Abstract

Echelles of the type now produced by the Bausch & Lomb Optical Company lie intermediate in dispersive properties between ordinary diffraction gratings and such interferometers as the Fabry-Perot etalon. When crossed with a concave grating in a stigmatic mount of the type recently described ( Harrison, Archer, and Camus, J. Opt. Soc. Am. 42, 706 [ 1952]) an echelle might be expected to give wavelength precision between the approximately one part in 106 of which the grating is capable and the one part in 25×106 of the etalon. We find precision to about 1 part in 5×106 attainable with the echelle.

Identification of the order of interference m of any cycle on an echellegram can be made quickly and exactly by use of a standard plate or scale, which can be marked uniquely after photography of two or three known lines. A horizontal fiducial line of constant mλ0 is recorded on the spectrogram by reflecting light from a mirror which can be swung into position in front of the echelle. The exact mλ0 value for the plate is determined from the two or three standard lines photographed on it. Wavelength reduction is most conveniently made in terms of mλ, using the mλ0 line as a reference. The vertical mλ dispersion is first assumed constant over the entire plate, and an approximate mλ value is determined for each line in terms of its distance l from mλ0. A small correction is then added for each line, values of for the entire fixed focal surface having been determined in advance with some complex spectrum having many known lines, such as thorium. Values of are found to not exceed 0.050 m order-angstroms with our instrument. This range includes empirical corrections for error of coincidence, nonuniformity of dispersion along a cycle, variable magnification of the spectrograph, and all other deviations from vertical linearity or horizontal constancy of mλ.

On division by three-figure integral values of m, wavelengths can be obtained to within about 0.001A throughout the visible and ultraviolet spectrum, with little added complexity beyond that required for reducing grating spectrograms, and with greater precision, compactness, and spectrum coverage on a single plate.

A discussion of the so-called “error of concidence” is included, as this phenomenon, which has been principally of historical importance since the early days of spectroscopy, now affects the accuracy attainable with a single fiducial line and two or three Hg 198 lines, when substituted for the large number of standard lines needed for precision wavelength determinations with concave gratings.

© 1953 Optical Society of America

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References

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  1. H. Kayser, Astrophys. J. 20, 327 (1904); G. R. Harrison, Introduction to M.I.T. Wavelength Tables (John Wiley and Sons, Inc., New York, 1939), p. xv.
    [Crossref]
  2. W. F. Meggers and K. G. Kessler, J. Opt. Soc. Am. 40, 737 (1950).
    [Crossref]
  3. G. R. Harrison, J. Opt. Soc. Am. 36, 644 (1946).
    [Crossref]
  4. G. R. Harrison, J. Opt. Soc. Am. 39, 522 (1949); G. R. Harrison and C. L. Bausch, Proc. London Conf. Opt. Instruments (1946); (John Wiley and Sons, Inc., New York, 1947).
    [Crossref]
  5. Harrison, Lord, and Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., New York, 1948), p. 555.
  6. Harrison, Archer, and Camus, J. Opt. Soc. Am. 42, 706 (1952).
    [Crossref]
  7. W. E. Williams, Proc. Phys. Soc. (London) 45, 699 (1933); W. E. Williams and A. Middleton, Proc. Roy. Soc. (London) A172, 159 (1939).
    [Crossref]
  8. N. A. Finkelstein, J. Opt. Soc. Am. 42, 90 (1953).
    [Crossref]
  9. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
    [Crossref]
  10. H. A. Rowland, Physical Papers (Johns Hopkins Press, Baltimore, Maryland, 1902).
  11. J. T. Howell, Astrophys. J. 39, 230 (1914).
    [Crossref]
  12. A. A. Michelson, Astrophys. J. 18, 278 (1903).
    [Crossref]
  13. H. Kayser, Astrophys. J. 19, 157 (1904).
    [Crossref]
  14. H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903).
    [Crossref]
  15. E. Ingelstam and E. Djurle, J. Opt. Soc. Am. (to be published); Camus, Francon, Ingelstam, and Maréchal, Rev. Optique 30, 121 (1951).

1953 (1)

1952 (1)

1950 (1)

1949 (1)

1946 (1)

1945 (1)

1933 (1)

W. E. Williams, Proc. Phys. Soc. (London) 45, 699 (1933); W. E. Williams and A. Middleton, Proc. Roy. Soc. (London) A172, 159 (1939).
[Crossref]

1914 (1)

J. T. Howell, Astrophys. J. 39, 230 (1914).
[Crossref]

1904 (2)

H. Kayser, Astrophys. J. 20, 327 (1904); G. R. Harrison, Introduction to M.I.T. Wavelength Tables (John Wiley and Sons, Inc., New York, 1939), p. xv.
[Crossref]

H. Kayser, Astrophys. J. 19, 157 (1904).
[Crossref]

1903 (1)

A. A. Michelson, Astrophys. J. 18, 278 (1903).
[Crossref]

1902 (1)

H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903).
[Crossref]

Allen, H. S.

H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903).
[Crossref]

Archer,

Beutler, H. G.

