Abstract

The design of a new plane grating monochromator is described. The system employs off-axis parabolical mirrors both in the collimator and the camera. The entrance and exit slits lie on the same side of the grating and are curved to obtain the invariance of the curvature of the spectral lines with respect to wavelength variations. The grating is oriented to avoid multiple dispersions. The system is free from aberrations in the center of the field, and since the dependence of the aberrations on any other point of the field is very weak, it is possible to use long slits. The images obtained with this design are of excellent quality and may be improved even further using mirrors with slightly different off-axis angles and focal lengths for the collimator and the camera. Analytical expressions of the aberrations are obtained by the plate diagram method; the results are checked by finite ray tracing for a particular case.

© 1983 Optical Society of America

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References

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  1. M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
    [CrossRef]
  2. R. A. Hill, Appl. Opt. 7, 2184 (1968).
    [CrossRef] [PubMed]
  3. R. A. Hill, Appl. Opt. 8, 575 (1969).
    [CrossRef] [PubMed]
  4. V. L. Chupp, P. C. Grantz, Appl. Opt. 8, 925 (1969).
    [CrossRef] [PubMed]
  5. K. P. Miyake, Opt. Acta 22, 603 (1975).
    [CrossRef]
  6. M. A. Gil, Tesis Doctoral, Dto. de Física, FCEN-UBA (1981).
  7. H. Ebert, Wied. Ann. 38, 489 (1889).
    [CrossRef]
  8. W. G. Fastie, J. Opt. Soc. Am. 42, 641 (1952).
    [CrossRef]
  9. W. T. Welford, J. Opt. Soc. Am. 53, 766 (1963).
  10. A. S. Filler, J. Opt. Soc. Am. 54, 429 (1964).
    [CrossRef]
  11. M. A. Gil, J. M. Simon, Appl. Opt. 18, 2280 (1979).
    [CrossRef] [PubMed]
  12. M. A. Gil, J. M. Simon, Opt. Acta, to be published.
  13. J. M. Simon, Opt. Acta 20, 345 (1973).
    [CrossRef]
  14. J. M. Simon, M. A. Gil, Opt. Acta 25, 381 (1978).
    [CrossRef]
  15. J. M. Simon, M. C. Simon, Opt. Acta 25, 153 (1978).
    [CrossRef]
  16. M. A. Gil, J. M. Simon, Opt. Acta, in press.
  17. G. W. Stroke, in Handbuch der Physik, Vol. 29, S. Flugge, Ed. (New York, Springer, 1967).
  18. J. M. Simon, M. A. Gil, Opt. Acta 25, 83 (1978).
    [CrossRef]
  19. K. P. Miyake, K. Masutani, J. Opt. Paris 8, 175 (1977).
    [CrossRef]

1979 (1)

1978 (3)

J. M. Simon, M. A. Gil, Opt. Acta 25, 381 (1978).
[CrossRef]

J. M. Simon, M. C. Simon, Opt. Acta 25, 153 (1978).
[CrossRef]

J. M. Simon, M. A. Gil, Opt. Acta 25, 83 (1978).
[CrossRef]

1977 (1)

K. P. Miyake, K. Masutani, J. Opt. Paris 8, 175 (1977).
[CrossRef]

1975 (1)

K. P. Miyake, Opt. Acta 22, 603 (1975).
[CrossRef]

1973 (1)

J. M. Simon, Opt. Acta 20, 345 (1973).
[CrossRef]

1969 (2)

1968 (1)

1964 (1)

A. S. Filler, J. Opt. Soc. Am. 54, 429 (1964).
[CrossRef]

1963 (1)

1952 (1)

1930 (1)

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

1889 (1)

H. Ebert, Wied. Ann. 38, 489 (1889).
[CrossRef]

Chupp, V. L.

Czerny, M.

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

Ebert, H.

H. Ebert, Wied. Ann. 38, 489 (1889).
[CrossRef]

Fastie, W. G.

Filler, A. S.

A. S. Filler, J. Opt. Soc. Am. 54, 429 (1964).
[CrossRef]

Gil, M. A.

M. A. Gil, J. M. Simon, Appl. Opt. 18, 2280 (1979).
[CrossRef] [PubMed]

J. M. Simon, M. A. Gil, Opt. Acta 25, 381 (1978).
[CrossRef]

J. M. Simon, M. A. Gil, Opt. Acta 25, 83 (1978).
[CrossRef]

M. A. Gil, J. M. Simon, Opt. Acta, in press.

M. A. Gil, Tesis Doctoral, Dto. de Física, FCEN-UBA (1981).

M. A. Gil, J. M. Simon, Opt. Acta, to be published.

Grantz, P. C.

