Abstract

In this paper I discuss the construction and the aberration properties of plane-holographic diffraction gratings in a Czerny–Turner mounting. A ray-tracing scheme has been formulated for computing the aberrations of the system. It has been found that in the area near the recording wavelength for the holographic grating, the system has better resolution than does a conventional grating system. The design parameters of a medium-sized holographic grating spectrograph are specified. The performance of the spectrograph is evaluated by plotting spot diagrams, which show that astigmatic defects are much reduced.

© 1991 Optical Society of America

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References

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  1. G. Schmahl, D. Rudolph, “Holographic diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 195.
  2. M. V. R. K. Murty, R. P. Shukla, “A simple method of producing holographic gratings,” Indian J. Pure Appl. Phys. 14, 153–154 (1976).
  3. S. Johansson, K. Biedermann, “Holographic gratings at the Institute of Optical Research, Stockholm,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O'Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 44–51 (1980).
  4. R. P. Shukla, “A stable laser interferometer for recording holographic gratings,” Indian J. Pure Appl. Phys. 24, 320–323 (1986).
  5. Jobin-Yvon Instruments SA, Diffraction Gratings Ruled and Holographic (Jobin-Yvon, Longjumeau, France, 1973).
  6. M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
    [CrossRef]
  7. M. V. R. K. Murty, “Theory and principle of monochromators, spectrometers and spectrographs,” Opt. Eng. 13, 23–39 (1974).
  8. A. B. Shafer, L. R. Megill, L. Dropplemann, “Optimization of Czerny–Turner spectrometer,” J. Opt. Soc. Am. 54, 879–887 (1964).
    [CrossRef]
  9. W. G. Fastie, U.S. Patent3,011,391 (5December1961).
  10. C. D. Allemand, “Coma correction in Czerny–Turner spectrographs,” J. Opt. Soc. Am. 58, 159–163 (1968).
    [CrossRef]
  11. S. A. Khrsnavoskii, “On the properties of the focal surfaces of mirror spectrographs,” Opt. Spectrosc. (USSR) 9, 207–210 (1960).
  12. N. Sassa, “Optical properties of Ebert spectrograph,” Sci. Light (Tokyo) 10, 53–58 (1961).
  13. K. D. Mielenz, “Theory of mirror spectrographs III, focal surfaces and slit curvature of Ebert and Ebert–Fastie spectrograph,” J. Res. Natl. Bur. Stand. Sect. C 68, 205–213 (1964).
  14. J. Reader, “Optimizing Czerny–Turner spectrographs: a comparison between analytic theory and ray tracing,” J. Opt. Soc. Am. 59, 1189–1196 (1969).
    [CrossRef]
  15. A. Thévonon, J. Flamand, J. P. Laude, B. Touzet, “Aberration-corrected plane gratings,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 136–145 (1987).
  16. G. H. Spencer, M. V. R. K. Murty, “General Ray-Tracing Procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
    [CrossRef]

1986 (1)

R. P. Shukla, “A stable laser interferometer for recording holographic gratings,” Indian J. Pure Appl. Phys. 24, 320–323 (1986).

1976 (1)

M. V. R. K. Murty, R. P. Shukla, “A simple method of producing holographic gratings,” Indian J. Pure Appl. Phys. 14, 153–154 (1976).

1974 (1)

M. V. R. K. Murty, “Theory and principle of monochromators, spectrometers and spectrographs,” Opt. Eng. 13, 23–39 (1974).

1969 (1)

1968 (1)

1964 (2)

A. B. Shafer, L. R. Megill, L. Dropplemann, “Optimization of Czerny–Turner spectrometer,” J. Opt. Soc. Am. 54, 879–887 (1964).
[CrossRef]

K. D. Mielenz, “Theory of mirror spectrographs III, focal surfaces and slit curvature of Ebert and Ebert–Fastie spectrograph,” J. Res. Natl. Bur. Stand. Sect. C 68, 205–213 (1964).

1962 (1)

1961 (2)

W. G. Fastie, U.S. Patent3,011,391 (5December1961).

N. Sassa, “Optical properties of Ebert spectrograph,” Sci. Light (Tokyo) 10, 53–58 (1961).

1960 (1)

S. A. Khrsnavoskii, “On the properties of the focal surfaces of mirror spectrographs,” Opt. Spectrosc. (USSR) 9, 207–210 (1960).