Camus,

Djurle, E.

E. Ingelstam and E. Djurle, J. Opt. Soc. Am. (to be published); Camus, Francon, Ingelstam, and Maréchal, Rev. Optique 30, 121 (1951).

Finkelstein, N. A.

Harrison,

Harrison, Archer, and Camus, J. Opt. Soc. Am. 42, 706 (1952).
[Crossref]

Harrison, Lord, and Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., New York, 1948), p. 555.

Harrison, G. R.

Howell, J. T.

J. T. Howell, Astrophys. J. 39, 230 (1914).
[Crossref]

Ingelstam, E.

E. Ingelstam and E. Djurle, J. Opt. Soc. Am. (to be published); Camus, Francon, Ingelstam, and Maréchal, Rev. Optique 30, 121 (1951).

Kayser, H.

H. Kayser, Astrophys. J. 20, 327 (1904); G. R. Harrison, Introduction to M.I.T. Wavelength Tables (John Wiley and Sons, Inc., New York, 1939), p. xv.
[Crossref]

H. Kayser, Astrophys. J. 19, 157 (1904).
[Crossref]

Kessler, K. G.

Loofbourow,

Harrison, Lord, and Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., New York, 1948), p. 555.

Lord,

Harrison, Lord, and Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., New York, 1948), p. 555.

Meggers, W. F.

Michelson, A. A.

A. A. Michelson, Astrophys. J. 18, 278 (1903).
[Crossref]

Rowland, H. A.

H. A. Rowland, Physical Papers (Johns Hopkins Press, Baltimore, Maryland, 1902).

Williams, W. E.

W. E. Williams, Proc. Phys. Soc. (London) 45, 699 (1933); W. E. Williams and A. Middleton, Proc. Roy. Soc. (London) A172, 159 (1939).
[Crossref]

Astrophys. J. (4)

H. Kayser, Astrophys. J. 20, 327 (1904); G. R. Harrison, Introduction to M.I.T. Wavelength Tables (John Wiley and Sons, Inc., New York, 1939), p. xv.
[Crossref]

J. T. Howell, Astrophys. J. 39, 230 (1914).
[Crossref]

A. A. Michelson, Astrophys. J. 18, 278 (1903).
[Crossref]

H. Kayser, Astrophys. J. 19, 157 (1904).
[Crossref]

J. Opt. Soc. Am. (6)

Phil. Mag. (1)

H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903).
[Crossref]

Proc. Phys. Soc. (London) (1)

W. E. Williams, Proc. Phys. Soc. (London) 45, 699 (1933); W. E. Williams and A. Middleton, Proc. Roy. Soc. (London) A172, 159 (1939).
[Crossref]

Other (3)

H. A. Rowland, Physical Papers (Johns Hopkins Press, Baltimore, Maryland, 1902).

Harrison, Lord, and Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., New York, 1948), p. 555.

E. Ingelstam and E. Djurle, J. Opt. Soc. Am. (to be published); Camus, Francon, Ingelstam, and Maréchal, Rev. Optique 30, 121 (1951).

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Figures (9)

Fig. 1
Fig. 1

Portions of spectrograms taken (a) With a diffraction grating, the dispersion being horizontal. (b) With an echelle giving horizontal dispersion, crossed with a grating giving small vertical dispersion. (c) With a Fabry-Perot etalon giving horizontal dispersion, crossed with a prism giving small vertical dispersion. The three spectrograms, respectively, cover 1/50, 7, and 21 free spectral ranges.

Fig. 2
Fig. 2

Portion of a typical echellegram of thorium, showing a vertical fiducial line crossing all cycles, and four mercury lines (marked with dots) which serve as calibrating standards. Range 5300–6000A.

Fig. 3
Fig. 3

The vertical focal curve of the echelle, showing approximation to best focus by use of a flat plate curved horizontally. Ca and Cb are two mλ0 positions.

Fig. 4
Fig. 4

The geometry of an inclined echelle cycle, showing the relation of the line distance l to the fiducial line: (a) Which is used as mλ0; (b) Is another possible fiducial line.

Fig. 5
Fig. 5

Relation of Ca, Δ, and to the mλ curve.

Fig. 6
Fig. 6

Typical average correction curve of for a group of ten neighboring cycles.

Fig. 7
Fig. 7

One-half of the symmetrical focal curves in the horizontal axial plane for the horizontal focus Ph, for the vertical focus Pv, for a uniform projection distance Pc, and for a straight plate Pl perpendicular to the optic axis.

Fig. 8
Fig. 8

The change q2q1 with density of the apparent position of a spectrum line as produced by an imperfect grating for an emulsion having the characteristic curve shown at the left.

Fig. 9
Fig. 9

An experimental curve as determined for a group of ten typical echelle cycles, using thorium arc lines. The wavelength values assumed were those repeatedly measured with a large diffraction grating and reported in the M.I.T. Wavelength Tables.

Equations (1)

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Δ λ / λ = 3 / 2 W [ h - ( p λ / sin α + sin β ) ]