Abstract

For the convenience of monochromator users, the constant-bandwidth operation of a Czerny–Turner monochromator is reviewed and clarified for continuously variable and for discretely variable slit widths. A procedure for selecting the discrete slit widths that are necessary for nearly constant-bandwidth scanning is presented.

© 2000 Optical Society of America

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References

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  1. M. Czerny, A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys. 61, 792–797 (1930).
    [CrossRef]
  2. See, e.g., M. A. Gil, J. M. Simon, A. N. Fantino, “Czerny–Turner spectrograph with a wide spectral range,” Appl. Opt. 27, 4069–4072 (1988).
  3. See, e.g., J. W. Russell, H. L. Strauss, “Czerny–Turner far IR spectrometer for the 300–10-cm-1 region,” Appl. Opt. 4, 1131–1136 (1965).
  4. M. Bass, ed., Handbook of Optics (McGraw-Hill, New York, 1995).
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  6. M. L. Dalton, “Astigmatism compensation in the Czerny–Turner spectrometer,” Appl. Opt. 5, 1121–1123 (1966).
    [CrossRef] [PubMed]
  7. A. B. Sharer, “Correcting for astigmatism in the Czerny–Turner spectrometer and spectrograph,” Appl. Opt. 6, 159–160 (1967).
    [CrossRef]
  8. C. D. Allemand, “Coma correction in Czerny–Turner spectrographs,” J. Opt. Soc. Am. 58, 159–163 (1968).
    [CrossRef]
  9. W. T. Foreman, “Lens correction of astigmatism in a Czerny–Turner spectrograph,” Appl. Opt. 7, 1053–1059 (1968).
    [CrossRef] [PubMed]
  10. A. M. Ghodgaonkar, K. Ramani, “Coma correction for a Czerny–Turner monochromator,” Appl. Opt. 20, 3474–3475 (1981).
    [CrossRef] [PubMed]
  11. J. N. Howard, “Coma correction for a Czerny–Turner monochromator: comment,” Appl. Opt. 21, 1708 (1982).
    [CrossRef]
  12. J. M. Simon, M. A. Gil, A. N. Fantino, N. Angelo, “Czerny–Turner monochromator: astigmatism in the classical and in the crossed beam dispositions,” Appl. Opt. 25, 3715–3720 (1986).
    [CrossRef]
  13. N. C. Das, “Aberration properties of a Czerny–Turner spectrograph using plane-holographic diffraction grating,” Appl. Opt. 30, 3589–3597 (1991).
    [CrossRef] [PubMed]
  14. J. J. Mitteldorf, D. O. Landon, “Multiply diffracted light in the Czerny–Turner spectrometer,” Appl. Opt. 7, 1431–1435 (1968).
    [CrossRef] [PubMed]
  15. J. K. Pribram, C. M. Penchina, “Stray light in Czerny–Turner and Ebert spectrometers,” Appl. Opt. 7, 2005–2014 (1968).
    [CrossRef] [PubMed]
  16. R. C. Hawes, “Multiply diffracted light in the Czerny–Turner spectrometer,” Appl. Opt. 8, 1063 (1969).
    [CrossRef]
  17. A. B. Sharer, D. O. Landon, “Comments on multiple diffracted light in the Czerny–Turner spectrometer,” Appl. Opt. 8, 1063–1064 (1969).
  18. A. B. Shafer, L. R. Megill, L. A. Droppleman, “Optimization of the Czerny–Turner spectrometer,” J. Opt. Soc. Am. 54, 879–887 (1964).
    [CrossRef]
  19. G. G. Chandler, “Optimization of a 4-m asymmetric Czerny–Turner spectrograph,” J. Opt. Soc. Am. 58, 895–899 (1968).
    [CrossRef]
  20. P. E. Rouse, B. Brixner, J. V. Kline, “Optimization of a 4-m asymmetric Czerny–Turner spectrograph,” J. Opt. Soc. Am. 59, 955–960 (1969).
  21. J. Reader, “Optimizing Czerny–Turner spectrographs: a comparison between analytic theory and ray tracing,” J. Opt. Soc. Am. 59, 1189–1196 (1969).
    [CrossRef]
  22. A. Takahashi, “Automatic design of a Czerny–Turner spectrograph by a nonlinear optimization method,” J. Mod. Opt. 34, 679–691 (1987).
    [CrossRef]
  23. L. J. Radziemski, “Calculation of dispersion for a plane grating in a Czerny–Turner mount: a comment,” Appl. Opt. 20, 1948–1950 (1981).
    [CrossRef] [PubMed]
  24. L. J. Radziemski, “Calculation of dispersion for a plane grating in a Czerny–Turner mount: a comment; errata,” Appl. Opt. 20, 2883 (1981).
    [CrossRef]
  25. G. Wunsch, A. Wennemer, J. W. McLaren, “On the design and performance of the Czerny–Turner monochromator in ICP-AES,” Spectrochim. Acta 46B, 1517–1531 (1991).
    [CrossRef]
  26. Copyright Georgia Tech Research Corporation, Atlanta, Ga., 1999.

