Abstract

In a radial gradient, the refractive index profile is normally represented by a polynomial with only even powers of r. If, however, odd powers of r are present in the representation, the effect on aberrations can be serious. A Wood lens serves as an example.

© 1990 Optical Society of America

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References

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  1. E. Marchand, “Pseudoaxicon Lenses,” Appl. Opt. 28, 154–156 (1989).
    [CrossRef] [PubMed]
  2. E. Marchand, Gradient Index Optics (Academic, New York, 1978), Eq. (5.20).

1989

Marchand, E.

E. Marchand, “Pseudoaxicon Lenses,” Appl. Opt. 28, 154–156 (1989).
[CrossRef] [PubMed]

E. Marchand, Gradient Index Optics (Academic, New York, 1978), Eq. (5.20).

Appl. Opt.

Other

E. Marchand, Gradient Index Optics (Academic, New York, 1978), Eq. (5.20).

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Equations (12)

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z = a 1 r + a 2 r 2 + a 3 r 3 + ,
n = N 0 + N 2 r 2 + N 4 r 4 + N 6 r 6 + .
n = N 0 1 + r / a = N 0 [ 1 - r a + ( r a ) 2 - ] .
z = 0 y d y ( n / l ) 2 - 1 ,
l = l 0 = n 0 cos ( γ 0 )
n 2 = N 0 [ 1 - ( g r ) 2 + h 3 ( g r ) 3 + h 4 ( g r ) 4 + ]
X = g x ,             Y = g y ,             Z = g z ,             t = N 0 Z / l
Y + Y = H 3 Y 2 + 2 h 4 Y 3 + ,
H 3 = ( 3 / 2 ) h 3 .
S = f Y 0 H 3 B 1 / s ,             C = e 2 g H 3 B 1 / s , D = V 0 H 3 ( B 1 z ¯ 2 + 2 z ¯ B 2 + B 3 ) , P = - A = ( f / 2 ) V 0 H 3 ( B 1 z ¯ + B 2 ) / s .
z ¯ = - N 0 g z e ,
B 1 = s - s 3 / 3 ,             B 2 = ( 1 - c 3 ) / 3 ,             B 3 = s 3 / 3.

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