Abstract

In this work we show a geometrical method—the unified plate diagram—which makes it possible to estimate simply and rapidly the dependence of image sharpness aberrations (spherical, coma, and astigmatism) on the basic design parameters of plane grating spectrographic systems. We also present analytical equations with the help of which additional parameters may be adjusted, such as off-axis relations, position, and form of the focal surface.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. R. Burch, “On Aspheric Anastigmatic Systems,” Proc. Phys. Soc. London 55, 433 (1943).
    [CrossRef]
  2. C. R. Burch, “Application of the Plate Diagram to Reflecting Telescope Design,” Opt. Acta 26, 493 (1979).
    [CrossRef]
  3. J. M. Simon, “The Plate Diagram and Its Application to Off-Axis Systems and Spectrographs,” Opt. Acta 20, 345 (1973).
    [CrossRef]
  4. 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]
  5. M. A. Gil, J. M. Simon, “Calculation of the Field Curvature by the Plate Diagram Method for Off-Axis Systems,” Opt. Acta 30, 65 (1983).
    [CrossRef]
  6. M. A. Gil, J. M. Simon, “Aberrations in Plane Grating Spectrometers,” Opt. Acta 30, 777 (1983).
    [CrossRef]
  7. M. A. Gil, J. M. Simon, “Aberrations in Off-Plane Spectrometers,” Opt. Acta 30, 1287 (1983).
    [CrossRef]
  8. M. A. Gil, J. M. Simon, “New Plane Grating Monochromator with Off-Axis Parabolical Mirrors,” Appl. Opt. 22, 152 (1983).
    [CrossRef] [PubMed]
  9. W. G. Fastie, “Image Forming Properties of the Ebert Monochromator,” J. Opt. Soc. Am. 42, 647 (1952).
    [CrossRef]
  10. R. A. Hill, “A New Plane Grating Monochromator with Off-Axis Paraboloids and Curved Slits,” Appl. Opt. 8, 575 (1969).
    [CrossRef] [PubMed]
  11. V. L. Chupp, P. C. Grantz, “Coma Canceling Monochromator with No Slit Mismatch,” Appl. Opt. 8, 925 (1969).
    [CrossRef] [PubMed]
  12. M. A. Gil, J. M. Simon, “Coma Compensation in a Parabolized Ebert Monochromator,” Appl. Opt. 18, 2280 (1979).
    [CrossRef] [PubMed]
  13. J. M. Simon, M. A. Gil, “Slit Curvatures of Plane Grating Spectrometers with Off-Axis Parabolic Mirrors,” Opt. Acta 25, 83 (1978).
    [CrossRef]
  14. M. A. Gil, J. M. Simon, A. N. Fantino, “Czerny-Turner Spectrograph with a Wide Spectral Range,” Appl. Opt. 27, 4069 (1988).
    [CrossRef] [PubMed]
  15. R. C. M. Learner, “Spectrograph Design, 1918–68,” J. Scientific Instruments (J. Physics E).Series 2, 1, 589 (1968).
    [CrossRef]
  16. J. H. Rush, G. K. Schnable, “High Altitude Observatory’s New Coronagraph and Spectrograph,” Appl. Opt. 3, 1347 (1964).
    [CrossRef]
  17. M. V. R. Murty, “Cary Principle in Monochromator Design,” Appl. Opt. 12, 2018 (1973).
    [CrossRef] [PubMed]
  18. J. M. Simon, M. A. Gil, A. N. Fantino, “Czerny-Turner Monochromator: Astigmatism in the Classical and in the Crossed Beam Dispositions,” Appl. Opt. 25, 3715 (1986).
    [CrossRef] [PubMed]
  19. W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241 (1965).
    [CrossRef]

1988

1986

1983

M. A. Gil, J. M. Simon, “New Plane Grating Monochromator with Off-Axis Parabolical Mirrors,” Appl. Opt. 22, 152 (1983).
[CrossRef] [PubMed]

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

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

M. A. Gil, J. M. Simon, “Aberrations in Off-Plane Spectrometers,” Opt. Acta 30, 1287 (1983).
[CrossRef]

1979

C. R. Burch, “Application of the Plate Diagram to Reflecting Telescope Design,” Opt. Acta 26, 493 (1979).
[CrossRef]

M. A. Gil, J. M. Simon, “Coma Compensation in a Parabolized Ebert Monochromator,” Appl. Opt. 18, 2280 (1979).
[CrossRef] [PubMed]

