Abstract

This paper describes the design and tests of an all-reflection two-beam interferometer. The unique feature of this interferometer is the use of a combination of three diffraction gratings as a beam splitter. The use of reflection-type diffraction gratings as a beam splitter eliminates the need for transmission elements and thereby extends the applicability of two-beam interferometry to regions of the electromagnetic spectrum such as the vacuum ultraviolet where transmitting beam splitters are not available. A preliminary type of grating beam splitter using a single grating is discussed, and its disadvantages are described. Finally, an interferometer that uses three gratings as a beam splitter and which can function as an all-reflection Fourier-transform spectrometer is described. Interferograms of simple spectra taken with this instrument are presented.

© 1972 Optical Society of America

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References

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  1. G. H. C. Freeman (private communication).
  2. J. O. Stoner and H. Lyle, Appl. Opt. 8, 831 (L) (1969).
    [Crossref]
  3. A. S. Filler, J. Opt. Soc. Am. 61, 835 (1971).
    [Crossref]
  4. C. Barus, The Interferometry of Reversed and Non-Reversed Spectra, Publ., 149, Part I (Carnegie Institute, Washington, D. C., 1911).
  5. C. R. Munnerlyn, Appl. Opt. 8, 827 (1968).
    [Crossref]
  6. F. J. Weinburg and N. B. Wood, J. Sci. Instr. 36, 227 (1959).
    [Crossref]
  7. J. R. Davis, thesis, University of Rochester, 1940.
  8. P. Connes, Rev. Opt. 38, 198 (1959).
  9. J. Strong and G. A. Vanasse, J. Opt. Soc. Am. 50, 113 (1960).
    [Crossref]
  10. M. Anderson and S. Brown, Rev. Sci. Instr. 40, 1626 (1969).
    [Crossref]
  11. K. Yoshihara, Japan J. Appl. Phys. 2, 818 (1963).
    [Crossref]
  12. J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Ch. 2.
  13. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
    [Crossref]

1971 (1)

1969 (2)

J. O. Stoner and H. Lyle, Appl. Opt. 8, 831 (L) (1969).
[Crossref]

M. Anderson and S. Brown, Rev. Sci. Instr. 40, 1626 (1969).
[Crossref]

1968 (1)

1963 (1)

K. Yoshihara, Japan J. Appl. Phys. 2, 818 (1963).
[Crossref]

1960 (1)

1959 (2)

F. J. Weinburg and N. B. Wood, J. Sci. Instr. 36, 227 (1959).
[Crossref]

P. Connes, Rev. Opt. 38, 198 (1959).

1954 (1)

Anderson, M.

M. Anderson and S. Brown, Rev. Sci. Instr. 40, 1626 (1969).
[Crossref]

Barus, C.

C. Barus, The Interferometry of Reversed and Non-Reversed Spectra, Publ., 149, Part I (Carnegie Institute, Washington, D. C., 1911).

Brown, S.

M. Anderson and S. Brown, Rev. Sci. Instr. 40, 1626 (1969).
[Crossref]

Connes, P.

P. Connes, Rev. Opt. 38, 198 (1959).

Davis, J. R.

J. R. Davis, thesis, University of Rochester, 1940.

Filler, A. S.

Freeman, G. H. C.

G. H. C. Freeman (private communication).

Jacquinot, P.

Lyle, H.

J. O. Stoner and H. Lyle, Appl. Opt. 8, 831 (L) (1969).
[Crossref]

Munnerlyn, C. R.

Samson, J. A. R.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Ch. 2.

Stoner, J. O.

J. O. Stoner and H. Lyle, Appl. Opt. 8, 831 (L) (1969).
[Crossref]

Strong, J.

Vanasse, G. A.

Weinburg, F. J.

F. J. Weinburg and N. B. Wood, J. Sci. Instr. 36, 227 (1959).
[Crossref]

Wood, N. B.

F. J. Weinburg and N. B. Wood, J. Sci. Instr. 36, 227 (1959).
[Crossref]

Yoshihara, K.

K. Yoshihara, Japan J. Appl. Phys. 2, 818 (1963).
[Crossref]

Appl. Opt. (2)

J. O. Stoner and H. Lyle, Appl. Opt. 8, 831 (L) (1969).
[Crossref]

C. R. Munnerlyn, Appl. Opt. 8, 827 (1968).
[Crossref]

J. Opt. Soc. Am. (3)

J. Sci. Instr. (1)

F. J. Weinburg and N. B. Wood, J. Sci. Instr. 36, 227 (1959).
[Crossref]

Japan J. Appl. Phys. (1)

K. Yoshihara, Japan J. Appl. Phys. 2, 818 (1963).
[Crossref]

Rev. Opt. (1)

P. Connes, Rev. Opt. 38, 198 (1959).

Rev. Sci. Instr. (1)

M. Anderson and S. Brown, Rev. Sci. Instr. 40, 1626 (1969).
[Crossref]

Other (4)

G. H. C. Freeman (private communication).

J. R. Davis, thesis, University of Rochester, 1940.

C. Barus, The Interferometry of Reversed and Non-Reversed Spectra, Publ., 149, Part I (Carnegie Institute, Washington, D. C., 1911).

