. 123, 497 (1962);Astron. J. 69, 334 (1964).

E. Archbold and H. A. Gebbie, Proc. Phys. Soc. 80, 793 (1962).
[CrossRef]

1961 (1)

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).

1959 (1)

J. Connes and P. Gush, J. Physique (France) 20, 915 (1959),and J. Physique (France) 21, 645 (1960).

1958 (1)

L. Mertz, J. Phys. (France) 19, 233 (1958).

1954 (1)

P. Jacquinot, 17e Congrès GAMS 25 (1954).

Archbold, E.

E. Archbold and H. A. Gebbie, Proc. Phys. Soc. 80, 793 (1962).
[CrossRef]

Bowers, H. C.

Connes, J.

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).

J. Connes and P. Gush, J. Physique (France) 20, 915 (1959),and J. Physique (France) 21, 645 (1960).

J. Pinard, Echantillonnage des interferogrammes en spectroscopic par transformation de Fourier—These de 3eme cycle, Uni-versité de Paris, 1963—Preliminary results were also briefly described by J. Connes at the Liège Colloquium on Infrared Astronomical Spectra, June 1963[Mem. Soc. Roy. Sci. de Liège 9, 81 (1964)].

Cuisenier, M.

M. Cuisenier, Interferomètre de Michelson pour spectroscopie par transformation de Fourier, These de 3eme cycle, Université de Paris, 1964.

Delbouille, L.

Several reasons for preferring pure cosine transforms have been given earlier (Ref. 11, p. 133): Optimum signal-to-noise ratio and perfect linearity in the computed spectrum; reduction in the scanning length and the computing time.Another important reason is given by L. Delbouille, G. Roland, and H. A. Gebbie, [Mem. Soc. Roy. Sci. de Liège 9, 125 (1964)]; it is the only method which does not rectify negative portions of the spectrum. It has, however, the disadvantage that an extremely accurate value of ∊ is needed.

H. A. Gebbie, G. Roland, and L. Delbouille, Monthly Notices Roy. Astron. Soc. 123, 497 (1962);Astron. J. 69, 334 (1964).

Fellgett, P.

P. Fellgett, thesis, Cambridge1951,and J. Physique (France) 19,187 (1958).

Gebbie, H. A.

Several reasons for preferring pure cosine transforms have been given earlier (Ref. 11, p. 133): Optimum signal-to-noise ratio and perfect linearity in the computed spectrum; reduction in the scanning length and the computing time.Another important reason is given by L. Delbouille, G. Roland, and H. A. Gebbie, [Mem. Soc. Roy. Sci. de Liège 9, 125 (1964)]; it is the only method which does not rectify negative portions of the spectrum. It has, however, the disadvantage that an extremely accurate value of ∊ is needed.

E. Archbold and H. A. Gebbie, Proc. Phys. Soc. 80, 793 (1962).
[CrossRef]

H. A. Gebbie, G. Roland, and L. Delbouille, Monthly Notices Roy. Astron. Soc. 123, 497 (1962);Astron. J. 69, 334 (1964).

Gush, P.

J. Connes and P. Gush, J. Physique (France) 20, 915 (1959),and J. Physique (France) 21, 645 (1960).

Jacquinot, P.

P. Jacquinot, 17e Congrès GAMS 25 (1954).

For this reason apodization is never used with gratings. However, it has been shown [P. Jacquinot and B. Roizen Dossier, in Progress in Optics III, edited by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), p. 31.], that it is actually possible to improve the diffraction pattern of an extremely good grating. But the device used for the demonstration, a diamond-shaped diaphragm, would be inconvenient in any practical spectrometer or spectrograph because it needs a point source. Also, the making of an apodizing screen of the size of a large modern grating would no doubt be a delicate operation.

Kuiper, G.

G. Kuiper, Comm. Lun. and Plan. Lab., Univ. of Arizona1, 83 (1962).

Kuiper, G. P.

G. P. Kuiper, Mem. Soc. Roy. Sci. Liège 9, 365 (1964).

Mertz, L.

L. Mertz, Mem. Soc. Roy. Sci. de Liège 9, 120 (1964).

L. Mertz, J. Phys. (France) 19, 233 (1958).

Mitchell, W. E.

Mohler, O. C.

Pinard, J.

J. Pinard, Echantillonnage des interferogrammes en spectroscopic par transformation de Fourier—These de 3eme cycle, Uni-versité de Paris, 1963—Preliminary results were also briefly described by J. Connes at the Liège Colloquium on Infrared Astronomical Spectra, June 1963[Mem. Soc. Roy. Sci. de Liège 9, 81 (1964)].

