Abstract

The properties of a nonfocusing collimating parabolic telescope are studied in detail by a ray-tracing method. The best optical quality with respect to coma and astigmatism is calculated for rays close to the optical axis of the telescope. For rectangular fields of view the borders are not sharp because of the aberration. A combination of a parabolic telescope and an echelle-type spectrometer gives very high spectral resolution. Wadsworth, Ebert-Fastie, and other types of spectrometers are equally well suited to be combined with this telescope. For some cases spot diagrams demonstrate the optical performance. In addition, diffraction by the aperture and its implications are discussed.

© 1980 Optical Society of America

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References

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  1. G. Schmidtke, Appl. Opt. 16, 244 (1977).
    [CrossRef] [PubMed]
  2. H. Wolter, Ann. Phys. 10, 94 (1952).
    [CrossRef]
  3. R. Giacconi, B. Rossi, J. Geophys. Res. 65, 773 (1960).
    [CrossRef]
  4. J. D. Mangus, J. H. Underwood, Appl. Opt. 8, 95 (1969).
    [CrossRef] [PubMed]
  5. H. Wolter, Opt. Acta 18, 425 (1971).
    [CrossRef]
  6. D. Korsch, J. Opt. Soc. Am. 66, 938 (1976).
    [CrossRef]
  7. W. Werner, Appl. Opt. 16, 764 (1977).
    [CrossRef] [PubMed]
  8. C. E. Winkler, D. Korsch, Appl. Opt. 16, 2464 (1977).
    [CrossRef] [PubMed]

1977 (3)

1976 (1)

1971 (1)

H. Wolter, Opt. Acta 18, 425 (1971).
[CrossRef]

1969 (1)

1960 (1)

R. Giacconi, B. Rossi, J. Geophys. Res. 65, 773 (1960).
[CrossRef]

1952 (1)

H. Wolter, Ann. Phys. 10, 94 (1952).
[CrossRef]

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Figures (23)

Fig. 1
Fig. 1

Elements of a paraboloid.

Fig. 2
Fig. 2

Parabolic telescope for grazing incidence AA.

Fig. 3
Fig. 3

Parabolic telescope for normal incidence BB.

Fig. 4
Fig. 4

Symbols for ray-tracing relations.

Fig. 5
Fig. 5

Spot diagram of a parallel incident beam.

Fig. 6
Fig. 6

Spot diagram of parallel incident beams.

Fig. 7
Fig. 7

Spot diagram for 2ϑ close to 90°.

Fig. 8
Fig. 8

Spot diagram for 2ϑ close to 70°.

Fig. 9
Fig. 9

Spot diagram for 2ϑ close to 20°.

Fig. 10
Fig. 10

Designation of parameters relevant for studying different forms of aperture.

Fig. 11
Fig. 11

Images of field points A in the focal plane.

Fig. 12
Fig. 12

Images of field points A in the focal plane.

Fig. 13
Fig. 13

Images of field points A in the focal plane.

Fig. 14
Fig. 14

Combination of parabolic telescope and Wadsworth spectrometer.

Fig. 15
Fig. 15

Spot diagram of the Wadsworth mounting.

Fig. 16
Fig. 16

Spot diagram of the Wadsworth mounting (3° off-plane).

Fig. 17
Fig. 17

Spot diagram of the Wadsworth mounting (3° off-plane).

Fig. 18
Fig. 18

Parabolic telescope and Wadsworth mounting with a set of four gratings.

Fig. 19
Fig. 19

Telescope and Rowland spectrometer.

Fig. 20
Fig. 20

Telescope and echelle grating spectrometer.

Fig. 21
Fig. 21

Telescope and Ebert-Fastie spectrometer.

Fig. 22
Fig. 22

Position of the first minimum of diffraction.

Fig. 23
Fig. 23

Position of the first minimum of diffraction.