Hill, R. A.

Masutani, K.

K. P. Miyake, K. Masutani, J. Opt. Paris 8, 175 (1977).
[CrossRef]

Miyake, K. P.

K. P. Miyake, K. Masutani, J. Opt. Paris 8, 175 (1977).
[CrossRef]

K. P. Miyake, Opt. Acta 22, 603 (1975).
[CrossRef]

Simon, J. M.

M. A. Gil, J. M. Simon, Appl. Opt. 18, 2280 (1979).
[CrossRef] [PubMed]

J. M. Simon, M. C. Simon, Opt. Acta 25, 153 (1978).
[CrossRef]

J. M. Simon, M. A. Gil, Opt. Acta 25, 381 (1978).
[CrossRef]

J. M. Simon, M. A. Gil, Opt. Acta 25, 83 (1978).
[CrossRef]

J. M. Simon, Opt. Acta 20, 345 (1973).
[CrossRef]

M. A. Gil, J. M. Simon, Opt. Acta, to be published.

M. A. Gil, J. M. Simon, Opt. Acta, in press.

Simon, M. C.

J. M. Simon, M. C. Simon, Opt. Acta 25, 153 (1978).
[CrossRef]

Stroke, G. W.

G. W. Stroke, in Handbuch der Physik, Vol. 29, S. Flugge, Ed. (New York, Springer, 1967).

Turner, A. F.

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

Welford, W. T.

Appl. Opt. (4)

J. Opt. Paris (1)

K. P. Miyake, K. Masutani, J. Opt. Paris 8, 175 (1977).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Acta (5)

K. P. Miyake, Opt. Acta 22, 603 (1975).
[CrossRef]

J. M. Simon, M. A. Gil, Opt. Acta 25, 83 (1978).
[CrossRef]

J. M. Simon, Opt. Acta 20, 345 (1973).
[CrossRef]

J. M. Simon, M. A. Gil, Opt. Acta 25, 381 (1978).
[CrossRef]

J. M. Simon, M. C. Simon, Opt. Acta 25, 153 (1978).
[CrossRef]

Wied. Ann. (1)

H. Ebert, Wied. Ann. 38, 489 (1889).
[CrossRef]

Z. Phys. (1)

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

Other (4)

M. A. Gil, Tesis Doctoral, Dto. de Física, FCEN-UBA (1981).

M. A. Gil, J. M. Simon, Opt. Acta, in press.

G. W. Stroke, in Handbuch der Physik, Vol. 29, S. Flugge, Ed. (New York, Springer, 1967).

M. A. Gil, J. M. Simon, Opt. Acta, to be published.

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Figures (9)

Fig. 1
Fig. 1

Coordinate system and parameters that describe the plate diagram. The ζ axis connects the center of the pupil with the center of the field. The ξ and η axes lie in the pupil plane which is normal to the ζ axis. The z axis is the principal ray of the beam and connects the image point with the center of the pupil. The x and y coordinates are measured from the z axis and are taken parallel to the ξ and η axes, respectively. The coordinates of the center of the plates are ξ0 and η0, measured from the ζ axis, and ξ and η from the z axis. The angles formed by the z axis with the planes (η,ζ) and (ξ,ζ) are, respectively, α and β. Γi is the strength of the ith plate and li is the distance of that plate from the center of the pupil along the ζ axis.

Fig. 2
Fig. 2

Schematic representation of the proposed mounting.

Fig. 3
Fig. 3

Schematic representation of the collimator and diagrams for the collimator and the camera.

Fig. 4
Fig. 4

Images corresponding to (a) coma, (b) astigmatism, and (c) field curvature on the paraxial plane and at the edge of the field; (d) shows the image of field curvature obtained by rotating the surfaces containing the slits. The spectral line is represented by a dotted curve.

Fig. 5
Fig. 5

Images of coma corresponding to different values of a for the edge of the field and for λ = 5000 Å. The spectral line is represented by a dotted curve.

Fig. 6
Fig. 6

Variation of the image width (Δx) with a for different λ.

Fig. 7
Fig. 7

Variation of the image width (Δx) with λ for fixed values of f and f′ (compensated design). The dotted curve corresponds to the symmetrical or uncompensated design (a = 0).

