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References

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  1. L. Epstein, Sky Telesc. 33 (1967).
  2. L. Epstein, Appl. Opt. 12, 926 (1973).
    [CrossRef] [PubMed]
  3. T. Chu, U.S. Patent3,617,107 (1971).
  4. K. Henize, “The Role of Surveys in Space Astronomy,” in Optical Telescope Technology, NASA-SP-233 (U. S. Government Printing Office, Washington, D.C., 1970).
  5. C. Caratheodory, Gesammelte Math. Schriften (C. H. Beck, München, 1955), Vol. 2.
  6. F. Ross, Astrophys. J. 92, 400 (1940).
    [CrossRef]
  7. F. Lucy, J. Opt. Soc. Am. 30, 251 (1940).
    [CrossRef]
  8. E. Linfoot, Recent Advances in Optics (Oxford U.P., New York, 1955).
  9. K. Bahner, Handb. Phys. 29, 272 (1967).
  10. A. Bowers, Achievements in Optics (Delft, Holland1950).

1973

1967

L. Epstein, Sky Telesc. 33 (1967).

K. Bahner, Handb. Phys. 29, 272 (1967).

1940

Bahner, K.

K. Bahner, Handb. Phys. 29, 272 (1967).

Bowers, A.

A. Bowers, Achievements in Optics (Delft, Holland1950).

Caratheodory, C.

C. Caratheodory, Gesammelte Math. Schriften (C. H. Beck, München, 1955), Vol. 2.

Chu, T.

T. Chu, U.S. Patent3,617,107 (1971).

Epstein, L.

Henize, K.

K. Henize, “The Role of Surveys in Space Astronomy,” in Optical Telescope Technology, NASA-SP-233 (U. S. Government Printing Office, Washington, D.C., 1970).

Linfoot, E.

E. Linfoot, Recent Advances in Optics (Oxford U.P., New York, 1955).

Lucy, F.

Ross, F.

F. Ross, Astrophys. J. 92, 400 (1940).
[CrossRef]

Appl. Opt.

Astrophys. J.

F. Ross, Astrophys. J. 92, 400 (1940).
[CrossRef]

Handb. Phys.

K. Bahner, Handb. Phys. 29, 272 (1967).

J. Opt. Soc. Am.

Sky Telesc.

L. Epstein, Sky Telesc. 33 (1967).

Other

E. Linfoot, Recent Advances in Optics (Oxford U.P., New York, 1955).

T. Chu, U.S. Patent3,617,107 (1971).

K. Henize, “The Role of Surveys in Space Astronomy,” in Optical Telescope Technology, NASA-SP-233 (U. S. Government Printing Office, Washington, D.C., 1970).

C. Caratheodory, Gesammelte Math. Schriften (C. H. Beck, München, 1955), Vol. 2.

A. Bowers, Achievements in Optics (Delft, Holland1950).

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Figures (4)

Fig. 1
Fig. 1

The geometry of an all-reflective Schmidt system.

Fig. 2
Fig. 2

The performance with a conventional corrector, curve (1), and with an off-axis corrector, curve (2).

Fig. 3
Fig. 3

The configuration of an all-reflective Schmidt telescope.

Fig. 4
Fig. 4

Performance with the off-axis corrector in two orthogonal planes.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

l 1 + l 2 Z = 3 / 2 ,
l 1 = cos α 1 / 4 sin 2 α , and l 2 = cos α { [ sin α · sin ( β 2 α ) Z ] / [ cos ( β 2 α ) ] } .
Z ( 1 + cos ( β 2 α ) ) = [ 2 cos α 1 / 2 ( 1 4 sin 2 α ) 1 / 2 3 / 2 ] . cos ( β 2 α ) sin α · sin ( β 2 α ) ,
sin β = 2 · sin α .
sin ( β 2 α ) = 2 sin α ( 1 sin 2 α ) ( 1 4 sin 2 α ) 1 / 2 · ( 1 sin 2 α ) 1 / 2 · 2 sin α = 2 X ¯ · [ 1 2 X ¯ 2 ( 1 5 X ¯ 2 + 4 X ¯ 4 ) 1 / 2 ] = 2 X ¯ · [ 1 2 X ¯ 2 1 + ( 5 / 2 ) X ¯ 2 2 X ¯ 4 + ( 25 / 8 ) X ¯ 4 ] X ¯ 3 + ( 9 / 4 ) X ¯ 5 ,
X ¯ = sin α ,
[ 1 / cos ( β 2 α ) ] 1.
Z = ( 1 X ¯ 2 ) 1 / 2 ( 1 / 4 ) ( 1 4 X ¯ 2 ) 1 / 2 ( 1 / 4 ) X ¯ 4 ( 9 / 8 ) X ¯ 6 3 / 4 .
X ¯ X , since | X X ¯ | < 2.5 · 10 7 for β 15 ° .
Z = ( X 4 / 16 ) ( 3 X 2 + 2 ) ;
Z = [ X 4 / ( 16 r 5 ) ] ( 3 X 2 + 2 r 2 ) .
Z = γ 2 · [ ( γ 2 2 X 2 + Y 2 ) 2 / 16 r 5 ] · ( 3 ( γ 2 2 X 2 + Y 2 ) + 2 r 2 ) .

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