Abstract

The effects introduced by a plane diffraction grating on the diffracted wave front when a quasi-plane beam incides on it are calculated. These effects are evaluated by ray tracing and by analytical expressions.

© 1985 Optical Society of America

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References

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  1. J. M. Simon, M. A. Gil, “Diffraction Gratings and Optical Aberrations,” Appl. Opt. 23, 1075 (1984).
    [CrossRef] [PubMed]
  2. A. S. Filler, “Stigmatic Ebert-Type Plane-Grating Mounting,” J. Opt. Soc. Am. 54, 424 (1964).
  3. G. M. Stroke, “Diffraction Gratings,” in Handbuch der Physik, Vol. 29, S. Flugge, Ed. (Springer, Berlin, 1967).
    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1955).
  5. M. A. Gil, J. M. Simon, “Aberrations in Off-Plane Spectrometers,” Opt. Acta 30, 1287 (1983).
    [CrossRef]

1984 (1)

1983 (1)

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

1964 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1955).

Filler, A. S.

Gil, M. A.

J. M. Simon, M. A. Gil, “Diffraction Gratings and Optical Aberrations,” Appl. Opt. 23, 1075 (1984).
[CrossRef] [PubMed]

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

Simon, J. M.

J. M. Simon, M. A. Gil, “Diffraction Gratings and Optical Aberrations,” Appl. Opt. 23, 1075 (1984).
[CrossRef] [PubMed]

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

Stroke, G. M.

G. M. Stroke, “Diffraction Gratings,” in Handbuch der Physik, Vol. 29, S. Flugge, Ed. (Springer, Berlin, 1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1955).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

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

Other (2)

G. M. Stroke, “Diffraction Gratings,” in Handbuch der Physik, Vol. 29, S. Flugge, Ed. (Springer, Berlin, 1967).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1955).

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Figures (5)

Fig. 1
Fig. 1

Coordinate system employed: (x′,y′,z′) are orthogonal coordinates with the y′ axis parallel to the grooves of the grating and the (x′,z′) normal to the same. The points on the surface of the grating (z′ = 0) are indicated with coordinates (x,y). z1 and z2 coincide with the direction of the incident and diffracted rays, respectively. θ and θ′ are the angles formed, respectively, between the incident and diffracted rays and their respective projections on the (x′,z′) plane. ϕ and ϕ′ are the angles between these projections and the normal to the grating (z′ axis). In the orthogonal coordinate sets (x1,y1,z1) and (x2,y2,z2), the planes (x1,z1) and (x2,z2) are parallel to the grooves.

Fig. 2
Fig. 2

Schematic representation of an off-plane parabolized Ebert spectrometer.

Fig. 3
Fig. 3

Images corresponding to the center of the field of a parabolized Ebert spectrometer, (a), (b), (c), and (d) correspond to a circular grating 20 cm in diameter, a square grating with a side length of 20 cm, a circular entrance pupil, and a circular exit pupil, respectively. The horizontal axis is parallel to the grooves of the grating, while the width of the image is indicated on the vertical axis. In all cases, the following values are used: ϕ = ϕ′ = −60°, θ = −θ′ = −0.159, and f = 1 m.

Fig. 4
Fig. 4

Intersection of the incident beam on the surface of the grating (a) and on the exit pupil (b) for different incidence angles and supposing a circular entrance pupil of unit radius, (x,y) are coordinates on the surface of the grating, and (x2,y2) are coordinates on the exit pupil.

Fig. 5
Fig. 5

Images corresponding to the center of the field of a parabolized Ebert spectrometer due to effects originated in the grating. The full curves represent the images obtained analytically, while those calculated by ray tracing are represented by symbols. The symbols blank, ·,+,*, and M indicate 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. In (a), (b), and (c) the values used are θ = −θ′ = −0.159, f = 1 m, and ϕ = ϕ′ = −45°, −60°, and −80°, respectively, while (d) corresponds to the values θ = −θ′ = −0.5236 = −30°, ϕ = ϕ′ = −60°, and f = 1 m.

Equations (5)

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E ( x , y , z ) = A a a b b exp { i 2 π λ [ ( m λ d 1 δ 2 sin ϕ ) 1 δ 2 x + δ y + φ ( x , y ) + l ( x , y , x , y , z ) } d x d y ,
z 2 ( x 2 , y 2 ) = z 1 ( x 1 , y 1 ) + O [ ( z 1 / x 1 ) 2 , ( z 1 / y 1 ) 2 , ( z 1 / x 1 ) ( z 2 / x 2 ) ] ,
x 1 = x 2 cos ϕ cos ϕ , y 1 = y 2 + δ ( sin ϕ + sin ϕ ) cos ϕ x 2 .
δ x 2 = z 2 / x 2 = ( z 1 / x 1 ) cos ϕ cos ϕ + ( z 1 / y 1 ) [ δ ( sin ϕ + sin ϕ ) cos ϕ ] , δ y 2 = z 2 / y 2 = z 1 / y 1 ,
z 1 ( x 1 , y 1 ) = θ 4 f 2 y 1 ( x 1 2 + y 1 2 ) ,

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