Abstract

A family of catadioptric telescopes is investigated, characterized with two-element, full-aperture, afocal corrector lenses and aspherical, focusing, primary mirrors or primary-secondary mirror combinations. Third-order aberration and design equations are provided for anastigmatic systems in which corrector position must be a free parameter, forcing the consideration of aspherics on the mirrored surfaces.

© 2003 Optical Society of America

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References

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  1. H. Rutten, M. van Venrooij, “Other compound systems,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), pp. 126–128.
  2. J. L. Houghton, “Lens system,” U.S. Patent2,350,112 (30May1944).
  3. R. Gelles, “A new family of flat field cameras,” Appl. Opt. 2, 1081–1084 (1963).
    [CrossRef]
  4. R. D. Sigler, “Compound catadioptric telescopes with all spherical surfaces,” Appl. Opt. 17, 1519–1526 (1978).
    [CrossRef] [PubMed]
  5. S. C. B. Gascoigne, “Recent advances in astronomical optics,” Appl. Opt. 12, 1419–1429 (1973).
    [CrossRef] [PubMed]
  6. Ref. 1, pp. 126–127.
  7. Ref. 4, p. 1522.
  8. Ref. 4, p. 1523.

1978 (1)

1973 (1)

1963 (1)

Gascoigne, S. C. B.

Gelles, R.

Houghton, J. L.

J. L. Houghton, “Lens system,” U.S. Patent2,350,112 (30May1944).

Rutten, H.

H. Rutten, M. van Venrooij, “Other compound systems,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), pp. 126–128.

Sigler, R. D.

van Venrooij, M.

H. Rutten, M. van Venrooij, “Other compound systems,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), pp. 126–128.

Appl. Opt. (3)

Other (5)

H. Rutten, M. van Venrooij, “Other compound systems,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), pp. 126–128.

J. L. Houghton, “Lens system,” U.S. Patent2,350,112 (30May1944).

Ref. 1, pp. 126–127.

Ref. 4, p. 1522.

Ref. 4, p. 1523.

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Figures (1)

Fig. 1
Fig. 1

Schematic of Houghton telescope.

Tables (11)

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Table 1 Anastigmatic Lurie-Houghton Systems with Q2 = Q1

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Table 2 Anastigmatic Lurie-Houghton Systems with Q2Q1 and L = 4

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Table 3 Anastigmatic Lurie-Houghton Systems with Q2 = 1

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Table 4 Anastigmatic Lurie-Houghton Systems with Q1 = 1

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Table 5 Anastigmatic Houghton-Cassegrain Systems with Q2 = Q1 and bS = 0

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Table 6 Anastigmatic Houghton-Cassegrain Systems with Q2 = Q1 and bP = 0

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Table 7 Anastigmatic Houghton-Cassegrain Systems with Q2 = Q1 and L = 4

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Table 8 Anastigmatic Houghton-Cassegrain Systems with Q2 = Q1 = 1 and bS = 0

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Table 9 Anastigmatic Houghton-Cassegrain Systems with Q2 = Q1 = 1 and bP = 0

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Table 10 Anastigmatic Houghton-Cassegrain Systems with Q2Q1, bS = 0, and L = 4

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Table 11 Anastigmatic Houghton-Cassegrain Systems with Q2Q1, bP = 0, and L = 4

Equations (64)

