Abstract

The one-radius triplet is an optical system that consists of three lenses. Either the radii of curvature of the lenses have the same absolute value or one radius of curvature has an infinitely large value. The advantage of such optical systems is that their production cost is less than that of systems with ordinary triplets. Here a theory of one-radius triplets is described and tables of parameters for their modification are provided. Residual aberrations are given for several selected triplets. One-radius triplets are suitable for use in laser technology and metrology.

© 2002 Optical Society of America

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References

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  1. A. Mikš, “One radius doublet,” Fine Mech. Opt. 24, 115–118 (1979).
  2. A. C. Van Heel, “One radius doublets,” Opt. Acta 2, 29–35 (1955).
    [CrossRef]
  3. P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 227–249.
  4. A. Mikš, “Modified relations for calculation of third order aberrations for thin lenses in Coddington variables,” Fine Mech. Opt. 23, 57–58 (1978).

1979

A. Mikš, “One radius doublet,” Fine Mech. Opt. 24, 115–118 (1979).

1978

A. Mikš, “Modified relations for calculation of third order aberrations for thin lenses in Coddington variables,” Fine Mech. Opt. 23, 57–58 (1978).

1955

A. C. Van Heel, “One radius doublets,” Opt. Acta 2, 29–35 (1955).
[CrossRef]

Macdonald, J.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 227–249.

Mikš, A.

A. Mikš, “One radius doublet,” Fine Mech. Opt. 24, 115–118 (1979).

A. Mikš, “Modified relations for calculation of third order aberrations for thin lenses in Coddington variables,” Fine Mech. Opt. 23, 57–58 (1978).

Mouroulis, P.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 227–249.

Van Heel, A. C.

A. C. Van Heel, “One radius doublets,” Opt. Acta 2, 29–35 (1955).
[CrossRef]

Fine Mech. Opt.

A. Mikš, “One radius doublet,” Fine Mech. Opt. 24, 115–118 (1979).

A. Mikš, “Modified relations for calculation of third order aberrations for thin lenses in Coddington variables,” Fine Mech. Opt. 23, 57–58 (1978).

Opt. Acta

A. C. Van Heel, “One radius doublets,” Opt. Acta 2, 29–35 (1955).
[CrossRef]

Other

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 227–249.

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Figures (2)

Fig. 1
Fig. 1

Dependence of shapes of the lenses on shape parameters.

Fig. 2
Fig. 2

Shapes of selected ORTs.

Tables (9)

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Table 1 Refractive Indices of Lenses of an ORT with Parameters 0, 1, 1, 1, -1, and 1 for S I = S II = 0

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Table 2 Refractive Indices of Lenses of an ORT with Parameters 0, 1, 1, 1, -1, and 1 for S I = 0

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Table 3 Refractive Indices of Lenses of an ORT with Parameters 0, 0, 1, 1, -1, and 1 for S I = S II = 0

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Table 4 Refractive Indices of Lenses of an ORT with Parameters 1, 0, 0, 1, 1, and -1 for S I = S II = 0

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Table 5 Refractive Indices of Lenses of an ORT with Parameters 0, 0, 0, 1, -1, and 1 for S I = S II = 0

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Table 6 Parameters of an Aplanatic ORTa

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Table 7 Residual Spherical Aberration δs′ and Sine Condition δf′ of the ORT for Apertures H and 0.63H

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Table 8 Parameters of an ORT for Monochromatic Lighta

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Table 9 Parameters of an Achromatic ORTa

Equations (26)

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φ=φ1+φ2+φ3,
φi=ni-11ri-1ri, i=1, 2, 3,
Xi=ri+rri-ri.
ri=2ni-1φiXi+1, ri=2ni-1φiXi-1.
Ki=sign φi,
r=f i=13 Ki2ni-1Xi+1,
φi=Ki2ni-1rXi+1.
δφλ=0,
φ=2ri=13 Kini-1Xi+1.
δφλ=2ri=13 KiδniXi+1,
δni=niλ2-niλ1
i=13 KiδniXi+1=0.
SI=i=3 hi4Mi,
SII=i=13 hi3h¯iMi+i=13 hi2Ni,
Mi=φi3AiXi2+BiXiYi+CiYi2+Di, Ni=φi2EiXi+FiYi;
Xi=ri+riri-ri, Yi=si+sisi-si;
Ai=ni+24nini-12, Bi=ni+1nini-1, Ci=3ni+24ni, Di=ni24ni-12, Ei=Bi/2, Fi=2ni+12ni,
Yi=-1-2siφi, Yi+1=hiφihi+1φi+1Yi-1-1.
hi=1, h¯i=0, i=1, 2, 3.
SI=i=13 Mi,
SII=i=13 Ni.
r1=r, r2=-r, r3=, r4=r, r5=.
2δn1-δn2+δn3=0.
r1=r, r2=-r, r3=r, r4=.
r1=r, r2=, r3=r, r4=-r, r5=r.
r1=r, r2=-r, r3=r, r4=-r.

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