Abstract

The images obtained with a classical Czerny-Turner design and a crossed beam Czerny-Turner design are compared, imposing in both cases the Fastie and the Pribram and Penchina conditions. The results show that the astigmatic line may be made parallel to the spectral line only with the classical design, which makes it superior to the crossed beam design. Also, the importance of an adequate choice of the construction parameters is shown. The analytical calculations are checked by ray tracing.

© 1986 Optical Society of America

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References

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  1. J. F. James, R. S. Stenberg, The Design of the Optical Spectrometers (Chapman & Hall, London, 1969).
  2. J. K. Pribram, C. M. Penchina, “Stray Light in Cerny-Turner and Ebert spectrometers,” Appl. Opt. 7, 2005 (1968).
    [CrossRef] [PubMed]
  3. W. G. Fastie, “Image Forming Properties of the Ebert Monochromator,” J. Opt. Soc. Am. 42, 647 (1952).
    [CrossRef]
  4. C. S. Rupert, “Slit Curvature in Grating Monochromators Employing Single or Multiple Diffraction,” J. Opt. Soc. Am. 42, 779 (1952).
    [CrossRef]
  5. M. A. Gil, J. M. Simon, “Aberrations in Plane Grating Spectrometers,” Opt. Acta 30, 777 (1983).
    [CrossRef]
  6. C. r. Burch, “On Aspheric Anastigmatic Systems,” Proc. Phys. Soc. 55, 433 (1943).
    [CrossRef]
  7. J. M. Simon, “The Plate Diagram and Its Application to Off-Axis Systems and Spectrographs,” Opt. Acta 20, 345 (1973).
    [CrossRef]
  8. J. M. Simon, M. A. Gil, “Distortion and Slit Image Curvature Calculated by the Plate Diagram Analysis in Monochromators with Off-Axis Mirrors,” Opt. Acta 25, 381 (1978).
    [CrossRef]
  9. M. A. Gil, J. M. Simon, “Calculation of the Field Curvature by the Plate Diagram Method for Off-Axis System,” Opt. Acta 30, 65 (1983).
    [CrossRef]
  10. M. V. R. K. Murty, “Cary Principle in Monochromator Design,” Appl. Opt. 12, 2018 (1973).
    [CrossRef] [PubMed]

1983

M. A. Gil, J. M. Simon, “Aberrations in Plane Grating Spectrometers,” Opt. Acta 30, 777 (1983).
[CrossRef]

M. A. Gil, J. M. Simon, “Calculation of the Field Curvature by the Plate Diagram Method for Off-Axis System,” Opt. Acta 30, 65 (1983).
[CrossRef]

1978

J. M. Simon, M. A. Gil, “Distortion and Slit Image Curvature Calculated by the Plate Diagram Analysis in Monochromators with Off-Axis Mirrors,” Opt. Acta 25, 381 (1978).
[CrossRef]

1973

J. M. Simon, “The Plate Diagram and Its Application to Off-Axis Systems and Spectrographs,” Opt. Acta 20, 345 (1973).
[CrossRef]

M. V. R. K. Murty, “Cary Principle in Monochromator Design,” Appl. Opt. 12, 2018 (1973).
[CrossRef] [PubMed]

1968

1952

1943

C. r. Burch, “On Aspheric Anastigmatic Systems,” Proc. Phys. Soc. 55, 433 (1943).
[CrossRef]

Burch, C. r.

C. r. Burch, “On Aspheric Anastigmatic Systems,” Proc. Phys. Soc. 55, 433 (1943).
[CrossRef]

Fastie, W. G.

Gil, M. A.

M. A. Gil, J. M. Simon, “Calculation of the Field Curvature by the Plate Diagram Method for Off-Axis System,” Opt. Acta 30, 65 (1983).
[CrossRef]

M. A. Gil, J. M. Simon, “Aberrations in Plane Grating Spectrometers,” Opt. Acta 30, 777 (1983).
[CrossRef]

J. M. Simon, M. A. Gil, “Distortion and Slit Image Curvature Calculated by the Plate Diagram Analysis in Monochromators with Off-Axis Mirrors,” Opt. Acta 25, 381 (1978).
[CrossRef]

James, J. F.