Richards, P. L.

Roizen Dossier, B.

For this reason apodization is never used with gratings. However, it has been shown [P. Jacquinot and B. Roizen Dossier, in Progress in Optics III, edited by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), p. 31.], that it is actually possible to improve the diffraction pattern of an extremely good grating. But the device used for the demonstration, a diamond-shaped diaphragm, would be inconvenient in any practical spectrometer or spectrograph because it needs a point source. Also, the making of an apodizing screen of the size of a large modern grating would no doubt be a delicate operation.

Roland, G.

Several reasons for preferring pure cosine transforms have been given earlier (Ref. 11, p. 133): Optimum signal-to-noise ratio and perfect linearity in the computed spectrum; reduction in the scanning length and the computing time.Another important reason is given by L. Delbouille, G. Roland, and H. A. Gebbie, [Mem. Soc. Roy. Sci. de Liège 9, 125 (1964)]; it is the only method which does not rectify negative portions of the spectrum. It has, however, the disadvantage that an extremely accurate value of ∊ is needed.

H. A. Gebbie, G. Roland, and L. Delbouille, Monthly Notices Roy. Astron. Soc. 123, 497 (1962);Astron. J. 69, 334 (1964).

Sinton, W. M.

W. M. Sinton, J. Quant. Spectry. Radiative Transfer 2 (1964).

17e Congrès GAMS (1)

P. Jacquinot, 17e Congrès GAMS 25 (1954).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Phys. (France) (1)

L. Mertz, J. Phys. (France) 19, 233 (1958).

J. Physique (France) (1)

J. Connes and P. Gush, J. Physique (France) 20, 915 (1959),and J. Physique (France) 21, 645 (1960).

J. Quant. Spectry. Radiative Transfer (1)

W. M. Sinton, J. Quant. Spectry. Radiative Transfer 2 (1964).

Mem. Soc. Roy. Sci. de Liège (2)

Several reasons for preferring pure cosine transforms have been given earlier (Ref. 11, p. 133): Optimum signal-to-noise ratio and perfect linearity in the computed spectrum; reduction in the scanning length and the computing time.Another important reason is given by L. Delbouille, G. Roland, and H. A. Gebbie, [Mem. Soc. Roy. Sci. de Liège 9, 125 (1964)]; it is the only method which does not rectify negative portions of the spectrum. It has, however, the disadvantage that an extremely accurate value of ∊ is needed.

L. Mertz, Mem. Soc. Roy. Sci. de Liège 9, 120 (1964).

Mem. Soc. Roy. Sci. Liège (1)

G. P. Kuiper, Mem. Soc. Roy. Sci. Liège 9, 365 (1964).

Monthly Notices Roy. Astron. Soc. (1)

H. A. Gebbie, G. Roland, and L. Delbouille, Monthly Notices Roy. Astron. Soc. 123, 497 (1962);Astron. J. 69, 334 (1964).

Proc. Phys. Soc. (1)

E. Archbold and H. A. Gebbie, Proc. Phys. Soc. 80, 793 (1962).
[CrossRef]

Rev. Opt. (1)

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).

Other (24)

Another method of estimating noise is of course to compare spectra computed from different interferograms.

P. L. Richards (Ref. 3) has recently built a stepping drive for his far-infrared interferometer and has used it with very good success, for reasons which are comparable to our own. The main differences are that he does not use true integration nor interferometric control. L. Delbouille at the Institut d’Astrophysique Université de Liège, has also been independently developing a stepping drive.

J. Pinard, Echantillonnage des interferogrammes en spectroscopic par transformation de Fourier—These de 3eme cycle, Uni-versité de Paris, 1963—Preliminary results were also briefly described by J. Connes at the Liège Colloquium on Infrared Astronomical Spectra, June 1963[Mem. Soc. Roy. Sci. de Liège 9, 81 (1964)].

While the interferometer itself remained basically unchanged throughout the experiments, the fore optics suffered considerable modifications; only the latest version need be fully described here.

This is by far the greatest part of the time, if we can believe most astronomers.

The automatic guider was not available during the early part of the experiments (Mount Wilson and Kitt Peak).

In fact, this system was used only for Mars at Observatoire de Saint Michel and the dimensions were then Φ=3 mm, l=100 mm. For Venus and Jupiter at Mount Wilson and Kitt Peak a different device was tried, because it could be improvised more quickly: a rapidly rotating dove prism was placed right after the coudé focus and made the whole beam rotate at 300 revolutions/sec. The results were about as good as those with the light pipe, but the system was very noisy and cumbersome; moreover, since the speed of revolution was not very stable it was difficult to avoid beats with harmonics of the chopper frequency.