Tables (1)

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Table I Transmission According to Eq. (12) for the Paraboloid p = 20 mm, a = 80 mm, L = 183 mm, and φ/2 = ±5°

Equations (38)

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F ( Y ) = π { Y 2 [ ( Y 2 + L 2 ) 1 / 2 L ] × ( 2 1 cos 2 ϑ 1 ) } ,
F ( p ) = π ( 2 pL + p 2 p 2 tan 2 ϑ ) .
F max ( ϑ ) = π [ Y max 2 ( P max sin 2 ϑ 1 cos 2 ϑ ) 2 ] = π [ Y max 2 ( P max tan ϑ ) 2 ]
Y max = { [ L ( 1 + cos 2 ϑ ) 2 cos 2 ϑ ] 2 L 2 } 1 / 2 ,
P max = L ( 1 cos 2 ϑ ) 2 cos 2 ϑ .
ŝ 1 ( φ ) = [ cos w cos 2 ϑ sin w cos φ sin 2 ϑ sin w ( 1 cos 2 φ cos 2 ϑ ) cos w cos φ sin 2 ϑ cos w sin φ sin 2 ϑ sin w sin 2 φ cos 2 ϑ ] ,
y 1 = r cos φ + a sin w ( 1 2 cos 2 φ cos 2 ϑ ) cos w cos φ sin 2 ϑ cos w cos 2 ϑ sin w cos φ sin 2 ϑ ,
z 1 = r sin φ a cos w sin φ sin 2 ϑ + sin w sin 2 φ cos 2 ϑ cos w cos 2 ϑ sin w cos φ sin 2 ϑ .
a tan 2 ϑ = r
B = tan 2 2 ϑ + cos 2 ϑ + 1 cos 2 ϑ ,
C = tan 2 2 ϑ + cos 2 ϑ 1 cos 2 ϑ ,
y f = ( r a tan 2 ϑ ) cos φ a 2 tan w ( B cos 2 φ + C ) ,
z f = ( r a tan 2 ϑ ) sin φ a 2 tan w ( B sin 2 φ ) ,
y f + a 2 C tan w = a 2 B tan w cos 2 φ ,
z f = a 2 B tan w sin 2 φ .
y 0 = ( a / 2 ) C tan w ,
R 0 = ( a / 2 ) B tan w .
R 0 = a 2 ( tan 2 2 ϑ + cos 2 ϑ + 1 cos 2 ϑ ) tan w .
tan 2 ϑ = r / a ,
a = [ r 2 / ( 2 p ) ] ( p / 2 )
r = p ( 1 + cos 2 ϑ sin 2 ϑ ) ,
a = p [ cos 2 ϑ ( 1 + cos 2 ϑ ) sin 2 2 ϑ ] ,
R 0 = p 2 ( 1 + cos 2 ϑ 1 cos 2 ϑ ) ( 1 cos 2 ϑ ) tan w .
y = x tan φ + a w z ( 0 ) cos φ ,
w z = 2 φ [ 1 D ( a ) ] w y + w z ( 0 ) .
w z = 2 φ [ 1 D ( s ) ] w y + a s w z ( 0 ) ;
D ( s ) = D ( a ) w z ( 0 ) 2 φ w y ( 1 a s ) .
dF ~ rdr ,
I ~ r ( a ) r ( L ) D ( s ) rdr = p 0 a + L D ( s ) ds .
D = 1 w z 2 φ w y [ 1 a L × w z ( 0 ) w z × log ( 1 + L a ) ] .
Δ λ Δ s = g m R G × cos α + cos β cos β × 1 A ,
A = [ 1 + ( tan β × 2 cos α + 3 cos β cos α + cos β ) 2 ] 1 / 2 ,
Δ α = [ R 0 cos 2 ϑ ( 1 cos 2 ϑ ) ] / p ,
Δ α Tel = Δ α ( r 1 / r 2 ) .
B 2 = 8 3 × A tan β cos α ( cos α + cos β ) × m R G 2 g × Δ λ .
a = R 2 ( 1 + cos α ) = 127.9 mm ,
b = R 2 [ ( 1 + cos α ) × ( 1 + 3 2 cos α ) ] 1 / 2 = 114.7 mm ,
S T = ( S T ) / ( cos x ) ,

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