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 BLENS+ BMIRROR=0,
 FLENS+ FMIRROR=0,
 CLENS+ CMIRROR=0.
8fP3  BLENS=Q1+12-Q2-12A1/L3-Q1+Q2A2/L3,
8fP2  FLENS=-Q1+Q2A4/L2+D8fP3  BLENS,
8fP  CLENS=-2Q1+Q2DA4/L2+D28fP3  BLENS,
8fP3  BMIRROR=1+bP,
8fP2  FMIRROR=2,
8fP  CMIRROR=4.
8fP3  BMIRRORS=bP-G2bS+J1=A3,
8fP2  FMIRRORS=G3bS+J2=A5,
8fP  CMIRRORS=-G6bS+J3=A6,
G1=M+12/M-12, G2=M-131-R/M3, J1=1-G1G2, G3=M-13R/M3, G4=2/M2, J2=G4+G1G3, G5=4M-R/M21-R, G6=M-13R2/M31-R, J3=G5-G1G6.
-4QA4/L3+1+bP=0,-2QA4/L2-D1+bP+2=0,D21+bP-4D-1=0.
bP=4D-1/D2-1,
L=22-D-DbP/1+bP,
Q=L22-D-DbP/2A4.
D2-D3/D-12=A4,
N=A4+2+A42+12A4+41/2/2A4.
Q1+12-Q2-12A1/L3-Q1+Q2A2/L3+1+bP=0,Q1+Q2A4/L2+D1+bP-2=0,D21+bP-4D-1=0.
bP=Eq.14,Q2=2-D-DbPL2/2A4+A4L1+bP/2A12-D-DbP-A4/A1,
Q1=L22-D-DbP/A4-Q2.
bP = Eq.14;L=-A421+bP±A441+bP2+4A1A2A42-D-DbP31/2/2A12-D-DbP2,
Q1=L22-D-DbP/A4-1.
bP=Eq.14,L=A421+bP±A441+bP2-4A1A42-D-DbP3A2-4A11/2/2A12-D-DbP2,
Q2=L22-D-DbP/A4-1.
2QA4/L3-A3=0, 2QA4/L2+DA3-A5=0,D2A3-2DA5+A6=0.
bP=-D2J1+2DJ2-J3/D2,
L=-2J2-DA3/A3,
Q=L3A3/4A4,
bS=D2J1-2DJ2+J3/DG2D+2G3+G6,
L=2A5-DA3/A3,
Q=L3A3/4A4,
Q=L3G3G5+G4G6/4DA4G3D+G6+2LA42G3D+G6,
bS=L2J3-G4D-G1G3D-2QA4D/L2G3D+G6,
bP=[bSG2D2+2G3D+G6-D2J1+2DJ2-J3/D2.
4J22-A3J33-A34A42=0,
bP=A3-J1,
D=J2-A32A4/21/3/A3,
L=4A4/A31/3.
4J22-A3J33-A34A42=0,
bS=A3-J1+A4/G2,
D=J2-A32A4/21/3/A3,
L=4A4/A31/3.
A4=4J22-J1J33/J141/2, D=J2-A4J12/21/3/J1.
Q1+12-Q2-12A1/L3-Q1+Q2A2/L3+A3=0,
Q1+Q2A4/L2+DA3-A5=0,
D2A3-2DA5+A6=0.
bP=Eq.26,
Q2=LA3A4/2A1J2-DA3+L2J2-DA3/2A4-A4/A1,
Q1=L2J2-DA3/A4-Q2.
bS= Eq.29, Q2=LA3A4/2A1A5-DA3+L2A5-DA3/2A4-A4/A1,
Q1=L2A5-DA3/A4-Q2.
bP= Eq.26,L=A3A42±A32A44-4A1A4J2-DA33×A2-4A11/2/2A1J2-DA32,
Q2=L2J2-DA3/A4-1.
bS= Eq.29, L=A3A42±A32A44-4A1A4A5-DA33×A2-4A11/2/2A1A5-DA32,
Q2=L2A5-DA3/A4-1.
bP= Eq.26, L=-A3A42±A32A44+4A1A2A4×J2-DA331/2/2A1J2-DA32,
Q1=L2J2-DA3/A4-1.
bS= Eq.29, L=-A3A42±A32A44+4A1A2A4×A5-DA331/2/2A1A5-DA32,
Q1=L2A5-DA3/A4-1.
c1,2=Q±1/[2fPLN-1.
fPc|Q±1/L|<2.0.
L=1-Q2S/N-1.

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