Abstract

Stray light due to undesired multiple dispersions has been investigated for Czerny-Turner and Ebert grating spectrometers. Both double dispersion and higher multiple dispersions are discussed in all orders of diffraction. Experimental and theoretical results are presented. An upper bound on the wavelength of this stray light is found as a function of the grating spacing. This shows that over any wavelength range of interest, the stray light due to multiple dispersion often can be eliminated by use of sufficiently finely ruled gratings. The results are also used to propose improvements on a previously suggested [ C. M. Penchina, Appl. Opt. 6, 1029 ( 1967)] masking technique.

© 1968 Optical Society of America

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References

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  1. C. M. Penchina, Appl. Opt. 6, 1029 (1967).
    [CrossRef] [PubMed]
  2. M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
    [CrossRef]
  3. H. Ebert, Ann. Phys. 38, 489 (1889); W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
    [CrossRef]
  4. R. F. Stamm, C. F. Salzman, J. Opt. Soc. Amer. 43, 126 (1953).
    [CrossRef]
  5. J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 56, 1390 (1966).
    [CrossRef]
  6. A. Watanabe, G. C. Tabisz, Appl. Opt. 6, 1132 (1967).
    [CrossRef] [PubMed]
  7. W. T. Welford, J. Opt. Soc. Amer. 53, 766 (1963).
  8. D. Landon, S. P. S. Porto, Appl. Opt. 4, 762 (1965).
    [CrossRef]
  9. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc., New York, 1957), pp. 333, 334 and 342.
  10. The Spex Speaker 11, No. 2, 1 (1966). The value 3500 Å that appears in this reference is apparently in error. It is interesting to note that this source of scattered light occurs in all mirror spectrometers. In the Czerny-Turner and Ebert, the longest wavelength setting at which it occurs depends essentially on the grating spacing and f number and is essentially independent of such things as slit separation.
  11. T. Lyman, Phys. Rev. 12, 1 (1901); Phys. Rev. 16, 257 (1903).
  12. W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
    [CrossRef]
  13. C. F. Meyer, The Diffraction of Light, X-rays, and Material Particles (The University of Chicago Press, Chicago, 1934), pp. 180–185.
  14. A. J. Mittledorf, The Spex Speaker 10, No. 3, 1 (1965).
  15. H. A. Rowland, Phil. Mag. 35, 397 (1893); The Physical Papers of Henry Augustus Rowland (The Johns Hopkins Press, Baltimore, 1902), p. 525.
  16. R. S. Wiley, Bausch & Lomb, Inc., Rochester, N. Y., private communication.

1967

1966

J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 56, 1390 (1966).
[CrossRef]

The Spex Speaker 11, No. 2, 1 (1966). The value 3500 Å that appears in this reference is apparently in error. It is interesting to note that this source of scattered light occurs in all mirror spectrometers. In the Czerny-Turner and Ebert, the longest wavelength setting at which it occurs depends essentially on the grating spacing and f number and is essentially independent of such things as slit separation.

1965

A. J. Mittledorf, The Spex Speaker 10, No. 3, 1 (1965).

D. Landon, S. P. S. Porto, Appl. Opt. 4, 762 (1965).
[CrossRef]

1963

W. T. Welford, J. Opt. Soc. Amer. 53, 766 (1963).

1953

R. F. Stamm, C. F. Salzman, J. Opt. Soc. Amer. 43, 126 (1953).
[CrossRef]

1930

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

1922

W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
[CrossRef]

1901

T. Lyman, Phys. Rev. 12, 1 (1901); Phys. Rev. 16, 257 (1903).

1893

H. A. Rowland, Phil. Mag. 35, 397 (1893); The Physical Papers of Henry Augustus Rowland (The Johns Hopkins Press, Baltimore, 1902), p. 525.

1889

H. Ebert, Ann. Phys. 38, 489 (1889); W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
[CrossRef]

Anderson, J. A.

W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
[CrossRef]

Czerny, M.

