Abstract

The effects introduced by a plane diffraction grating on the diffracted wave front when a quasi-plane beam incides on it are calculated. Effects not previously discussed appear.

© 1984 Optical Society of America

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References

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  1. A. S. Filler, J. Opt. Soc. Am. 54, 424 (1964).
    [CrossRef]
  2. G. W. Stroke, Handbuch der Physik, Vol. 29 (Springer, Berlin, 1967).
  3. J. M. Simon, L. R. Novarini, R. Platzeck, Opt. Acta 18, 829 (1971).
    [CrossRef]
  4. M. A. Gil, J. M. Simon, Opt. Acta 30, 1287 (1983).
    [CrossRef]
  5. W. T. Welford, Prog. Opt. 6, 241 (1965).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), 752.
  7. E. H. Linfoot, Recent Advances in Optics (Clarendon, Oxford, 1955).
  8. C. R. Burch, Mon. Not. R. Astron. Soc. 102, 159 (1943).
  9. C. R. Burch, Proc. Phys. Soc. 55, 433 (1943).
    [CrossRef]
  10. C. R. Burch, Proc. Phys. Soc. 59, 41 (1947).
    [CrossRef]
  11. C. R. Burch, Opt. Acta 26, 493 (1979).
    [CrossRef]
  12. J. M. Simon, Opt. Acta 20, 345 (1973).
    [CrossRef]
  13. M. A. Gil, J. M. Simon, Appl. Opt. 18, 2280 (1979).
    [CrossRef] [PubMed]

1983 (1)

M. A. Gil, J. M. Simon, Opt. Acta 30, 1287 (1983).
[CrossRef]

1979 (2)

1973 (1)

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

1971 (1)

J. M. Simon, L. R. Novarini, R. Platzeck, Opt. Acta 18, 829 (1971).
[CrossRef]

1965 (1)

W. T. Welford, Prog. Opt. 6, 241 (1965).
[CrossRef]

1964 (1)

1947 (1)

C. R. Burch, Proc. Phys. Soc. 59, 41 (1947).
[CrossRef]

1943 (2)

C. R. Burch, Mon. Not. R. Astron. Soc. 102, 159 (1943).

C. R. Burch, Proc. Phys. Soc. 55, 433 (1943).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), 752.

Burch, C. R.

C. R. Burch, Opt. Acta 26, 493 (1979).
[CrossRef]

C. R. Burch, Proc. Phys. Soc. 59, 41 (1947).
[CrossRef]

C. R. Burch, Proc. Phys. Soc. 55, 433 (1943).
[CrossRef]

C. R. Burch, Mon. Not. R. Astron. Soc. 102, 159 (1943).

Filler, A. S.

Gil, M. A.

Linfoot, E. H.

E. H. Linfoot, Recent Advances in Optics (Clarendon, Oxford, 1955).

Novarini, L. R.

J. M. Simon, L. R. Novarini, R. Platzeck, Opt. Acta 18, 829 (1971).
[CrossRef]

Platzeck, R.

J. M. Simon, L. R. Novarini, R. Platzeck, Opt. Acta 18, 829 (1971).
[CrossRef]

Simon, J. M.

M. A. Gil, J. M. Simon, Opt. Acta 30, 1287 (1983).
[CrossRef]

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

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

J. M. Simon, L. R. Novarini, R. Platzeck, Opt. Acta 18, 829 (1971).
[CrossRef]

Stroke, G. W.

G. W. Stroke, Handbuch der Physik, Vol. 29 (Springer, Berlin, 1967).

Welford, W. T.

W. T. Welford, Prog. Opt. 6, 241 (1965).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), 752.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Mon. Not. R. Astron. Soc. (1)

C. R. Burch, Mon. Not. R. Astron. Soc. 102, 159 (1943).

Opt. Acta (4)

C. R. Burch, Opt. Acta 26, 493 (1979).
[CrossRef]

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

J. M. Simon, L. R. Novarini, R. Platzeck, Opt. Acta 18, 829 (1971).
[CrossRef]

M. A. Gil, J. M. Simon, Opt. Acta 30, 1287 (1983).
[CrossRef]

Proc. Phys. Soc. (2)

C. R. Burch, Proc. Phys. Soc. 55, 433 (1943).
[CrossRef]

C. R. Burch, Proc. Phys. Soc. 59, 41 (1947).
[CrossRef]

Prog. Opt. (1)

W. T. Welford, Prog. Opt. 6, 241 (1965).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), 752.

E. H. Linfoot, Recent Advances in Optics (Clarendon, Oxford, 1955).

G. W. Stroke, Handbuch der Physik, Vol. 29 (Springer, Berlin, 1967).

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of an off-plane parabolized Ebert spectrometer.

