Abstract

Pointing errors in telescopes carried by space vehicles can be compensated by servo-control of the secondary mirror. This introduces some aberrations in the stabilized image, the magnitude of which depends on the asphericity of the telescope mirrors. A configuration is presented in which the centered image of an off-axis object point is free from coma. The required aspheric corrections and the residual aberrations are calculated. Also included is a summary of the third order aberration constants for some well-known centered cassegrain-type telescopes.

© 1971 Optical Society of America

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References

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  1. M. Bottema, W. G. Fastie, H. W. Moos, Appl. Opt. 8, 1821 (1969).
    [CrossRef] [PubMed]
  2. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 5.
  3. A. R. Kirkham, Sci. Amer. 158, 374 (1938).
    [CrossRef]
  4. H. Chrétien, Rev. Opt. 1, 13, 49 (1922).
  5. J. W. Ritchey, H. Chrétien, Compt. Rend. 185, 266 (1927).
  6. R. T. Jones, J. Opt. Soc. Amer. 44, 630 (1954).
    [CrossRef]
  7. A. B. Meinel, in Telescopes, G. P. Kuiper, B. M. Middlehurst, Eds., Vol. I of Stars and Stellar Systems (Univ. of Chicago PressChicago, 1960), p. 26.
  8. R. V. Shack, Opt. Sci. Cent. Newsletter (Univ. of Arizona, Tucson) 3, 64 (1969).
  9. J. Landi-Dessy, A. Puch, Mem. Soc. Astr. Ital. 37, 657 (1966).

1969 (1)

1966 (1)

J. Landi-Dessy, A. Puch, Mem. Soc. Astr. Ital. 37, 657 (1966).

1954 (1)

R. T. Jones, J. Opt. Soc. Amer. 44, 630 (1954).
[CrossRef]

1938 (1)

A. R. Kirkham, Sci. Amer. 158, 374 (1938).
[CrossRef]

1927 (1)

J. W. Ritchey, H. Chrétien, Compt. Rend. 185, 266 (1927).

1922 (1)

H. Chrétien, Rev. Opt. 1, 13, 49 (1922).

Bottema, M.

Chrétien, H.

J. W. Ritchey, H. Chrétien, Compt. Rend. 185, 266 (1927).

H. Chrétien, Rev. Opt. 1, 13, 49 (1922).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 5.

Fastie, W. G.

Jones, R. T.

R. T. Jones, J. Opt. Soc. Amer. 44, 630 (1954).
[CrossRef]

Kirkham, A. R.

A. R. Kirkham, Sci. Amer. 158, 374 (1938).
[CrossRef]

Landi-Dessy, J.

J. Landi-Dessy, A. Puch, Mem. Soc. Astr. Ital. 37, 657 (1966).

Meinel, A. B.

A. B. Meinel, in Telescopes, G. P. Kuiper, B. M. Middlehurst, Eds., Vol. I of Stars and Stellar Systems (Univ. of Chicago PressChicago, 1960), p. 26.

Moos, H. W.

Puch, A.

J. Landi-Dessy, A. Puch, Mem. Soc. Astr. Ital. 37, 657 (1966).

Ritchey, J. W.

J. W. Ritchey, H. Chrétien, Compt. Rend. 185, 266 (1927).

Shack, R. V.

R. V. Shack, Opt. Sci. Cent. Newsletter (Univ. of Arizona, Tucson) 3, 64 (1969).

Appl. Opt. (1)

Compt. Rend. (1)

J. W. Ritchey, H. Chrétien, Compt. Rend. 185, 266 (1927).

J. Opt. Soc. Amer. (1)

R. T. Jones, J. Opt. Soc. Amer. 44, 630 (1954).
[CrossRef]

Mem. Soc. Astr. Ital. (1)

J. Landi-Dessy, A. Puch, Mem. Soc. Astr. Ital. 37, 657 (1966).

Rev. Opt. (1)

H. Chrétien, Rev. Opt. 1, 13, 49 (1922).

Sci. Amer. (1)

A. R. Kirkham, Sci. Amer. 158, 374 (1938).
[CrossRef]

Other (3)

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 5.

A. B. Meinel, in Telescopes, G. P. Kuiper, B. M. Middlehurst, Eds., Vol. I of Stars and Stellar Systems (Univ. of Chicago PressChicago, 1960), p. 26.

R. V. Shack, Opt. Sci. Cent. Newsletter (Univ. of Arizona, Tucson) 3, 64 (1969).

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Figures (1)

Fig. 1
Fig. 1

Cassegrain-type telescope with tilted secondary.

Tables (4)

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Table I Aberration Constants in Cassegrain Telescopes

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Table II Conditions for Zero Spherical Aberration

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Table III Aberration Constants in Telescopes with Centered Secondary Mirror

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Table IV Aberration Constants for Centered Image Point in Telescopes with Tilted Secondary Mirror

Equations (18)

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r 2 = 4 f 1 z 1 - e 1 z 1 2 ,
r 2 2 = 4 f 2 z 2 - e 2 z 2 2 .
η 1 = - 1 8 e 1 ( r / f 1 ) 3 cos θ + 1 4 ( r / f 1 ) 2 α ( 2 + cos 2 θ ) - ( r / f 1 ) α 2 cos θ ,
ξ 1 = - 1 8 e 1 ( r / f 1 ) 3 sin ϑ + 1 4 ( r / f 1 ) 2 α sin 2 θ ,
η 2 = a 1 ( r 2 / q ) 3 cos θ 2 + a 2 ( r 2 / q ) 2 α 2 ( 2 + cos 2 θ 2 ) + ( 2 a 3 + a 4 ) ( r 2 / q ) α 2 2 cos θ 2 + a 5 α 2 3 ,
ξ 2 = a 1 ( r 2 / q ) 3 sin θ 2 + a 2 ( r 2 / q ) 2 α 2 sin 2 θ 2 + a 4 ( r 2 / q ) α 2 2 sin θ 2 ,
a 1 = 1 8 ( m - 1 ) [ 4 m + ( m - 1 ) 2 e 2 ] , a 2 = - 1 4 ( m 2 - 1 ) , a 3 = 1 2 ( m - 1 ) , a 4 = 0 , a 5 = 0.
tan α 2 = - γ - 1 tan α .
r 2 sin θ 2 = γ r sin θ ,
r 2 cos θ 2 = γ r cos θ + α d .
η = - η 1 + γ η 2 = A 1 ( r / f ) 3 cos θ + A 2 ( r / f ) 2 α ( 2 + cos 2 θ ) + ( 2 A 3 + A 4 ) ( r / f ) α 2 cos θ + A 5 α 3 ,
ξ = - ξ 1 + ξ 2 = A 1 ( r / f ) 3 sin θ + A 2 ( r / f ) 2 α sin 2 θ + A 4 ( r / f ) α 2 sin θ .
γ = s ( m + s ) - 1 and t = ( m + s ) - 1 .
2 ( A 4 - A 3 ) / f = - ( 1 / f 1 ) + ( 1 / f 2 ) = - { m ( m - 1 ) / s - 1 } / f .
a 2 = - 1 8 ( m 2 - 1 )             ( tilted secondary , centered image ) , a 3 = 1 8 ( m - 1 ) .
Δ q = 1 2 ( 3 m + 1 ) q ( 1 2 α 2 ) 2 .
a 4 = 1 8 ( 3 m + 1 )             ( tilted secondary , centered image ) .
a 1 = - 1 8 ( m + s ) ( m 2 + 1 )             ( tilted secondary ) .

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