Fig. 8
Fig. 8

Images corresponding to the center and edge of the field obtained by ray tracing with the uncompensated design. The symbols blank, ●,+,*, and M denote the number of rays that pass through a given point in the focal plane and correspond to 0; 1; 2 or 3; 4, 5, 6, or 7 and 8 or more rays, respectively.

Fig. 9
Fig. 9

Images corresponding to the edge of the field and to different wavelengths obtained by ray tracing with the compensated design.

Equations (39)

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r 4 i Γ i ;
4 r 2 ( x i Γ i ξ i + y i Γ i η i ) ;
4 x 2 i Γ i ξ i 2 + 4 y 2 i Γ i η i 2 + 8 x y i Γ i ξ i η i ,
ξ i = ξ 0 i α l i , η i = η 0 i β l i , r 2 = x 2 + y 2 .
δ x c = ( α 3 + β 2 α ) c l i R i ( α 2 + β 2 ) c ξ 0 i R i , δ y c = ( α 2 β + β 3 ) c l i R i .
δ x c = ( α 3 + β 2 α ) c l i R i , δ y c = ( α 2 β + β 3 ) c l i R i ( β 2 + α 2 ) c η 0 i R i .
δ x p = 4 i Γ i ( ξ 0 i 3 α 3 l i 3 + 3 ξ 0 i α 2 l i 2 3 ξ 0 i 2 α l i + β 2 l i 2 ξ 0 i β 2 l i 3 α ) , δ y p = 4 i Γ i ( β l i ξ 0 i 2 β l i 3 α 2 + 2 β l i 2 α ξ 0 i β 3 l i 3 ) .
δ x p = 4 i Γ i ( α l i η 0 i 2 α l i 3 β 2 + 2 α β l i 2 η 0 i α 3 l i 3 ) δ y p = 4 i Γ i ( η 0 i 3 β 3 l i 3 + 3 η 0 i β 2 l i 2 3 η 0 i 2 β l i + α 2 l i 2 η 0 i β α 2 l i 3 ) .
α 0 = 1 2 β 0 2 sin ϕ 0 + sin ϕ 0 cos ϕ 0 + α 0 cos ϕ 0 cos ϕ 0 , β 0 = β 0 .
α 0 cos γ = ( sin ϕ 1 + sin ϕ 1 ) cos ϕ 1 ( β 0 2 / 2 γ β 0 ) + α 0 cos γ cos ϕ 1 cos ϕ 1 , β 0 = β 0 .
α 0 = α + ( δ x p + δ x c ) , β 0 = β + ( δ y p + δ y c ) .
α = α 0 + ( δ x p + δ x c ) , β = β 0 + ( δ y p + δ y c ) .
z = 2 r 2 i Γ i [ ξ 0 i 2 + ( α 2 + β 2 ) l i 2 2 α l i ξ 0 i ] + r 2 2 f 2 [ α c ξ 0 i ρ 2 ( α 2 + β 2 ) f 2 ] .
z = 2 r 2 i Γ i [ ξ 0 i 2 + ( α 2 + β 2 ) l i 2 2 α l i ξ 0 i ] + r 2 2 f 2 [ α c ξ 0 i ρ 2 ( α 2 + β 2 ) f 2 ] .
Γ 1 = 1 32 f 3 , ξ 01 = 0 , η 01 = 2 f θ , l 1 = 2 f D , Γ 2 = 1 32 f 3 , ξ 02 = 0 , η 02 = 2 f θ , l 2 = D , Γ 3 = 1 32 f 3 , ξ 03 = 0 , η 03 = 2 f θ , l 3 = ( 2 f D ) , Γ 4 = 1 32 f 3 , ξ 04 = 0 , η 04 = 2 f θ , l 4 = D .
x = x t , y = y ,
α 0 = α 0 = p 0 β 0 2 , β 0 = β 0 ,
p 0 = 1 2 cot ϕ 0 ϕ 0 2 .
spherical aberration = 0 ,
coma = 1 4 p 0 β 0 2 x 3 [ 1 / f 2 1 / f 2 3 ( t 1 ) f 2 ] + 1 4 β 0 x 2 y [ 1 / f 2 1 / f 2 2 ( t 1 ) f 2 ] + 1 4 p 0 β 0 2 x y 2 [ 1 / f 2 1 / f 2 ( t 1 ) f 2 ] + 1 4 β 0 y 3 ( 1 / f 2 1 / f 2 ) ,