M. Cuisenier, Interferomètre de Michelson pour spectroscopie par transformation de Fourier, These de 3eme cycle, Université de Paris, 1964.

We have also made a CaF2 beam splitter with Ge coating for use at longer wavelengths. Since the absorption of Ge would be too large in the visible, the quadrants corresponding to C and D are covered with a TiO layer.

These were cut from a single paraboloid of 20-mm focal length and 120-mm aperture by the Atelier de l′Institut d’Optique de Paris under the direction of J. Demarcq and were found, even when used at full aperture, to give an image definition better than 0.1 mm.

On the other hand, balancing does not depend on the sensitivity of the receivers and it is not necessary to match them.

198Hg with high-frequency excitation is used for D>5 cm.

Sanborn Company, Waltham, Massachusetts.

Prior to the speed servo, an oil damper was used to stabilize the velocity. It gave reasonably good results, but the speed was still subject to large, slow variations and had to be readjusted by hand control; also, transportation of the instrument was made difficult. On the other hand, it gave better damping of high-frequency external vibrations.

Bell Telephone Company.

Even airplane transmission is not error proof. The tapes sometimes went to London.

G. Kuiper, Comm. Lun. and Plan. Lab., Univ. of Arizona1, 83 (1962).

The unapodized profile from the same interferogram shows a resolving power R0=105.

For this reason apodization is never used with gratings. However, it has been shown [P. Jacquinot and B. Roizen Dossier, in Progress in Optics III, edited by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), p. 31.], that it is actually possible to improve the diffraction pattern of an extremely good grating. But the device used for the demonstration, a diamond-shaped diaphragm, would be inconvenient in any practical spectrometer or spectrograph because it needs a point source. Also, the making of an apodizing screen of the size of a large modern grating would no doubt be a delicate operation.

To a physicist turned astronomer some of the environmental difficulties involved appeared rather more severe than anticipated. For instance, the usually reliable servo once refused to operate. A check of the electrical, then of the optical system, was made, and revealed the unexpected combination of a “cat’s eye” with a mouse’s nest inside. On a different occasion, the paper punch appeared to be making a slightly irregular noise; upon investigation a rattlesnake was found to be responsible.

Furthermore, the 1965 opposition was not a near one; the energy available in 1971 should be larger by a factor of 3.

P. Fellgett, thesis, Cambridge1951,and J. Physique (France) 19,187 (1958).

For instance, the PbS cells were then much too large, because the system had originally been designed with the hope of using it with a bigger telescope.

Defined by taking the center of the half-width on special plots, using 50 spectral points per resolution width. Since the resolving power is not large enough to separate these lines completely, their profiles are slightly asymmetrical and there would be no point in giving the absolute positions.

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Figures (22)

F. 1
F. 1

Occupied spectral range, resolution, and noise in Fourier transform spectroscopy.

F. 2
F. 2

(a) Narrow-band spectrum and corresponding interferogram. (b) Spectrum computed from the same interferogram sampled with optimum spacing Da. (c) Reference-fringe system from which sampling is triggered.

F. 3
F. 3

(a) Path difference vs time in a stepping recording. (b) Signal-integrator output.

F. 4
F. 4

Fore optics.

F. 5
F. 5

Interferometer. Projection upon a horizontal plane of the light rays from the telescope. Mirrors M′10, M10″ are situated above the figure plane, and M13′, M13″ below.

F. 6
F. 6

Intersection of various beams with the beam splitter, and side view.

F. 7
F. 7

Interferometer: path of rays from mercury lamp Hg and white light source W.

F. 8
F. 8

General block diagram of electrical system.

F. 9
F. 9

Position-servo response (lower trace) to square-wave perturbation (upper trace). (a) Overdamped, (b) optimum, (c) underdamped. A large number of traces has been averaged; the trace width is due to photomultiplier noise.

F. 10
F. 10

One cycle of operation of the stepping drive. Upper trace: monitoring integrator output. Lower trace: reference-fringe signal. At left the carriage moves and the integrator is zeroed; at right the carriage is stopped and the integration takes place; at extreme right the digital voltmeter measures the signal-integrator output. Integration time is usually much longer than shown here.

F. 11
F. 11

Error signal from the position servo. Upper trace: Mount Wilson. Lower trace: Pasadena. The differences are due to laboratory ground vibrations.