J. F. James, R. S. Stenberg, The Design of the Optical Spectrometers (Chapman & Hall, London, 1969).

Murty, M. V. R. K.

Penchina, C. M.

Pribram, J. K.

Rupert, C. S.

Simon, J. M.

M. A. Gil, J. M. Simon, “Aberrations in Plane Grating Spectrometers,” Opt. Acta 30, 777 (1983).
[CrossRef]

M. A. Gil, J. M. Simon, “Calculation of the Field Curvature by the Plate Diagram Method for Off-Axis System,” Opt. Acta 30, 65 (1983).
[CrossRef]

J. M. Simon, M. A. Gil, “Distortion and Slit Image Curvature Calculated by the Plate Diagram Analysis in Monochromators with Off-Axis Mirrors,” Opt. Acta 25, 381 (1978).
[CrossRef]

J. M. Simon, “The Plate Diagram and Its Application to Off-Axis Systems and Spectrographs,” Opt. Acta 20, 345 (1973).
[CrossRef]

Stenberg, R. S.

J. F. James, R. S. Stenberg, The Design of the Optical Spectrometers (Chapman & Hall, London, 1969).

Appl. Opt.

J. Opt. Soc. Am.

Opt. Acta

M. A. Gil, J. M. Simon, “Aberrations in Plane Grating Spectrometers,” Opt. Acta 30, 777 (1983).
[CrossRef]

J. M. Simon, “The Plate Diagram and Its Application to Off-Axis Systems and Spectrographs,” Opt. Acta 20, 345 (1973).
[CrossRef]

J. M. Simon, M. A. Gil, “Distortion and Slit Image Curvature Calculated by the Plate Diagram Analysis in Monochromators with Off-Axis Mirrors,” Opt. Acta 25, 381 (1978).
[CrossRef]

M. A. Gil, J. M. Simon, “Calculation of the Field Curvature by the Plate Diagram Method for Off-Axis System,” Opt. Acta 30, 65 (1983).
[CrossRef]

Proc. Phys. Soc.

C. r. Burch, “On Aspheric Anastigmatic Systems,” Proc. Phys. Soc. 55, 433 (1943).
[CrossRef]

Other

J. F. James, R. S. Stenberg, The Design of the Optical Spectrometers (Chapman & Hall, London, 1969).

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Figures (5)

Fig. 1
Fig. 1

(a) Classical Czerny-Turner design; (b) crossed beam Czerny-Turner design; (c) diagrams corresponding to both designs.

Fig. 2
Fig. 2

Transverse deviations in the paraxial plane due to (a1) and (a2) spherical aberration; (b1) and (b2) coma in the center of the field; (c1) and (c2) coma at the edge of the field; (d1) and (d2) astigmatism at the center of the field; (e1) and (e2) astigmatism at the edge of the field. Indices 1 and 2 correspond to the classical and crossed beam designs, respectively.

Fig. 3
Fig. 3

Images corresponding to astigmatism at the center and edge of the field, in the plane in which the astigmatic line is parallel to the spectral line in the center of the field. The images represented in (a) correspond to the classical design, and those of (b) to the crossed beam design. The spectral line is represented by a dotted curve.

Fig. 4
Fig. 4

Images corresponding to the center and edge of the field obtained by ray tracing. The symbols blank, ·, +, *, and M denote the number of rays passing through a given point of the imageplane, and correspond to 0; 1; 2 or 3; 4, 5, 6 or 7; and 8 or more rays, respectively. The images represented in (a) correspond to the classical design, and those of (b) to the crossed beam design. The spectral line is represented by a dashed curve.

Fig. 5
Fig. 5

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.