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

Ebert, H.

H. Ebert, Ann. Phys. 38, 489 (1889); W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc., New York, 1957), pp. 333, 334 and 342.

Kiess, C. C.

W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
[CrossRef]

Landon, D.

Lyman, T.

T. Lyman, Phys. Rev. 12, 1 (1901); Phys. Rev. 16, 257 (1903).

Meggars, W. F.

W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
[CrossRef]

Meyer, C. F.

C. F. Meyer, The Diffraction of Light, X-rays, and Material Particles (The University of Chicago Press, Chicago, 1934), pp. 180–185.

Mittledorf, A. J.

A. J. Mittledorf, The Spex Speaker 10, No. 3, 1 (1965).

Penchina, C. M.

Porto, S. P. S.

Rowland, H. A.

H. A. Rowland, Phil. Mag. 35, 397 (1893); The Physical Papers of Henry Augustus Rowland (The Johns Hopkins Press, Baltimore, 1902), p. 525.

Runge, C.

W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
[CrossRef]

Salzman, C. F.

R. F. Stamm, C. F. Salzman, J. Opt. Soc. Amer. 43, 126 (1953).
[CrossRef]

Smith, R. C.

J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 56, 1390 (1966).
[CrossRef]

Stamm, R. F.

R. F. Stamm, C. F. Salzman, J. Opt. Soc. Amer. 43, 126 (1953).
[CrossRef]

Tabisz, G. C.

Turner, A. F.

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

Tyler, J. E.

J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 56, 1390 (1966).
[CrossRef]

Watanabe, A.

Welford, W. T.

W. T. Welford, J. Opt. Soc. Amer. 53, 766 (1963).

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc., New York, 1957), pp. 333, 334 and 342.

Wiley, R. S.

R. S. Wiley, Bausch & Lomb, Inc., Rochester, N. Y., private communication.

Ann. Phys.

H. Ebert, Ann. Phys. 38, 489 (1889); W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Amer.

R. F. Stamm, C. F. Salzman, J. Opt. Soc. Amer. 43, 126 (1953).
[CrossRef]

J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 56, 1390 (1966).
[CrossRef]

W. T. Welford, J. Opt. Soc. Amer. 53, 766 (1963).

W. F. Meggars, C. C. Kiess, C. Runge, J. A. Anderson, J. Opt. Soc. Amer. 6, 417 (1922).
[CrossRef]

Phil. Mag.

H. A. Rowland, Phil. Mag. 35, 397 (1893); The Physical Papers of Henry Augustus Rowland (The Johns Hopkins Press, Baltimore, 1902), p. 525.

Phys. Rev.

T. Lyman, Phys. Rev. 12, 1 (1901); Phys. Rev. 16, 257 (1903).

The Spex Speaker

A. J. Mittledorf, The Spex Speaker 10, No. 3, 1 (1965).

The Spex Speaker 11, No. 2, 1 (1966). The value 3500 Å that appears in this reference is apparently in error. It is interesting to note that this source of scattered light occurs in all mirror spectrometers. In the Czerny-Turner and Ebert, the longest wavelength setting at which it occurs depends essentially on the grating spacing and f number and is essentially independent of such things as slit separation.

Z. Phys.

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

Other

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc., New York, 1957), pp. 333, 334 and 342.

C. F. Meyer, The Diffraction of Light, X-rays, and Material Particles (The University of Chicago Press, Chicago, 1934), pp. 180–185.

R. S. Wiley, Bausch & Lomb, Inc., Rochester, N. Y., private communication.

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Figures (8)

Fig. 1
Fig. 1

Illustration showing placement of mask over grating to block (a) all multiply diffracted light, (b) selected wavelengths of multiply diffracted light.

Fig. 2
Fig. 2

Schematic of the top view of a Czerny-Turner monochromator showing path of first order diffracted light under normal conditions.

Fig. 3
Fig. 3

Schematic showing a possible path of doubly diffracted light where light after first diffraction hits collimating mirror.