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]

J. M. Simon, M. A. Gil, “Slit Curvatures of Plane Grating Spectrometers with Off-Axis Parabolic Mirrors,” Opt. Acta 25, 83 (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. Murty, “Cary Principle in Monochromator Design,” Appl. Opt. 12, 2018 (1973).
[CrossRef] [PubMed]

1969

1968

R. C. M. Learner, “Spectrograph Design, 1918–68,” J. Scientific Instruments (J. Physics E).Series 2, 1, 589 (1968).
[CrossRef]

1965

W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241 (1965).
[CrossRef]

1964

1952

1943

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

Burch, C. R.

C. R. Burch, “Application of the Plate Diagram to Reflecting Telescope Design,” Opt. Acta 26, 493 (1979).
[CrossRef]

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

Chupp, V. L.

Fantino, A. N.

Fastie, W. G.

Gil, M. A.

M. A. Gil, J. M. Simon, A. N. Fantino, “Czerny-Turner Spectrograph with a Wide Spectral Range,” Appl. Opt. 27, 4069 (1988).
[CrossRef] [PubMed]

J. M. Simon, M. A. Gil, A. N. Fantino, “Czerny-Turner Monochromator: Astigmatism in the Classical and in the Crossed Beam Dispositions,” Appl. Opt. 25, 3715 (1986).
[CrossRef] [PubMed]

M. A. Gil, J. M. Simon, “New Plane Grating Monochromator with Off-Axis Parabolical Mirrors,” Appl. Opt. 22, 152 (1983).
[CrossRef] [PubMed]

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

M. A. Gil, J. M. Simon, “Aberrations in Off-Plane Spectrometers,” Opt. Acta 30, 1287 (1983).
[CrossRef]

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

M. A. Gil, J. M. Simon, “Coma Compensation in a Parabolized Ebert Monochromator,” Appl. Opt. 18, 2280 (1979).
[CrossRef] [PubMed]

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, M. A. Gil, “Slit Curvatures of Plane Grating Spectrometers with Off-Axis Parabolic Mirrors,” Opt. Acta 25, 83 (1978).
[CrossRef]

Grantz, P. C.

Hill, R. A.

Learner, R. C. M.

R. C. M. Learner, “Spectrograph Design, 1918–68,” J. Scientific Instruments (J. Physics E).Series 2, 1, 589 (1968).
[CrossRef]

Murty, M. V. R.

Rush, J. H.

Schnable, G. K.

Simon, J. M.

M. A. Gil, J. M. Simon, A. N. Fantino, “Czerny-Turner Spectrograph with a Wide Spectral Range,” Appl. Opt. 27, 4069 (1988).
[CrossRef] [PubMed]

J. M. Simon, M. A. Gil, A. N. Fantino, “Czerny-Turner Monochromator: Astigmatism in the Classical and in the Crossed Beam Dispositions,” Appl. Opt. 25, 3715 (1986).
[CrossRef] [PubMed]

M. A. Gil, J. M. Simon, “New Plane Grating Monochromator with Off-Axis Parabolical Mirrors,” Appl. Opt. 22, 152 (1983).
[CrossRef] [PubMed]

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

M. A. Gil, J. M. Simon, “Aberrations in Off-Plane Spectrometers,” Opt. Acta 30, 1287 (1983).
[CrossRef]

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

M. A. Gil, J. M. Simon, “Coma Compensation in a Parabolized Ebert Monochromator,” Appl. Opt. 18, 2280 (1979).
[CrossRef] [PubMed]

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, M. A. Gil, “Slit Curvatures of Plane Grating Spectrometers with Off-Axis Parabolic Mirrors,” Opt. Acta 25, 83 (1978).
[CrossRef]

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

Welford, W. T.

W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241 (1965).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Scientific Instruments (J. Physics E).