1991 (2)

N. C. Das, “Aberration properties of a Czerny–Turner spectrograph using plane-holographic diffraction grating,” Appl. Opt. 30, 3589–3597 (1991).
[CrossRef] [PubMed]

G. Wunsch, A. Wennemer, J. W. McLaren, “On the design and performance of the Czerny–Turner monochromator in ICP-AES,” Spectrochim. Acta 46B, 1517–1531 (1991).
[CrossRef]

1988 (1)

1987 (1)

A. Takahashi, “Automatic design of a Czerny–Turner spectrograph by a nonlinear optimization method,” J. Mod. Opt. 34, 679–691 (1987).
[CrossRef]

1986 (1)

1982 (1)

1981 (3)

1969 (4)

1968 (5)

1967 (1)

1966 (1)

1965 (1)

1964 (1)

1930 (1)

M. Czerny, A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys. 61, 792–797 (1930).
[CrossRef]

Allemand, C. D.

Angelo, N.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Brixner, B.

Chandler, G. G.

Czerny, M.

M. Czerny, A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys. 61, 792–797 (1930).
[CrossRef]

Dalton, M. L.

Das, N. C.

Droppleman, L. A.

Fantino, A. N.

Foreman, W. T.

Ghodgaonkar, A. M.

Gil, M. A.

Hawes, R. C.

Howard, J. N.

Kline, J. V.

Landon, D. O.

McLaren, J. W.

G. Wunsch, A. Wennemer, J. W. McLaren, “On the design and performance of the Czerny–Turner monochromator in ICP-AES,” Spectrochim. Acta 46B, 1517–1531 (1991).
[CrossRef]

Megill, L. R.

Mitteldorf, J. J.

Penchina, C. M.

Pribram, J. K.

Radziemski, L. J.

Ramani, K.

Reader, J.

Rouse, P. E.

Russell, J. W.

Shafer, A. B.

Sharer, A. B.

Simon, J. M.

Strauss, H. L.

Takahashi, A.

A. Takahashi, “Automatic design of a Czerny–Turner spectrograph by a nonlinear optimization method,” J. Mod. Opt. 34, 679–691 (1987).
[CrossRef]

Turner, A. F.

M. Czerny, A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys. 61, 792–797 (1930).
[CrossRef]

Wennemer, A.

G. Wunsch, A. Wennemer, J. W. McLaren, “On the design and performance of the Czerny–Turner monochromator in ICP-AES,” Spectrochim. Acta 46B, 1517–1531 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Wunsch, G.

G. Wunsch, A. Wennemer, J. W. McLaren, “On the design and performance of the Czerny–Turner monochromator in ICP-AES,” Spectrochim. Acta 46B, 1517–1531 (1991).
[CrossRef]

Appl. Opt. (15)

W. T. Foreman, “Lens correction of astigmatism in a Czerny–Turner spectrograph,” Appl. Opt. 7, 1053–1059 (1968).
[CrossRef] [PubMed]

A. M. Ghodgaonkar, K. Ramani, “Coma correction for a Czerny–Turner monochromator,” Appl. Opt. 20, 3474–3475 (1981).
[CrossRef] [PubMed]

J. N. Howard, “Coma correction for a Czerny–Turner monochromator: comment,” Appl. Opt. 21, 1708 (1982).
[CrossRef]

J. M. Simon, M. A. Gil, A. N. Fantino, N. Angelo, “Czerny–Turner monochromator: astigmatism in the classical and in the crossed beam dispositions,” Appl. Opt. 25, 3715–3720 (1986).
[CrossRef]

N. C. Das, “Aberration properties of a Czerny–Turner spectrograph using plane-holographic diffraction grating,” Appl. Opt. 30, 3589–3597 (1991).
[CrossRef] [PubMed]

J. J. Mitteldorf, D. O. Landon, “Multiply diffracted light in the Czerny–Turner spectrometer,” Appl. Opt. 7, 1431–1435 (1968).
[CrossRef] [PubMed]

J. K. Pribram, C. M. Penchina, “Stray light in Czerny–Turner and Ebert spectrometers,” Appl. Opt. 7, 2005–2014 (1968).
[CrossRef] [PubMed]

R. C. Hawes, “Multiply diffracted light in the Czerny–Turner spectrometer,” Appl. Opt. 8, 1063 (1969).
[CrossRef]

A. B. Sharer, D. O. Landon, “Comments on multiple diffracted light in the Czerny–Turner spectrometer,” Appl. Opt. 8, 1063–1064 (1969).