1930 (1)

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

Allemand, C. D.

Biedermann, K.

S. Johansson, K. Biedermann, “Holographic gratings at the Institute of Optical Research, Stockholm,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O'Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 44–51 (1980).

Czerny, M.

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

Dropplemann, L.

Fastie, W. G.

W. G. Fastie, U.S. Patent3,011,391 (5December1961).

Flamand, J.

A. Thévonon, J. Flamand, J. P. Laude, B. Touzet, “Aberration-corrected plane gratings,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 136–145 (1987).

Johansson, S.

S. Johansson, K. Biedermann, “Holographic gratings at the Institute of Optical Research, Stockholm,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O'Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 44–51 (1980).

Khrsnavoskii, S. A.

S. A. Khrsnavoskii, “On the properties of the focal surfaces of mirror spectrographs,” Opt. Spectrosc. (USSR) 9, 207–210 (1960).

Laude, J. P.

A. Thévonon, J. Flamand, J. P. Laude, B. Touzet, “Aberration-corrected plane gratings,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 136–145 (1987).

Megill, L. R.

Mielenz, K. D.

K. D. Mielenz, “Theory of mirror spectrographs III, focal surfaces and slit curvature of Ebert and Ebert–Fastie spectrograph,” J. Res. Natl. Bur. Stand. Sect. C 68, 205–213 (1964).

Murty, M. V. R. K.

M. V. R. K. Murty, R. P. Shukla, “A simple method of producing holographic gratings,” Indian J. Pure Appl. Phys. 14, 153–154 (1976).

M. V. R. K. Murty, “Theory and principle of monochromators, spectrometers and spectrographs,” Opt. Eng. 13, 23–39 (1974).

G. H. Spencer, M. V. R. K. Murty, “General Ray-Tracing Procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
[CrossRef]

Reader, J.

Rudolph, D.

G. Schmahl, D. Rudolph, “Holographic diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 195.

Sassa, N.

N. Sassa, “Optical properties of Ebert spectrograph,” Sci. Light (Tokyo) 10, 53–58 (1961).

Schmahl, G.

G. Schmahl, D. Rudolph, “Holographic diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 195.

Shafer, A. B.

Shukla, R. P.

R. P. Shukla, “A stable laser interferometer for recording holographic gratings,” Indian J. Pure Appl. Phys. 24, 320–323 (1986).

M. V. R. K. Murty, R. P. Shukla, “A simple method of producing holographic gratings,” Indian J. Pure Appl. Phys. 14, 153–154 (1976).

Spencer, G. H.

Thévonon, A.

A. Thévonon, J. Flamand, J. P. Laude, B. Touzet, “Aberration-corrected plane gratings,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 136–145 (1987).

Touzet, B.

A. Thévonon, J. Flamand, J. P. Laude, B. Touzet, “Aberration-corrected plane gratings,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 136–145 (1987).

Turner, A. F.

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

Indian J. Pure Appl. Phys. (2)

M. V. R. K. Murty, R. P. Shukla, “A simple method of producing holographic gratings,” Indian J. Pure Appl. Phys. 14, 153–154 (1976).

R. P. Shukla, “A stable laser interferometer for recording holographic gratings,” Indian J. Pure Appl. Phys. 24, 320–323 (1986).

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Stand. Sect. C (1)

K. D. Mielenz, “Theory of mirror spectrographs III, focal surfaces and slit curvature of Ebert and Ebert–Fastie spectrograph,” J. Res. Natl. Bur. Stand. Sect. C 68, 205–213 (1964).

Opt. Eng. (1)

M. V. R. K. Murty, “Theory and principle of monochromators, spectrometers and spectrographs,” Opt. Eng. 13, 23–39 (1974).

Opt. Spectrosc. (USSR) (1)

S. A. Khrsnavoskii, “On the properties of the focal surfaces of mirror spectrographs,” Opt. Spectrosc. (USSR) 9, 207–210 (1960).