R. C. M. Learner, “Spectrograph Design, 1918–68,” J. Scientific Instruments (J. Physics E).Series 2, 1, 589 (1968).
[CrossRef]

Opt. Acta

C. R. Burch, “Application of the Plate Diagram to Reflecting Telescope Design,” Opt. Acta 26, 493 (1979).
[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 Systems,” Opt. Acta 30, 65 (1983).
[CrossRef]

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

M. A. Gil, J. M. Simon, “Aberrations in Off-Plane Spectrometers,” Opt. Acta 30, 1287 (1983).
[CrossRef]

J. M. Simon, M. A. Gil, “Slit Curvatures of Plane Grating Spectrometers with Off-Axis Parabolic Mirrors,” Opt. Acta 25, 83 (1978).
[CrossRef]

Proc. Phys. Soc. London

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

Prog. Opt.

W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241 (1965).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Monochromators of the Z configuration; (b) unified diagram (spherical mirrors); (c) unified diagram [parabolic mirrors with parabolization vertices at arbitrary positions (a and a′)].

Fig. 2
Fig. 2

(a) Monochromators of the U configuration; (b) unified diagram (spherical mirrors); (c) unified diagram [parabolic mirrors with parabolization vertices at arbitrary positions (a and a′)].

Fig. 3
Fig. 3

Plate diagram for an arbitrary in-plane spectrograph (ξ0ir,0,lir) are the coordinates of the ith plate of intensity Γi, measured in the reference system (note that for the sake of simplicity we have not indicated the field angle β′).

Fig. 4
Fig. 4

(a) Spectrograph of the Z configuration; (b) unified diagram (Z1 design); (c) unified diagram (Z2 design); (d) unified diagram (Z3 design).

Fig. 5
Fig. 5

Spectrograph of the U4 configuration and its corresponding unified diagram.

Tables (1)

Tables Icon

Table I Total Zero-, First-, and Second-Order Moments of the Plates for the In-Plane Configurations Z1, Z2, Z3, and U4.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

r 4 i Γ i .
- 4 r 2 ( x i Γ i ξ i r + y i Γ i η i r ) .
4 x 2 i Γ i ξ i r 2 + 4 y 2 i Γ i η i r 2 + 8 x y i Γ i ξ i r η i r ,
ξ i r = ξ 0 i r - α 0 l i r , η i r = η 0 i r - β 0 l i r , r 2 = x 2 + y 2 .
δ x c = ( α 0 3 + β 0 2 α 0 ) c l i r R i - ( α 0 2 + β 0 2 ) c ξ 0 i r R i , δ y c = ( α 0 2 β 0 + β 0 3 ) c l i r R i .
δ x c = ( α 0 3 + β 0 2 α 0 ) c l i r R i , δ y c = ( α 0 2 β 0 + β 0 3 ) c l i r R i - ( β 0 2 + α 0 2 ) c η 0 i r R i .
δ x p = - 4 i Γ i ( ξ i r 3 + ξ i r β 0 2 l i r 2 ) , δ y p = 4 i Γ i ( ξ i r 2 β 0 l i r + β 0 3 l i r 3 ) .
δ x p = 4 i Γ i ( α 0 3 l i r 3 + η i r 2 α 0 l i r ) , δ y p = - 4 i Γ i ( α 0 2 l i r 2 η i r + η i r 3 ) .
α 0 λ = - 1 2 β 0 2 ( sin ϕ 0 + sin ϕ 0 λ ) cos ϕ 0 λ + α 0 cos ϕ 0 cos ϕ 0 λ , β 0 = β 0 .
α 0 λ cos γ = - ( sin ϕ 1 + sin ϕ 1 λ ) cos ϕ 1 λ ( β 0 2 / 2 - γ β 0 ) + α 0 cos γ cos ϕ 1 cos ϕ 1 λ , β 0 = β 0 .
α 0 = α + ( δ x p + δ x c ) , β 0 = β + ( δ y p + δ y c ) .
α λ = α 0 λ + ( δ x p + δ x c ) , β λ = β 0 + ( δ y p + δ y c ) .
Z = 2 r 2 i Γ i ( ξ i r 2 + β 0 2 l i r 2 ) + r 2 2 f 2 [ ± α 0 c ξ 0 i r - ρ 2 ( α 0 2 + β 0 2 ) f 2 ] ,
α 0 = α D ( λ ) + α 0 λ .
α D ( λ ) = - ( ϕ 0 λ - ϕ 0 r ) = - Δ ϕ λ .

Metrics