Equations (31)

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Γ 1 = - 1 / 32 f 3 ξ 01 = 2 f θ η 01 = 0 l 1 = 2 f - D , Γ 2 = 0 ξ 02 = 0 η 02 = 0 l 2 = - D , Γ 3 = - 1 / 32 f 3 ξ 03 = - 2 f θ η 03 = 0 l 3 = - ( 2 f - D ) , Γ 4 = 0 ξ 04 = 0 η 04 = 0 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 .
- 1 32 f 3 { x 4 [ 4 t - 3 + ( f f ) 3 ] + 2 x 2 y 2 [ 2 t - 1 + ( f f ) 3 ] + y 4 [ 1 + ( f f ) 3 ] } ;
- θ 4 f 2 ( x 3 { 3 t - 2 - θ f 2 θ f 2 - p 0 β 0 2 θ × [ ( 3 t - 2 ) ( 1 - D 2 f ) + f 2 f 2 ( 1 - D 2 f ) ] } - x 2 y β 0 θ [ ( 2 t - 1 ) ( 1 - D 2 f ) + f 2 f 2 ( 1 - D 2 f ) ] + x y 2 { ( t - θ f 2 θ f 2 ) - p 0 β 0 2 θ [ t ( 1 - D 2 f ) + f 2 f 2 ( 1 - D 2 f ) ] } - y 3 β 0 θ [ 1 - D 2 f + f 2 f 2 ( 1 - D 2 f ) ] ) ;
- θ 2 2 f ( x 2 ( 2 t - 1 + θ 2 f θ 2 f + 2 p 0 β 0 2 θ × { ( 2 t - 1 ) ( 1 - D 2 f ) + θ 2 f θ 2 f ( 1 + D 2 f ) - p 0 β 0 2 θ [ ( 2 t - 1 ) ( 1 - D 2 f ) 2 + f f ( 1 - D 2 f ) 2 ] } ) - 2 x y β 0 θ { t ( 1 - D 2 f ) + f f ( 1 - D 2 f ) - p 0 β 0 2 θ [ t ( 1 - D 2 f ) 2 + f f ( 1 - D 2 f ) 2 ] } + y 2 β 0 2 θ 2 [ ( 1 - D 2 f ) 2 + f f ( 1 - D 2 f ) 2 ] ) .
D = D = f = f = 1 m ,             θ = θ = 0.0175 , β 0 = 0.025 ( at the edge of the field ) ,             ϕ 0 - ϕ 0 = 0.3 ,
p 0 = 3.38 ,             ϕ 0 = 0.158 ,             ϕ 0 = 0.458 ,             t = 1.101 ,
p 0 = - 3.38 ,             ϕ 0 = 0.458 ,             ϕ 0 = 0.158 ,             t = 0.908.
x r = y r 2 2 ρ e + O ( y r 4 ) , x r = y r 2 2 ρ s + O ( y r 4 ) ,
1 ρ e = - 1 ρ s 2 f [ p 0 ( 1 + θ 2 2 ) + 3 4 θ ] .
- θ 2 f ( A x 2 + 2 B x y + C y 2 ) ,
A = ( 1 - p 0 β 0 2 b θ ) 2 , B = - β 0 b θ ( 1 - p 0 β 0 2 b θ ) , C = ( β 0 b θ ) 2 , b = 1 - D 2 f .
E = θ 2 f [ ( 1 - p 0 β 0 2 b θ ) 2 + ( β 0 b θ ) 2 ] ,
D x D y = β 0 b θ - p 0 β 0 2 b = - y r ρ s = 2 β 0 [ p 0 ( 1 + θ 2 2 ) + 3 4 θ ] .
p 0 = 1 2 cot ϕ 0 - ϕ 0 2 1 ϕ 0 - ϕ 0 b 2 θ = 1 - D 2 f 2 θ .
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 1 2 + 4 y 2 i Γ i η i 2 + 8 x y i Γ i ζ 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 i 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 c o s γ = - s i n ϕ 1 + s i n ϕ 1 c o s ϕ 1 ( β 0 2 2 - γ β 0 ) + α 0 c o s ϕ 1 c o s γ c o s 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 ] .

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