astigmatism = p 0 β 0 2 x y ( t θ / f θ / f ) + y 2 β 0 ( θ / f θ / f ) 1 2 p 0 2 β 0 4 x 2 [ 1 / f ( 1 D / f ) + 1 / f ( 1 D / f ) + 2 ( t 1 ) ( 1 D / f ) ] 1 2 β 0 2 y 2 [ 1 / f ( 1 D / f ) + 1 / f ( 1 D / f ) ] p 0 β 0 3 x y × [ t / f ( 1 D / f ) + 1 / f ( 1 D / f ) ] ,
field curvature = x 2 2 β 0 [ θ / f θ / f + 2 ( t 1 ) θ / f ] x 2 4 ( p 0 2 β 0 4 + β 0 2 ) [ 1 / f ( 2 D / f ) + 1 / f ( 2 D / f ) + 2 ( t 1 ) ( 2 D / f ) ] y 2 4 ( p 0 2 β 0 4 + β 0 2 ) [ 1 / f ( 2 D / f ) + 1 / f ( 2 D / f ) ] y 2 2 β 0 ( θ / f θ / f ] .
δ x p = 1 2 θ 2 p 0 β 0 2 [ ( 2 D / f ) + D / f ] + 1 2 p 0 β 0 3 θ [ ( 2 D / f ) 2 D 2 / f 2 ] 1 8 p 0 β 0 4 ( 1 + p 0 2 β 0 2 ) [ ( 2 D / f ) 3 + D 3 / f 3 ] ,
δ y p = 1 8 β 0 3 ( 1 + p 0 2 β 0 2 ) [ ( 2 D / f ) 3 + D 3 / f 3 ) 3 2 θ 2 β 0 [ ( 2 D / f ) + D / f ] + 1 4 θ β 0 2 × ( 3 + p 0 2 β 0 2 ) [ ( 2 D / f ) 2 D 2 / f 2 ] ,
δ x p = 1 2 θ 2 p 0 β 0 2 [ ( 2 D / f ) + D / f ] + 1 2 p 0 β 0 3 θ × [ ( 2 D / f ) 2 D 2 / f 2 ] + 1 8 p 0 β 0 4 ( 1 + p 0 2 β 0 2 ) × [ ( 2 D / f ) 3 + D 3 / f 3 ] ,
δ y p = 1 8 β 0 3 ( 1 + p 0 2 β 0 2 ) [ ( 2 D / f ) 3 + D 3 / f 3 ] + 3 2 θ 2 β 0 × [ ( 2 D / f ) 2 + D / f ] + 1 4 θ β 0 2 ( 3 + p 0 2 β 0 2 ) [ ( 2 D / f ) 2 D 2 / f 2 ] ,
δ x c = p 0 β 0 4 ( 1 + p 0 2 β 0 2 ) ( 1 D / 2 f ) ,
δ y c = β 0 2 ( 1 + p 0 2 β 0 2 ) [ β 0 ( 1 D / 2 f ) θ ] ,
δ x c = p 0 β 0 4 ( 1 + p 0 2 β 0 2 ) ( 1 D / 2 f ) ,
δ y c = β 0 2 ( 1 + p 0 2 β 0 2 ) [ β 0 ( 1 D / 2 f ) + θ ] .
D = f , D = f , θ = θ = 0.08 , β 0 = 0.035 , f = f = 1 m , ϕ 0 ϕ 0 = 0.28 , p 0 = 3.55.
d z = ( x 2 t 2 + y 2 ) 2 f 2 ( δ β 0 f + τ p 0 β 0 2 f ) ( x 2 + y 2 ) 2 f 2 ( δ β 0 f + τ p 0 β 0 2 f ) ,
τ = τ = 1 2 p 0 = 0.141 , δ = f / f θ = 0.08 , δ = θ
x r = y r 2 2 p e + O ( y r 4 ) , x r = y r 2 2 p s + O ( y r 4 ) ,
1 / p e = 2 p 0 / f ( 1 5 θ 2 ) cos τ cos 2 δ , 1 / p s = 2 p 0 / f ( 1 5 θ 2 ) cos τ cos 2 δ .
1 / f 2 = 1 / f 2 [ 1 + a ( t 1 ) ]
coma = p 0 β 0 2 x 3 ( t 1 ) ( a 3 ) + β 0 x 2 y 4 f 2 ( t 1 ) ( a 2 ) + p 0 β 0 2 x y 2 4 f 2 ( t 1 ) ( a 1 ) + β 0 2 y 3 a 4 f 2 ( t 1 ) .
a ( t 1 ) = f 2 / f 2 1 = 0.2404.
θ = θ f / f ,

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