F. 12
F. 12

Four different computed instrument line shapes, automatically plotted, with increasing apodizations. (A) Unapodized, half-width δσ = 0.6/Dmax, (B) δσ = 0.75/Dmax, (C) δσ = 0.85/Dmax, (D) δσ = 0.95/Dmax. (C) has the smallest overshoot but (D) has a much more rapid decrease in intensity beyond point 5.00 (units of diffraction width). We thank Madame B. Roizen-Dossier for providing us with functions B and C. D has been used before (Ref. 11, p. 54). Even better apodizations can of course be obtained.

F. 13
F. 13

Experimental instrument line shapes. Interferogram recorded with K line at 12 523 Å. Number of samples N = 5700, with n = 28 (which means 160 000 Hg reference fringes). Spectrum computed with profile D. Upper trace normalized to unity; lower trace expanded by a factor of 10 and compared with theoretical curve.

F. 14
F. 14

Experimental instrument line shape (identical to Fig. 13) compared to computed, but hand-plotted, instrument line shape from a perfect grating and a perfect Fabry–Perot étalon with the same half-width.

F. 15
F. 15

Three portions of a He spectrum. N = 5400, n = 31, profile D. Top: Line at 2.05 μ, normalized to unity. The other two traces, expanded by a factor of 100, show regions where harmonics (or more exactly, sampling “images” of the harmonics, which are fully equivalent) are expected.

F. 16
F. 16

Two ICH3 absorption spectra from different interferograms (profile D). Total spectral range is about 30 times larger than the portion given here. Both traces have been normalized to unity, but the maximum-intensity point falls outside the portion shown, and shifted vertically by 5%. Below: two noise traces, on both sides of the filter bandpass (same scale). Parameters: δσ = 0.125 cm−1 (profile A) or 0.2 cm−1 (profile D); Δσ = 400 cm−1, M = 3200, N = 5500, n = 16; max signal-to-rms-noise ratio 300; quality factor q = 4×105.

F. 17
F. 17

Two solar spectra computed from the same inteferogram. Upper trace; profile A; lower trace: profile D. Below: two noise traces. Parameters: δσ = 0.07 cm−1 (A) or 0.11 cm−1 (D); M = 5700 N=10.000, n = 16; s/n = 350; q=8×105. Center: same spectral region given by McMath–Hulbert grating spectrometer with resolution comparable to trace D. Recordings were not made at the same time and the air masses and atmospheric conditions are not identical. Most lines are due to telluric CH4.

F. 18
F. 18

Two superimposed spectra recorded on 29 Sept. 1964 with the 91-cm telescope, Steward Observatory, just before and after sunrise (thus air mass is not identical for both spectra). Version represented here is the unapodized one (profile A), which resolves best the CO2 lines but is unreliable for small features. Parameters: Δσ = 1000 cm−1 (about 10 times larger than the region shown), δσ = 0.7 cm−1 (A) or 1 cm−1 (D); M = 1300; N = 8300, n = 2, s/n = 70, q = 5×104. Upper trace: Laboratory CO2 spectrum (grating spectrometer).

F. 19
F. 19

Corresponding portion (marked by arrows) of a Venus spectrum by Kuiper,10 208-cm telescope, McDonald Observatory. The plot has been inverted from left to right and wavenumber scales added.

F. 20
F. 20

Two Mars spectra (26 and 28 March 1965, Observatoire de Saint-Michel, 193-cm telescope) recorded with the same air mass, on two different nights. Profile used here is B. Parameters:Δσ = 1000 cm−1, δσ = 1 cm−1 (A) or 1.25 cm−1 (B); M =1000, N = 11.500 n = 1, s/n=440,q=3×105. The lower trace shows the difference, expanded by a factor of 10, between the two Mars spectra; it appears to be purely random noise. Upper trace: Solar spectrum, same resolution and line shape. Across the portion shown, which is again but a fraction of the total range, most of the lines are telluric and due to H2O. By sheer luck the amount of precipitable water happened to be the same for the two Mars spectra—but not for the solar spectrum.

F. 21
F. 21

Corresponding portion (marked by arrows) of the Mars spectrum as recorded by Kuiper.36 Three traces are given, vertically shifted; the upper one was obtained with a larger time constant. The traces have been inverted and the wavenumber scale added by us.

F. 22
F. 22

Effect of atmospheric noise on the computed spectrum of a sampled interferogram. (a) Oversampled, (b) minimum number of samples taken. A1, A2, A3 are images of the zero frequency point A0, and the excess noise which in (a) appears near A0 is repeated again and again in (b) and coincides with S.