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Ch. 2.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of a simple interferometer using a grating G to split a beam of light into two beams. Light goes from the source to the concave mirror M and then to the grating G. Mirrors M1 and M2 reflect the two beams back to the grating where they are recombined. Haidinger fringes are observed in the image of the entrance aperture.

Fig. 2
Fig. 2

All-reflection interferometer for use as a Fourier-transform spectrometer; G1, G2, and G3 are diffraction gratings with identical groove spacings and M1 and M2 are plane front-surface mirrors. M is a concave mirror. The path difference Δ=2(L1L2) for normal-incidence rays is the same for the different wavelengths λ0 and λ1.

Fig. 3
Fig. 3

The interferometer of Fig. 1 unfolded and with gratings and grating images replaced by transmission gratings. Bold lines indicate gratings, or grating images. The interferometer is shown for zero path difference. The distances a and b are equal and are equivalent to S1 (or S2) in Fig. 2. Both normal- and non-normal-incidence rays arrive at zero path difference concurrently (x+y+z=u+v+w).

Fig. 4
Fig. 4

The interferometer of Fig. 2 unfolded at nonzero path difference. If the path difference for normal incidence rays between arms in the interferometer is Δ=2(L1L2), then the path difference for non-normal-incidence rays is Δ=2(L1L2) cosϕ, where ϕ is the angle of incidence. The insert is an enlargement of the circled portion in the figure.

Fig. 5
Fig. 5

Unfolded interferometer of Fig. 2 showing the effect of grating G1 having W/N lines/mm and gratings G2 and G3 having W/N′ lines/mm. A particular wavelength λ1 exits from the interferometer at an angle ϕ given by ϕ≃2k(NN′)λ1/W, where k is the diffraction order. A range of wavelengths Δλ = λ2−λ1 will be diffracted into a range of angles Δϕ given by

Fig. 6
Fig. 6

Walk-off effect with the three-grating interferometer. (a) For a particular wavelength λ the light diffracted from G1 does not all strike G2 (or G3). Only light that is split by G1 and that goes through both arms of the interferometer returning to G1 produces fringes. This light is indicated by the cross-hatched center portion of the beam. Light from other portions of G1 is lost in one arm but returns to G1 in the other arm. This light merely produces a background that lowers fringe contrast. (b) Only light diffracted between angles θ1 and θ2 gives rise to maximum-contrast interference fringes. The grating G1 is assumed to have a triangular groove shape with a blaze angle ξ = 1 2 θ B. Only the angles for rays going from G1 to G2 are shown, although there are similar rays going from G1 to G3.

Fig. 7
Fig. 7

The calculated efficiency of the three-grating beam splitter of Fig. 2 as a function of wave number and neglecting reflection losses. The wave number σBk is the blaze wave number in the kth diffraction order.

Fig. 8
Fig. 8

A perspective view of the actual test set up. Two focusing lenses were used. The light goes from the source to the first lens and then to grating G1. The light is diffracted to G2 and G3. Only the rays to G2 are shown. The light from G2 goes to M1, which is tilted slightly. The light from M1 returns through the system at a slight vertical angle to the incident light and is finally reflected at right angles to the incident beam by a mirror. Haidinger fringes are then formed in the image of the entrance aperture by a second lens. The zero-order reflection from G1 is reflected directly to the entrance aperture and does not reach the exit aperture. The test system was used for convenience. The lenses could be replaced by converging mirrors. The test system of Fig. 8 does not have as large an étendue as the system of Fig. 2.

Fig. 9
Fig. 9

Portions of interferograms taken with the interferometer of Fig. 2. (a) Interferogram of the 6328-Å emission from a Ne–He laser. Because the mirror motion was not smooth and because the source was not stabilized, the interferogram is not a perfect sine wave. (b) Interferogram of the sodium-D-line doublet (5890 and 5896 Å). The sequence from 1 to 3 to 5 shows the change of the contrast of the Haidinger fringes produced by the two D lines in the sodium spectrum as the path-length difference is changed. The number of fringes between the two minima shown in 1 and 5 is 982±10, corresponding to the 6-Å separation of the sodium D lines.

Equations (6)

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Δ ( ϕ ) = 2 ( L 1 - L 2 ) cos ϕ ,
sin ϕ = 2 k λ ( N - N ) / W = k λ / d ,
Δ λ = ( d / k ) ( sin θ 2 - sin θ 1 ) = ( d / k ) [ η W / ( Z 2 + η 2 W 2 ) 1 2 - W / ( Z 2 + W 2 ) 1 2 ] ,
Z = [ ( η 2 - η 2 3 ) / ( η 2 3 - 1 ) ] 1 2 W .
tan θ B = ( η + 1 ) W 2 Z = η + 1 2 [ ( η 2 - η 2 3 ) / ( η 2 3 - 1 ) ] 1 2 .
Δ ϕ = Δ λ / [ W / 2 k ( N - N ) ] .