Abstract

Surface equations for strictly aplanatic two-mirror telescopes of any configuration are given. They were used in a comparative performance analysis of the general Cassegrainian configuration as it changes continuously from near-normal to grazing incidence. The configuration of optimum performance, which resembles Schwarzschild aberration-free two-mirror telescope, is analyzed in some detail.

© 1980 Optical Society of America

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References

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  1. K. Schwarzschild, Astr. Mittheilungen Königl. Sternwarte Göttingen 10, 1 (1905).
  2. H. Wolter, Ann. Phys. Leipzig 6, 286 (1952).
    [CrossRef]
  3. W. B. Wetherell, M. P. Rimmer, Appl. Opt. 11, 2817 (1972).
    [CrossRef] [PubMed]

1972 (1)

1952 (1)

H. Wolter, Ann. Phys. Leipzig 6, 286 (1952).
[CrossRef]

1905 (1)

K. Schwarzschild, Astr. Mittheilungen Königl. Sternwarte Göttingen 10, 1 (1905).

Rimmer, M. P.

Schwarzschild, K.

K. Schwarzschild, Astr. Mittheilungen Königl. Sternwarte Göttingen 10, 1 (1905).

Wetherell, W. B.

Wolter, H.

H. Wolter, Ann. Phys. Leipzig 6, 286 (1952).
[CrossRef]

Ann. Phys. Leipzig (1)

H. Wolter, Ann. Phys. Leipzig 6, 286 (1952).
[CrossRef]

Appl. Opt. (1)

Astr. Mittheilungen Königl. Sternwarte Göttingen (1)

K. Schwarzschild, Astr. Mittheilungen Königl. Sternwarte Göttingen 10, 1 (1905).

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Figures (11)

Fig. 1
Fig. 1

Cassegrainian configuration from near-normal to grazing incidence.

Fig. 2
Fig. 2

Basic parameters of a two-mirror telescope.

Fig. 3
Fig. 3

Geometry of a two-mirror telescope.

Fig. 4
Fig. 4

Performance comparison of the aplanatic system with the classical paraboloid–hyperboloid configuration as a function of the ray–surface angle. The rms spot size was determined on the curved focal surface for an off-axis angle of 3 mrad.

Fig. 5
Fig. 5

Field curvature as a function of the configuration.

Fig. 6
Fig. 6

Defocus and spot size increase due to despace as a function of the configuration.

Fig. 7
Fig. 7

Sensitivity to decenter as a function of the configuration.

Fig. 8
Fig. 8

(a) Sensitivity to tilt as a function of the configuration. (b) Location of the neutral point. (c) Effective decenter.

Fig. 9
Fig. 9

Configuration of best performance.

Fig. 10
Fig. 10

Characteristics of the best performing system as a function of the ray–surface angle: (a) off-axis performance; (b) field curvature; (c) focal length; (d) system length.

Fig. 11
Fig. 11

Spot size as a function of field angle for γ01 = 95°

Equations (28)

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center - to - center separation :             d = ( ρ 01 - ρ 02 ) cot 2 γ 01 ,
ray - surface angle at center of second surface :             γ 02 = ½ arctan ρ 02 b - γ 01 ,
focal length : f = ρ 01 / sin α 0 , α 0 = 2 ( γ 01 + γ 02 ) .
s 1 + s 2 + z 1 = c 0 ,
c 0 = [ ( ρ 01 - ρ 02 ) 2 + d 2 ] 1 / 2 + ( ρ 02 2 + b 2 ) 1 / 2 .
ρ 1 = f · sin α .
s 1 cos 2 γ 1 + s 2 cos α = d + b - z 1 ,
s 1 sin 2 γ 1 + s 2 sin α = ρ 1 ,
2 γ 1 = α - 2 γ 2 ,
s 2 = ( b - z 2 ) / cos α ,
1 s 2 · s α = - cot γ 2 .
s 1 ( 1 - cos 2 γ 1 ) + s 2 ( 1 - cos α ) = c 0 - d - b ,
s 1 sin ( α - 2 γ 2 ) + s 2 ( sin α ) = f · sin α .
( f - s 2 ) sin α · tan ( α / 2 - γ 2 ) + s 2 ( 1 - cos α ) = c 0 - d - b .
tan γ 2 · tan α / 2 · ( 2 s 2 - c 0 + d + b - 2 f cos 2 α / 2 ) - c 0 + d + b - 2 f cos 2 α / 2 = 0.
cot γ 2 = - 1 s 2 · s 2 α = - tan α · κ - s 2 / f + cos 2 α / 2 κ - 1 + cos 2 α / 2 .
f / s 2 = 1 κ sin 2 α / 2 + q ( κ - sin 2 α / 2 ) 1 / 1 - κ · ( cos 2 α / 2 ) κ / κ - 1 ,
z 2 = b - f ( 1 - 2 sin 2 α / 2 ) 1 κ sin 2 α / 2 + q ( κ - sin 2 / α / 2 ) 1 / 1 - κ · ( cos 2 α / 2 ) κ / κ - 1 .
q = f / b - ( 2 f / b + 1 / κ ) sin 2 α 0 / 2 ( κ - sin 2 α 0 / 2 ) 1 / 1 - κ ( cos 2 α 0 / 2 ) κ / κ - 1 .
z 2 = b - f ( 1 - 2 sin 2 α / 2 ) 1 κ sin 2 α / 2 + q 2 ( κ - sin 2 α / 2 κ - sin 2 α 0 / 2 ) 1 / 1 - κ ( cos 2 α / 2 cos 2 α 0 / 2 ) κ / κ - 1 ,
q 2 = f / b - ( 2 f / b + 1 / κ ) sin 2 α 0 / 2.
s 1 2 sin 2 2 γ 1 = ( f - s 2 ) 2 sin 2 α .
s 1 2 - s 1 2 sin 2 2 γ 1 = s 1 2 + 2 s 1 [ s 2 ( 1 - cos α ) - c 0 + d + b ] + [ s 2 ( 1 - cos α ) - c + d + b ] 2 ,
s 1 = ( c 0 - d - b ) / 2 - s 2 sin 2 α / 2 + ( f - s 2 ) 2 · sin 2 α / 2 cos 2 α / 2 ( c 0 - d - b ) / 2 - s 2 sin 2 α / 2 .
z 1 = c 0 - κ f - f cos 2 α / 2 κ - 2 sin 2 α / 2 - ( f / s 2 ) sin 2 α / 2 κ f / s 2 - sin 2 α / 2 .
z 1 = c 0 - κ f - f 4 κ sin 2 α - q 1 × ( κ - sin 2 α / 2 κ - sin 2 α 0 / 2 ) 1 - 2 κ / 1 - κ ( cos 2 α / 2 cos 2 α 0 / 2 ) 1 / 1 - κ ,
q 1 = c 0 - κ f - f 4 κ sin 2 α 0 .
l = f 1 / ( 1 + f 1 2 f 2 · f 1 - e f + e ) - d ,

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