Abstract

A method for mapping, to first order, the spectrograms that result from echelle spectrographic systems is discussed. An in-depth description of the principles behind the method are given so that software may be generated. Such software is an invaluable echelle spectrograph design aid. Results from two applications are discussed.

© 1985 Optical Society of America

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References

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  1. D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).
  2. G. R. Harrison, “The Production of Diffraction Gratings: II. The Design of Echelle Gratings and Spectrographs,” J. Opt. Soc. Am. 39, 522 (1949).
    [CrossRef]
  3. D. J. Schroeder, “Design Considerations for Astronomical Echelle Spectrographs,” Publ. Astron. Soc. Pac. 82, 1253 (1970).
    [CrossRef]
  4. D. J. Schroeder, C. M. Anderson, “An Echelle Spectrograph for Astronomical Use,” Publ. Astron. Soc. Pac. 83, 438 (1971).
    [CrossRef]
  5. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 360.
  6. J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958), pp. 264–267.
  7. System Design Report for the I.U.E. Vol. 1: Scientific Instrument (NASA, 1976).
  8. F. A. Boggess et al., “The IUE Spacecraft and Instrumentation,” Nature London 275, 372 (1978).
    [CrossRef]
  9. H. D. Vitagliano, NASA GSFC; personal communication (Jan.1985).
  10. International Ultraviolet Explorer Image Processing Information Manual—Version 2.0 (Computer Sciences Corp., Beltsville, Md., 1985).

1981 (1)

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

1978 (1)

F. A. Boggess et al., “The IUE Spacecraft and Instrumentation,” Nature London 275, 372 (1978).
[CrossRef]

1971 (1)

D. J. Schroeder, C. M. Anderson, “An Echelle Spectrograph for Astronomical Use,” Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

1970 (1)

D. J. Schroeder, “Design Considerations for Astronomical Echelle Spectrographs,” Publ. Astron. Soc. Pac. 82, 1253 (1970).
[CrossRef]

1949 (1)

Anderson, C. M.

D. J. Schroeder, C. M. Anderson, “An Echelle Spectrograph for Astronomical Use,” Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

Boggess, F. A.

F. A. Boggess et al., “The IUE Spacecraft and Instrumentation,” Nature London 275, 372 (1978).
[CrossRef]

Harrison, G. R.

Jenkins, E. B.

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 360.

Long, D.

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

Lowrance, J. L.

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

Schroeder, D. J.

D. J. Schroeder, C. M. Anderson, “An Echelle Spectrograph for Astronomical Use,” Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

D. J. Schroeder, “Design Considerations for Astronomical Echelle Spectrographs,” Publ. Astron. Soc. Pac. 82, 1253 (1970).
[CrossRef]

Songaila, A.

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

Strong, J.

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958), pp. 264–267.

Vitagliano, H. D.

H. D. Vitagliano, NASA GSFC; personal communication (Jan.1985).

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 360.

York, D. G.

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

Zucchino, P.

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

J. Opt. Soc. Am. (1)

Nature London (1)

F. A. Boggess et al., “The IUE Spacecraft and Instrumentation,” Nature London 275, 372 (1978).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. G. York, E. B. Jenkins, P. Zucchino, J. L. Lowrance, D. Long, A. Songaila, “Echelle Spectroscopy with a Charge-Coupled Device,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 202 (1981).

Publ. Astron. Soc. Pac. (2)

D. J. Schroeder, “Design Considerations for Astronomical Echelle Spectrographs,” Publ. Astron. Soc. Pac. 82, 1253 (1970).
[CrossRef]

D. J. Schroeder, C. M. Anderson, “An Echelle Spectrograph for Astronomical Use,” Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

Other (5)

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 360.

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958), pp. 264–267.

System Design Report for the I.U.E. Vol. 1: Scientific Instrument (NASA, 1976).

H. D. Vitagliano, NASA GSFC; personal communication (Jan.1985).

International Ultraviolet Explorer Image Processing Information Manual—Version 2.0 (Computer Sciences Corp., Beltsville, Md., 1985).

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Figures (1)

Fig. 1
Fig. 1

Typical echellogram (14 orders).

Tables (2)

Tables Icon

Table I Input and Sample Output for EGRAM–IUE Comparison

Tables Icon

Table II Predicted and Actual Coordinates

Equations (27)

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χ x ψ .
λ B = d ( sin θ + sin χ x ) ,
Δ Λ = λ cen / m ,
α = ± λ 2 d cos ψ ,
d l d λ ( echelle ) = Δ Λ ( longest ) W
T = 4 ( p 2 + 1 ) ± { [ 16 ( p 2 + 1 ) 2 48 p 2 ] } 1 / 2 8 p 2 , W = 2 r p T 1 / 2 , H = r ( 1 T p 2 ) 1 / 2 + ( 1 T ) 1 / 2 ,
d l d λ = f cam m d cos χ x ,
Δ Λ ( longest ) = λ max m min .
d = f cam λ max W cos ψ .
R = λ Δ λ ,
Δ λ = W a p M [ d λ d l ( echelle ) ] ,
m min = R W a p M W .
m min = 2 d cos θ sin ψ λ max .
λ cen ( m ) = k m , m = m min , m min + 1 , , m max .
Y high ( m ) = f cam λ cen ( m ) 2 d cos ψ ,
Y low ( m ) = Y high ( m ) .
λ high ( m ) = λ cen ( m ) + λ cen ( m ) 2 m ,
λ low ( m ) = λ cen ( m ) λ cen ( m ) 2 m .
( d λ d y ) m = Δ Λ m Y high ( m ) Y low ( m ) .
d x d λ = H H a p M λ max λ min .
S m = d y d x = ( d λ d y ) m ( d x d λ ) .
X int ( m ) = X int ( m 1 ) { [ λ cen ( m 1 ) λ cen ( m ) ] d x d λ } .
Y = λ λ cen ( m ) ( d λ d y ) m ,
X = X int ( m ) + Y S m .
d c d = f cam ( d x d λ ) cos .
N X = [ X int ( m ) + Y S m ] .
R X = X cos γ + Y sin γ , R Y = X sin γ + Y cos γ .

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