See, e.g., M. A. Gil, J. M. Simon, A. N. Fantino, “Czerny–Turner spectrograph with a wide spectral range,” Appl. Opt. 27, 4069–4072 (1988).

See, e.g., J. W. Russell, H. L. Strauss, “Czerny–Turner far IR spectrometer for the 300–10-cm-1 region,” Appl. Opt. 4, 1131–1136 (1965).

M. L. Dalton, “Astigmatism compensation in the Czerny–Turner spectrometer,” Appl. Opt. 5, 1121–1123 (1966).
[CrossRef] [PubMed]

A. B. Sharer, “Correcting for astigmatism in the Czerny–Turner spectrometer and spectrograph,” Appl. Opt. 6, 159–160 (1967).
[CrossRef]

L. J. Radziemski, “Calculation of dispersion for a plane grating in a Czerny–Turner mount: a comment,” Appl. Opt. 20, 1948–1950 (1981).
[CrossRef] [PubMed]

L. J. Radziemski, “Calculation of dispersion for a plane grating in a Czerny–Turner mount: a comment; errata,” Appl. Opt. 20, 2883 (1981).
[CrossRef]

J. Mod. Opt. (1)

A. Takahashi, “Automatic design of a Czerny–Turner spectrograph by a nonlinear optimization method,” J. Mod. Opt. 34, 679–691 (1987).
[CrossRef]

J. Opt. Soc. Am. (5)

Spectrochim. Acta (1)

G. Wunsch, A. Wennemer, J. W. McLaren, “On the design and performance of the Czerny–Turner monochromator in ICP-AES,” Spectrochim. Acta 46B, 1517–1531 (1991).
[CrossRef]

Z. Phys. (1)

M. Czerny, A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys. 61, 792–797 (1930).
[CrossRef]

Other (3)

M. Bass, ed., Handbook of Optics (McGraw-Hill, New York, 1995).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Copyright Georgia Tech Research Corporation, Atlanta, Ga., 1999.

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Figures (3)

Fig. 1
Fig. 1

Czerny–Turner monochromator configuration in the coordinate system of the planar grating. All angles are defined as being positive when they are measured counterclockwise as illustrated.

Fig. 2
Fig. 2

Needed slit width Δx as a function of wavelength λ to produce a constant-wavelength spectral bandwidth Δλ across the exit slit of a Czerny–Turner monochromator.

Fig. 3
Fig. 3

Representative slit widths Δx selected when the slit width is adjustable in discrete steps according to the procedure described in the text.

Tables (3)

Tables Icon

Table 1 Slit Widths Δx (in µm) Needed To Produce Various Constant Bandwidths Δλ for a Czerny–Turner Monochromator with 1/Λ = 1200 grooves/mm, i = 1, ϕ = 5°, and f = 500 mm

Tables Icon

Table 2 Example of First Ten and Other Entries in a Look-Up Table for a Constant Bandwidth of Δλ = 1 nm for a Czerny–Turner Monochromator with 1/Λ = 1200 grooves/mm, i = 1, ϕ = 5.0°, f = 500 mm, and Δs = 1 µm

Tables Icon

Table 3 Bandwidth Error Values for a Desired Constant Bandwidth Δλ = 1 nm for a Czerny–Turner Monochromator with 1/Λ = 1200 grooves/mm, i = 1, ϕ = 5.0°, f = 500 mm, and Δs = 1 µm

Equations (20)

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sin θ+sin θi=iλ/Λ,
λ=2Λ/icos ϕ sin ρ.
dλ/dθi=Λ/icosρ-ϕ.
dλ/dx=Λ/ifcosρ-ϕ.
Δx=ifΔλ/Λ cosρ-ϕ
Δxλj=fΔλ/Λ cos ϕ.
Δxλj=Δxj-1-0.5Δs
λj=2Λ sinϕ-cos-1fΔλ/ΛΔxλjcos ϕ.
Δxj=Δxλj-0.5Δs.
Δxj=Δxλj-1+0.5Δs.
Δxλj=Δxλj+Δs
λj=2Λ sinϕ+cos-1fΔλ/ΛΔxλjcos ϕ.
Δxλj=Δxj+0.5Δs
λmax=2Λ sin90°-ϕcos ϕ.
Δxλj=Δxj-1+0.5Δs
λj=2Λ sinϕ+cos-1fΔλ/ΛΔxλjcos ϕ.
Δxj=Δxλj+0.5Δs.
e=Δλλ, Δxj-Δλc/Δλc,
emax=Λ cosρ-ϕ/fΔλcΔs/2,
eavg,j=1/λj+1-λjΔλcλjλj+1 |ΛΔxj/f×1-λ2/4Λ2 cos2 ϕ1/2 cos ϕ+λ tan ϕ/2Λ-Δλc|dλ.

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