Abstract

Two-mirror systems of the type conventionally used as astronomical objectives can be used noncoaxially to avoid the usual central obscuration. Third-order aberration theory is used to derive the conditions under which the primary and secondary mirrors can be tilted and decentered.

© 1975 Optical Society of America

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Corrections

Rubin Gelles, "Unobscured-aperture two-mirror systems: erratum," J. Opt. Soc. Am. 69, 208-208 (1979)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-1-208

References

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  1. R. Buchroeder, Sky and Telescope 38, 418 (1969).
  2. R. Buchroeder, Appl. Opt. 9, 2169 (1970).
    [Crossref] [PubMed]
  3. B. Tatian, J. Opt. Soc. Am. 61, 661A (1971).
    [Crossref]
  4. P. J. Sands, J. Opt. Soc. Am. 62, 1211 (1972).
    [Crossref]
  5. H. A. Buchdahl, J. Opt. Soc. Am. 62, 1314 (1972).
    [Crossref]
  6. P. J. Sands, J. Opt. Soc. Am. 63, 425 (1973).
    [Crossref]
  7. W. B. King, Appl. Opt. 13, 21 (1974).
    [Crossref] [PubMed]
  8. R. Gelles, Opt. Engr. 13, 534 (1974).

1974 (2)

W. B. King, Appl. Opt. 13, 21 (1974).
[Crossref] [PubMed]

R. Gelles, Opt. Engr. 13, 534 (1974).

1973 (1)

1972 (2)

1971 (1)

B. Tatian, J. Opt. Soc. Am. 61, 661A (1971).
[Crossref]

1970 (1)

1969 (1)

R. Buchroeder, Sky and Telescope 38, 418 (1969).

Buchdahl, H. A.

Buchroeder, R.

R. Buchroeder, Appl. Opt. 9, 2169 (1970).
[Crossref] [PubMed]

R. Buchroeder, Sky and Telescope 38, 418 (1969).

Gelles, R.

R. Gelles, Opt. Engr. 13, 534 (1974).

King, W. B.

Sands, P. J.

Tatian, B.

B. Tatian, J. Opt. Soc. Am. 61, 661A (1971).
[Crossref]

Appl. Opt. (2)

J. Opt. Soc. Am. (4)

Opt. Engr. (1)

R. Gelles, Opt. Engr. 13, 534 (1974).

Sky and Telescope (1)

R. Buchroeder, Sky and Telescope 38, 418 (1969).

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Figures (6)

FIG. 1
FIG. 1

Tilted stigmatic telescope.

FIG. 2
FIG. 2

Tilted Schwartzschild telescope objective.

FIG. 3
FIG. 3

Tilted, decentered Cassegrain.

FIG. 4
FIG. 4

Tilted, decentered Dall–Kirkham (aspheric primary).

FIG. 5
FIG. 5

Tilted, decentered Dall–Kirkham (aspheric secondary).

FIG. 6
FIG. 6

Tilted, decentered Ritchey–Chrétien.

Tables (4)

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TABLE I Cassegrain objective.

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TABLE II Dall–Kirkham (primary aspheric).

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TABLE III Dall–Kirkham (secondary aspheric).

Tables Icon

TABLE IV Ritchey–Chrétien.

Equations (27)

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S 1 ( k 1 + Q 1 ) + S ¯ 1 Q 1 + S 2 ( k 2 + Q 2 ) + S ¯ 2 Q 2 = 0
S 1 ( k 1 + Q 1 ) 2 + S ¯ 1 Q 1 2 + S 2 ( k 2 + Q 2 ) 2 + S ¯ 2 Q 2 2 = 0.
S ¯ 1 = - S 1 , S ¯ 2 = - S 2 , S 2 = - S 1 / M ,
S 1 k 1 - S 1 k 2 / M = 0 , S 1 k 1 2 - S 1 ( k 2 2 + 2 k 2 Q 2 ) / M = 0 ,
k 2 = M k 1 ,
Q 2 = k 1 ( M - 1 ) / 2.
k 1 = i p 1 / i 1 = - 2 u p 1 / y 1 ϕ 1
Q 2 = y p 2 / y 2 = M y p 2 / y 1 ,
Q 2 = - u p ( M - 1 ) / y 1 ϕ 1 .
y p 2 = - u p 1 ( M - 1 ) / M ϕ 1 .
d = ( M - 1 ) / M ϕ 1 ,
y p 2 = - u p 1 d .
S 1 ( k 1 + Q 1 ) + S 2 ( k 2 + Q 2 ) = 0 , S 1 ( k 1 + Q 1 ) 2 + S 2 ( k 2 + Q 2 ) 2 = 0.
k 1 + Q 1 = k 2 + Q 2 .
S 1 k 1 + S 2 k 2 = 0 , S 1 k 1 2 + S 2 k 2 2 + 2 S 2 k 2 Q 2 = 0.
k 2 = - S 1 k 1 / S 2 ,
Q 2 = k 1 ( 1 + S 1 / S 2 ) / 2.
i p = y p c - u p ,
k 2 = k 2 + Q 2 = ( y p 2 c 2 - u p 2 ) / i 2
u p 2 = y p 2 c 2 - i 2 k 2 .
S 1 k 1 - S 2 Q 1 + S 2 k 2 = 0 , S 1 ( k 1 2 + 2 k 1 Q 1 ) - S 2 Q 1 2 + S 2 k 2 2 = 0 ,
S ¯ 1 = - ( S 1 + S 2 ) .
Q 1 = k 2 ,
k 1 = 0.
Q 2 = k 1 ,
k 2 = 0.
k 2 2 = - S 1 [ k 1 2 ( S 2 + S ¯ 2 ) + S 1 2 k 1 2 ] / S 2 S ¯ 2 , Q 2 = - ( S 1 k 1 + S 2 k 2 ) / ( S 2 + S ¯ 2 ) .