Abstract

Absolute astigmatism correction for flat field spectrographs is possible over an arbitrary wavelength range, while absolute defocus correction is not possible.

© 1989 Optical Society of America

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References

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  1. T. Namioka, “Theory of the Concave Grating,” J. Opt. Soc. Am. 49, 446 (1959).
    [CrossRef]
  2. W. R. McKinney, C. Palmer, “Numerical Design Method for Aberration-Reduced Concave Grating Spectrometers,” Appl. Opt. 26, 3108 (1987).
    [CrossRef] [PubMed]

1987

1959

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Figures (1)

Fig. 1
Fig. 1

Flat field spectrometer geometry. Light from point A(r,α) is diffracted by the grating centered at O; the ideal image points of the ends of the spectrum (λS and λL) are located at BS and BL, the ends of the detector, respectively. An intermediate wavelength λ is diffracted to an ideal image point between BS and BL located at point (r′,β).

Equations (23)

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x = a y + b ,
r ( β ) = b cos β a sin β ,
m λ = d ( sin α + sin β ) .
F 20 = cos 2 α r + cos 2 β r 2 a 20 ( cos α + cos β ) + m λ λ 0 H 20 ,
F 02 = 1 r + 1 r 2 a 02 ( cos α + cos β ) + m λ λ 0 H 02 ,
r T ( β ) = cos 2 β A + B cos β + C sin β ,
r S ( β ) = 1 D + E cos β + F sin β ,
A = B cos α + C sin α cos 2 α r ,
B = 2 a 20 ,
C = 2 d H 20 λ 0 ,
D = E cos α + F sin α 1 r ,
E = 2 a 02 ,
F = 2 d H 02 λ 0 .
b = 1 , D = 0 , E = 1 , and F = a .
H 02 = a λ 0 2 d ,
a 02 = 1 2 ,
r = 1 cos α a sin α ,
x = r cos β = 1
r cos α = 1 .
r = cos α , r = cos β ,
β [ r T ( β ) r ideal ( β ) ] = β [ r T ( β ) r S ( β ) ] = 0 .
λ i = d m ( sin α + sin β i ) .
f ( β , H 20 ) = 0 ,

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