Fig. 4
Fig. 4

Schematic showing a possible path of doubly diffracted light where light after first diffraction hits focusing mirror.

Fig. 5
Fig. 5

Graph of λ vs λset for doubly diffracted light in orders (1,0) calculated from the program in Appendix I for the Spex model 1400 or model 1700 monochromator with a 600-line/mm grating. The input data were L = 640 mm, W = 76 mm, focal length of mirrors = 750 mm, G = 106 mm, and d−1 = 600 lines/mm.

Fig. 6
Fig. 6

Data taken with a Spex model 1400 used as a single monochromator, with a 600-line/mm, 1-μ blaze grating. The graph of Fig. 5 was used to explain these results.

Fig. 7
Fig. 7

Graph of λ vs λset for doubly diffracted light in orders (2,1) calculated from the program of Appendix II for the Spex model 1400 or model 1700 monochromator with a 600-line/mm grating. The input data were L = 640 mm, W = 76 mm, focal length of mirrors = 750 mm, G = 106 mm, and d−1 = 600 lines/mm.

Fig. 8
Fig. 8

Data taken with a Spex model 1400 used as a single monochromator with a 600-line/mm, 1-μ blaze grating. The graph of Fig. 7 was used to explain these results.

Equations (35)

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m λ = d ( sin i + sin r ) ,
β = sin - 1 [ λ set / ( 2 d cos α ) ] ,
μ = α - 2 β ,
Z = W - L tan μ + [ R - ( G / 2 ) ] ( cos β - sin β tan μ ) .
δ c = μ + 2 sin - 1 [ ( Z / 2 F ) - sin ( α / 2 ) ] ,
δ F = μ + 2 sin - 1 { [ ( Z - 2 W ) / 2 F ] + sin ( α / 2 ) } .
Y = ( Z - L tan δ + W tan β tan δ ) ( 1 + tan β tan δ ) - 1 .
m 1 λ = d [ sin ( β + α ) + sin ( β - δ ) ] .
m 1 λ 1 / d = sin ( α + β ) + sin ( β - δ ) ,
m 2 λ 2 / d = sin ( μ + β ) + sin ( β - α ) ,
m 1 λ / d 2 β + α - δ ,
m 2 λ / d 2 β - α + μ ,
β λ set / 2 d .
R L μ - W + 1 2 G + Z ,
Z F ( δ c + α - μ ) ,
Z F ( δ F - α - μ ) + 2 W ,
R c F ( L - F ) μ + F δ + 1 2 G ± ( F α - W ) ,
δ i j i λ i j / d + 2 β i j + α ,
μ i j j λ i j / d - 2 β i j + α ,
β i j λ set i j / 2 d .
λ k l λ i j ( i - j ) / ( k - l ) ,
λ set k l λ set i j + λ i j ( l i - k j ) / ( k - l ) ,
β k l λ set k l / 2 d .
m 1 λ / d < 2 β + α - δ ,
m 2 λ / d < 2 β - α + μ .
Y = Z - L δ .
0 R G ,
W - ( G / 2 ) Y W + ( G / 2 ) ,
- ( G / 2 ) W Z - W ( G / 2 ) W .
λ = [ 2 / ( m 1 - m 2 ) ] α d ,
λ set = m 1 + m 2 m 1 - m 2 α d ± W - ( G / 2 ) - α F 2 F - L d .
λ min = d m 1 - m 2 [ α - 2 ( G - W ) L + G 2 F ] ,
λ set = d m 1 - m 2 [ { m 2 m 1 } α - ( m 1 + m 2 ) G - W L + { m 1 m 2 } G 2 F ] .
λ max = d m 1 - m 2 [ 3 α + 2 ( G - W ) L - G 2 F ] ,
λ set = a m 1 - m 2 [ ( { m 1 m 2 } + 2 { m 2 m 1 } ) α + ( m 1 + m 2 ) G - W L - { m 1 m 1 } G 2 F ] ,

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