Abstract

Sands showed the equivalence of the third-order aspheric surface contribution of the aberration polynomial to the third-order inhomogenous surface contribution. This fact is exemplified by the substitution of an axial gradient for the aspheric surface of the Schmidt corrector plate. It is shown that a gradient-index corrector plate system is limited in its off-axis performance by fifth-order oblique spherical aberration just as the conventional Schmidt system is.

© 1977 Optical Society of America

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References

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  1. R. S. Hilbert, “A Study of Concentric and Schmidt-type Catadioptric Systems,” M. S. thesis (University of Rochester, 1963) (unpublished).
  2. Jonathan Maxwell, Catadioptric Imaging Systems (American Elsevier, New York, 1972).
  3. E. H. Linfoot, Recent Advances in Optics (Oxford U. P., New York, 1955), pp. 176–228.
  4. P. J. Sands, “Third Order Aberrations of Inhomogeneous Lenses,” J. Opt. Soc. Am. 60, 1436–1443 (1970).
    [Crossref]

1970 (1)

Hilbert, R. S.

R. S. Hilbert, “A Study of Concentric and Schmidt-type Catadioptric Systems,” M. S. thesis (University of Rochester, 1963) (unpublished).

Linfoot, E. H.

E. H. Linfoot, Recent Advances in Optics (Oxford U. P., New York, 1955), pp. 176–228.

Maxwell, Jonathan

Jonathan Maxwell, Catadioptric Imaging Systems (American Elsevier, New York, 1972).

Sands, P. J.

J. Opt. Soc. Am. (1)

Other (3)

R. S. Hilbert, “A Study of Concentric and Schmidt-type Catadioptric Systems,” M. S. thesis (University of Rochester, 1963) (unpublished).

Jonathan Maxwell, Catadioptric Imaging Systems (American Elsevier, New York, 1972).

E. H. Linfoot, Recent Advances in Optics (Oxford U. P., New York, 1955), pp. 176–228.

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Figures (6)

FIG. 1
FIG. 1

Schematics of conventional Schmidt corrector plate and of gradient-index corrector plate.

FIG. 2
FIG. 2

Effects of various shapes and various profiles on spherical aberration and paraxial axial chromatic aberration.

FIG. 3
FIG. 3

Spherochromatism of axial gradient corrector plate.

FIG. 4
FIG. 4

Plot of index of refraction vs position for axial gradient corrector plate.

FIG. 5
FIG. 5

Meridonal ray intercept plot: Off-axis aberration f/2. 5 system; N = 1. 6 −0. 04x +. 00298x2+ 0. 0018x3.

FIG. 6
FIG. 6

Sagittal ray intercept plot f/2. 5 system; N = 1. 6 − 0. 04x + 0. 0298x2 + 0. 0018x3.

Tables (3)

Tables Icon

TABLE I Third-order design of Schmidt systems (Ref. 2). f is the focal length of system. f# = f/number of system. The table assumes that the index of the plate equals 1. 5 and ν number is 60.

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TABLE II Third-order aberration coefficients. Spherical aberration.

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TABLE III Variations of index polynomials for corrector plates.

Equations (22)

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σ 1 , axial gradient = ( 1 / n k υ k ) ( 1 2 c 2 y a 4 Δ 0 ) ,
σ 1 asphere = ( 1 / n k υ k ) ( 4 A D y a 4 Δ n ) ,
Δ 0 = 8 A D Δ n / c 2 .
N 01 = 8 A D Δ n / c 2 ,
y a 3 4 c 3 3 1 2 y a 1 4 c 1 2 Δ 0 0 .
y a 3 4 c 3 3 y a 1 4 ( 1 2 c 1 2 ) Δ 0 , 1 y a 2 4 ( 1 2 c 2 2 ) Δ 0 , 2 = 0 .
c 3 3 1 2 c 1 2 ( Δ 0 , 1 + Δ 0 , 2 ) = 0 .
N 0 = N 00 + N 01 x + N 02 x 2 + .
0 = N 01 + 2 N 02 x + .
Δ 0 , 1 = N 01 ,
Δ 0 , 2 = ( N 01 + 2 N 02 t + ) .
c 3 3 + 1 2 c 1 2 ( 2 N 02 t + 3 N 03 t 2 + ) = 0 .
N = 1. 6 0. 04 x + 0. 0298 x 2 + 0. 0018 x 3 .
1 16 f 3
1 16 f 3
1 16 f 3
1 64 f f # 2
2 64 f f # 2
3 64 f f # 2
f 2049 f # 3
f 4096 f # 3
f 8192 f # 3