Fig. 2
Fig. 2

Images corresponding to the center of the field of a parabolized Ebert spectrometer due to additional effects arising in the grating. The horizontal axis is parallel to the grooves of the grating, while the width of the images is indicated on the vertical axis. The full curves represent the images evaluated by means of approximate analytical calculations and those obtained by means of ray tracing are represented by symbols. The symbols blank, ·, +, *, and M indicate the number of rays passing through a given point in the focal plane and correspond to 0; 1; 2 or 3; 4, 5, 6, or 7; and eight or more rays respectively. In (a) ϕ = 10°; in (b) ϕ = 45°; in (c) ϕ = 60°; and in (d) ϕ = 85°.

Fig. 3
Fig. 3

Coordinate system.

Fig. 4
Fig. 4

Images in the paraxial plane due to effects arising in the grating and corresponding to different incident wave fronts. These fronts represent in each case (a) spherical aberration; (b) coma; (c) astigmatism; and (d) defocusing. The horizontal axis is parallel to the grooves of the grating, and consequently the width of the image relative to the corresponding k value is represented on the vertical axis. (R and f represent the radius of the grating and the focal length of the optical system for focusing the diffracted beam, respectively.) In (c) and (d), besides the images in the paraxial plane, the corresponding astigmatic lines are also indicated.

Equations (15)

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sin ϕ + sin ϕ = m λ d 1 - δ 2 ,
E ( x , y , z ) = A - a a - b b exp ( i { 2 π λ [ ( m λ d + c ) x + φ ( x , y ) + l ( x , y , z , x , y ) ] } ) d x d y
f ( x , y , x , y , z ) = ( m λ d + c ) x + φ ( x , y ) + l ( x , y , x , y , z )
f x | x 0 , y 0 = f y | x 0 , y 0 = 0 ,
x 0 = x - z ( sin ϕ cos ϕ + γ cos 3 ϕ + 3 2 γ 2 sin ϕ cos 3 ϕ + η 2 sin ϕ 2 cos 2 ϕ ) , y 0 = y - z ( η / cos ϕ - γ η sin ϕ cos 3 ϕ ) ,
sin ϕ = m λ d + c , η = φ y | x 0 , y 0 , γ = φ x | x 0 , y 0 ,
- γ - 1 - η 2 sin ϕ 1 - η 2 - γ .
f ( x 0 , y 0 , x , y , z ) = constant .
x sin ϕ + z cos ϕ + ( γ 2 + η 2 cos 2 ϕ ) 2 cos 3 ϕ z + φ ( x 0 , y 0 ) = 0.
z 2 - sin ϕ ( γ 2 + η 2 cos 2 ϕ ) 2 cos 3 ϕ x 2 + φ [ ( x 2 cos ϕ + γ sin ϕ cos 3 ϕ ) , ( y 2 + η sin ϕ cos ϕ x 2 ) ] = 0.
z 2 = - sin ϕ ( γ 2 + η 2 cos 2 ϕ ) 2 cos 3 ϕ x 2 - φ ( x 2 cos ϕ , y 2 ) .
z 1 = sin ϕ ( γ 2 + η 2 cos 2 ϕ ) 2 cos 3 ϕ x 1 - φ ( x 1 cos ϕ , y 1 ) ,
x 0 x 1 / cos ϕ x 2 / cos ϕ , y 0 y 1 y 2 , γ - z 1 / x 1 cos ϕ = - γ 1 cos ϕ , η - z 1 / y 1 - η 1 ,
z 2 ( x 2 , y 2 ) = - γ 1 2 2 ( sin ϕ cos 2 ϕ + sin ϕ cos 2 ϕ ) cos 3 ϕ x 2 - η 1 2 2 ( sin ϕ + sin ϕ ) cos ϕ x 2 + z 1 ( x 2 cos ϕ cos ϕ , y 2 ) .
z 2 ( x 2 , y 2 ) = - 1 2 ( z 1 x 1 ) 2 ( cos 2 ϕ sin ϕ + cos 2 ϕ sin ϕ ) cos 3 ϕ x 2 - 1 2 ( z 1 y 1 ) 2 ( sin ϕ + sin ϕ ) cos ϕ x 2 - δ ( z 1 y 1 ) ( sin ϕ + sin ϕ ) cos ϕ x 2 - 1 2 δ 2 ( sin ϕ + sin ϕ ) cos ϕ x 2 + z 1 ( x 2 cos ϕ cos ϕ , y 2 ) + δ y 2 .

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