Sci. Light (Tokyo) (1)

N. Sassa, “Optical properties of Ebert spectrograph,” Sci. Light (Tokyo) 10, 53–58 (1961).

U.S. Patent (1)

W. G. Fastie, U.S. Patent3,011,391 (5December1961).

Z. Phys. (1)

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

Other (4)

G. Schmahl, D. Rudolph, “Holographic diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 195.

Jobin-Yvon Instruments SA, Diffraction Gratings Ruled and Holographic (Jobin-Yvon, Longjumeau, France, 1973).

S. Johansson, K. Biedermann, “Holographic gratings at the Institute of Optical Research, Stockholm,” in Periodic Structures, Gratings, Moiré Patterns, and Diffraction Phenomena I, C. H. Chi, E. G. Loewen, C. L. O'Bryan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.240, 44–51 (1980).

A. Thévonon, J. Flamand, J. P. Laude, B. Touzet, “Aberration-corrected plane gratings,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 136–145 (1987).

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Figures (6)

Fig. 1
Fig. 1

Diagram showing the construction and imaging properties of a plane-holographic grating using a Czerny–Turner mounting.

Fig. 2
Fig. 2

Typical ray-aberration curves of spectral images formed by a Czerny–Turner spectrograph made with a plane-holographic diffraction grating. Negative values of wavelength indicate that the images are formed in the negative order.

Fig. 3
Fig. 3

Typical ray-aberration curves of spectral images formed by a Czerny–Turner spectrograph made with a conventional diffraction grating. Negative values of wavelength indicate that the images are formed in the negative order.

Fig. 4
Fig. 4

Resolution curves of the spectral images formed by the conventional as well as the holographic-grating spectrograph for two different values of the grating width ω. Solid curves are for the holographic-grating system, whereas the dashed curves are for the conventional grating system.

Fig. 5
Fig. 5

Spot diagrams of the holographic-grating spectrograph at various wavelengths. The horizontal axis represents the image blur in micrometers, whereas the vertical axis represents the length of the spectral image in millimeters.

Fig. 6
Fig. 6

Spot diagrams of the conventional grating spectrograph at various wavelengths. The horizontal axis represents the image blur in micrometers, and the vertical axis represents the length of the spectral image in millimeters.

Tables (1)

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Table 1 Resolution of the Practical Spectrograph at Various Wavelengths

Equations (51)

