Abstract

Formulas have been established which express the flux given by a spectrometer as a function of the effective resolving power and of the dimension of the dispersive system (area of the base of the prism, or area of the grating, or area of the plates of the étalon). It is thus possible to compare the luminosities of the three types of instruments with, in each case, equal resolving power and equal dimension. This comparison reveals a great superiority of the grating over the prism for all regions of wavelengths, and a great superiority of the étalon over the grating. In the case of the étalon, the overlapping may be overcome by the use of several étalons in series.

© 1954 Optical Society of America

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References

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  1. P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 6, 91 (1948).
  2. P. Jacquinot, Compt. rend, du Xéme Congrés du G.A.M.S., p. 79 (1948). (The result is given here in a slightly different form, which can easily be related to the results given in the two previous articles.)
  3. Schuster and Nicholson, Theory of Optics (London, 1924), third edition, pp. 44, 158.
  4. R. Chabbal, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 24, 138–186 (1953).
  5. Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
    [Crossref]
  6. Bright, Jackson, and Kuhn, Proc. Roy. Soc. (London) A62, 225 (1949).
    [Crossref]
  7. P. Giacomo, Compt. rend. 235, 1627 (1952).
  8. For example, D. A. Jackson and H. Kuhn, Proc. Roy. Soc. (London) A167, 205 (1938).
    [Crossref]

1953 (1)

R. Chabbal, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 24, 138–186 (1953).

1952 (2)

Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
[Crossref]

P. Giacomo, Compt. rend. 235, 1627 (1952).

1949 (1)

Bright, Jackson, and Kuhn, Proc. Roy. Soc. (London) A62, 225 (1949).
[Crossref]

1948 (2)

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 6, 91 (1948).

P. Jacquinot, Compt. rend, du Xéme Congrés du G.A.M.S., p. 79 (1948). (The result is given here in a slightly different form, which can easily be related to the results given in the two previous articles.)

1938 (1)

For example, D. A. Jackson and H. Kuhn, Proc. Roy. Soc. (London) A167, 205 (1938).
[Crossref]

Bright,

Bright, Jackson, and Kuhn, Proc. Roy. Soc. (London) A62, 225 (1949).
[Crossref]

Brochard,

Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
[Crossref]

Chabbal,

Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
[Crossref]

Chabbal, R.

R. Chabbal, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 24, 138–186 (1953).

Chantrel,

Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
[Crossref]

Dufour, Ch.

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 6, 91 (1948).

Giacomo, P.

P. Giacomo, Compt. rend. 235, 1627 (1952).

Jackson,

Bright, Jackson, and Kuhn, Proc. Roy. Soc. (London) A62, 225 (1949).
[Crossref]

Jackson, D. A.

For example, D. A. Jackson and H. Kuhn, Proc. Roy. Soc. (London) A167, 205 (1938).
[Crossref]

Jacquinot,

Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
[Crossref]

Jacquinot, P.

P. Jacquinot, Compt. rend, du Xéme Congrés du G.A.M.S., p. 79 (1948). (The result is given here in a slightly different form, which can easily be related to the results given in the two previous articles.)

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 6, 91 (1948).

Kuhn,

Bright, Jackson, and Kuhn, Proc. Roy. Soc. (London) A62, 225 (1949).
[Crossref]

Kuhn, H.

For example, D. A. Jackson and H. Kuhn, Proc. Roy. Soc. (London) A167, 205 (1938).
[Crossref]

Nicholson,

Schuster and Nicholson, Theory of Optics (London, 1924), third edition, pp. 44, 158.

Schuster,

Schuster and Nicholson, Theory of Optics (London, 1924), third edition, pp. 44, 158.

Compt. rend, du Xéme Congrés du G.A.M.S. (1)

P. Jacquinot, Compt. rend, du Xéme Congrés du G.A.M.S., p. 79 (1948). (The result is given here in a slightly different form, which can easily be related to the results given in the two previous articles.)

Compt. rend. (1)

P. Giacomo, Compt. rend. 235, 1627 (1952).

J. phys. et radium (1)

Brochard, Chabbal, Chantrel, and Jacquinot, J. phys. et radium 13, 433 (1952);J. Blaise and H. Chantrel, ibid. 14, 135 (1953).
[Crossref]

J. recherches centre natl. recherche sci., Labs. Bellevue (Paris) (2)

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 6, 91 (1948).

R. Chabbal, J. recherches centre natl. recherche sci., Labs. Bellevue (Paris), No. 24, 138–186 (1953).

Proc. Roy. Soc. (London) (2)

Bright, Jackson, and Kuhn, Proc. Roy. Soc. (London) A62, 225 (1949).
[Crossref]

For example, D. A. Jackson and H. Kuhn, Proc. Roy. Soc. (London) A167, 205 (1938).
[Crossref]

Other (1)

Schuster and Nicholson, Theory of Optics (London, 1924), third edition, pp. 44, 158.

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Figures (8)

F. 1
F. 1

Diagram of a conventional spectrometer.

F. 2
F. 2

Line contour given by a monochromator with slits of equal spectral widths w.

F. 3
F. 3

Variation of the coefficient to be applied to the formula (1) as a function of the ratio of the effective to the theoretical resolving power.

F. 4
F. 4

Fundamental quantities for a prism.

F. 5
F. 5

(a) Fundamental quantities for a grating. (b) Blazed grating.

F. 6
F. 6

Variation, as a function of the wavelength (in logarithmic scale) of the ratio P, of the flux given by a prism to the flux given by a grating of the same size and with the same effective resolving power.

F. 7
F. 7

The Fabry-Perot étalon.

F. 8
F. 8

Variation of the transmission of an étalon as a function of the direction (cosi) or of the wave number σ.

Equations (23)

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Φ = τ B S Ω = τ B S β α 2 ,
Φ = τ B S β λ D 2 R .
D 2 = d i 2 / d λ = t W d μ d λ ,
S D 2 = t h d μ d λ = A d μ d λ .
D 2 = d i 2 / d λ = m · n cos i 2 and sin i 1 + sin i 2 = m n λ ,
S D 2 = A sin i 1 + sin i 2 λ .
i 1 = φ x i 2 = φ + x ( φ : blaze angle ) ,
sin i 1 + sin i 2 = 2 sin φ cos x ,
sin i 1 + sin i 2 = sin 2 φ
sin i 1 + sin i 2 = 2 sin φ ,
S D 2 = A 2 sin φ λ .
P = Φ ( prism ) Φ ( grating ) = λ d μ / d λ 2 sin φ .
P = λ d μ / d λ .
T = τ [ 1 + 4 R ( 1 R ) 2 sin 2 ( 2 π t σ cos i ) ] 1 ,
τ = [ T / ( 1 R ) ] 2
δ ( cos i ) cos i = δ σ σ = 1 R 0 ,
Ω = 2 π δ ( cos i ) 2 π / R 0 ,
Φ = π 2 2 τ B A R 0 3.4 τ B A R .
δ ( cos i ) = cos i 0 1 = 1 / R 0 ,
i 0 = ( 2 / R 0 ) 1 2 .
G = Φ ( F . - P . ) / Φ ( grating ) = 3.4 / β
B = λ λ + δ λ B λ d λ B λ δ λ = B λ λ / R ,
Φ = τ B S β λ 2 D 2 R 2 .