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sin 2 ϕ = λ 0 / σ 0 .
sin β = λ / σ 0 .
sin β = ( λ / λ 0 ) sin 2 ϕ .
sin ϕ = H / ( H 2 + f 2 ) 1 / 2 ,
sin ψ = H / ( H 2 + f 2 ) 1 / 2 ,
ψ = β + ϕ .
1 / σ 0 = 2 ( H / f ) / λ 0 ,
H = [ 2 ( λ / λ 0 ) + 1 ] H .
d λ / d H = λ 0 / 2 H .
Δ λ / λ 0 = Δ H / 2 H .
r 1 = [ ( X 1 H ) 2 + Y 1 2 + ( Z 1 R / 2 ) 2 ] 1 / 2 .
Z 1 = R [ R 2 ( X 1 2 + Y 1 2 ) ] 1 / 2 ,
k 1 = ( X 1 H ) / r 1 , l 1 = Y 1 / r 1 , m 1 = ( Z 1 R / 2 ) / r 1 .
K 1 = X 1 / R , L 1 = Y 1 / R , M 1 = 1.0 Z 1 / R .
k 1 = k 1 2 a 1 K 1 , l 1 = l 1 2 a 1 L 1 , m 1 = m 1 2 a 1 M 1 ;
a 1 = ( k 1 K 1 + l 1 L 1 + m 1 M 1 ) / ( K 1 2 + L 1 2 + M 1 2 ) .
X 01 = 0 , Y 01 = 0 , Z 01 = d .
X 12 = ( X 1 X 01 ) cos ϕ + ( Z 1 Z 01 ) sin ϕ , Y 12 = Y 1 Y 01 , Z 12 = ( X 1 X 01 ) sin ϕ + ( Z 1 Z 01 ) cos ϕ .
k 2 = k 1 cos ϕ + m 1 sin ϕ , l 2 = l 1 , m 2 = k 1 sin ϕ + m 1 cos ϕ .
X 2 = X 12 + k 2 D 2 , Y 2 = Y 12 + l 2 D 2 , Z 2 = Z 12 + m 2 D 2 ,
D = Z 12 / m 2 .
K 2 = 0 , L 2 = 0 , M 2 = 1.0 .
k 2 = k 2 Λ u 2 + T f K 2 , l 2 = l 2 Λ υ 2 + T f L 2 , m 2 = m 2 Λ w 2 + T f M 2 ,
Λ = λ / σ ,
T n + 1 = ( T n 2 b ) / 2 ( T n + a 2 ) ,
a 2 = ( k 2 K 2 + l 2 L 2 + m 2 M 2 ) / ( K 2 2 + L 2 2 + M 2 2 ) ,
b = [ Λ 2 2 Λ ( k 2 u 2 + l 2 υ 2 + m 2 w 2 ) ] / ( K 2 2 + L 2 2 + M 2 2 ) .
T 1 = b / 2 a 2 2 a 2 .
X 21 = X 2 cos ϕ Z 2 sin ϕ + X 01 , Y 21 = Y 2 + Y 01 , Z 21 = X 2 sin ϕ + Z 2 cos ϕ + Z 01 .
k 3 = k 2 cos ϕ m 2 sin ϕ , l 3 = l 2 , m 3 = k 2 sin ϕ + m 2 cos ϕ .
X 3 = X 21 + D 3 k 3 , Y 3 = Y 21 + D 3 l 3 , Z 3 = Z 21 + D 3 m 3 ,
D 3 = B + ( B 2 C ) ,
B = k 3 X 21 + l 3 Y 21 + m 3 ( Z 21 R ) ,
C = X 21 2 + Y 21 2 + Z 21 ( Z 21 2 R ) .
K 3 = X 3 / R , L 3 = Y 3 / R , M 3 = 1.0 Z 3 / R .
k 3 = k 3 2 a 3 K 3 , l 3 = l 3 2 a 3 L 3 , m 3 = m 3 2 a 3 M 3 ,
a 3 = ( k 3 K 3 + l 3 L 3 + m 3 M 3 ) / ( K 3 2 + L 3 2 + M 3 2 ) .
X = X 3 + k 3 D 3 , Y = Y 3 + l 3 D 3 , Z = Z 3 + m 3 D 3 ,
D 3 = ( R 2 Z 3 ) / 2 m 3 .
E x = H X , E y = Y .
K 2 u 2 + L 2 υ 2 + M 2 w 2 = 0 ,
u 2 2 + υ 2 2 + w 2 2 = 1.0 ,
u 2 = 1.0 / [ 1.0 + K 2 2 / ( L 2 2 + M 2 2 ) ] 1 / 2 , υ 2 = K 2 L 2 u 2 / ( L 2 2 + M 2 2 ) , w 2 = K 2 M 2 u 2 / ( L 2 2 + M 2 2 ) .
k 20 = k 2 Λ 0 u 2 + T 0 K 2 , l 20 = l 2 Λ 0 υ 2 + T 0 L 2 , m 20 = m 2 Λ 0 w 2 + T 0 M 2 ,
Λ 0 = λ 0 / σ .
T 0 = [ K 2 ( k 20 k 2 ) + L 2 ( l 20 l 2 ) + M 2 ( m 20 m 2 ) ] / × ( K 2 2 + L 2 2 + M 2 2 ) ,
Λ 0 = [ ( k 2 k 20 + T 0 K 2 ) 2 + ( l 2 l 20 + T 0 L 2 ) 2 + ( m 2 m 20 + T 0 M 2 ) 2 ] 1 / 2 ,
u 2 = ( k 2 k 20 + T 0 K 2 ) / Λ 0 , υ 2 = ( l 2 l 20 + T 0 L 2 ) Λ 0 , w 2 = ( m 2 m 20 + T 0 M 2 ) Λ 0 .
( δ Ex δ k 20 ) Δ k 20 + ( δ Ex δ l 20 ) Δ l 20 = x Ex ,
( δ Ey δ k 20 ) Δ k 20 + ( δ Ey δ l 20 ) Δ l 20 = y Ey ,
k 20 = k 20 + Δ k 20 , l 20 = l 20 + Δ l 20 , m 20 = [ 1.0 ( k 20 2 + l 20 2 ) ] 1 / 2 ,

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