Abstract

Simple equations used for analyzing chromatic aberrations of Selfoc lenses were derived in terms of Buchdahl chromatic coordinates and Buchdahl dispersion constants. The equations that employ gradient-index chromatic constants Ψ1 and Ψ2 are used for selecting suitable ion-exchange pairs to design an achromatic Selfoc lens.

© 1996 Optical Society of America

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References

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  1. K. Nishizawa, “Chromatic aberration of the Selfoc lens as an imaging system,”Appl. Opt. 19, 1052–1055 (1980).
  2. K. Siva Rama Krishna, A. Sharma, “Chromatic aberrations of radial gradient index lenses. I. Theory,” Appl. Opt. 34, 1032–1036 (1995).
  3. K. Fujii, S. Ogi, N. Akazawa, “Gradient-index rod lens with a high acceptance angle for color use by Na+ for Li+ exchange,” Appl. Opt. 33, 8087–8093 (1994).
  4. K. Siva Rama Krishna, A. Sharma, “Model for optical properties of silicate glasses,” Appl. Opt. 33, 8030–8035 (1994).
  5. K. Siva Rama Krishna, A. Sharma, “Evaluation of optical glass composition by optimization methods,” Appl. Opt. 34, 5628–5634 (1995).
  6. Selfoc Product Guide (NSG America, Somerset, N.J., 1994).

1995

K. Siva Rama Krishna, A. Sharma, “Chromatic aberrations of radial gradient index lenses. I. Theory,” Appl. Opt. 34, 1032–1036 (1995).

K. Siva Rama Krishna, A. Sharma, “Evaluation of optical glass composition by optimization methods,” Appl. Opt. 34, 5628–5634 (1995).

1994

1980

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Tables (3)

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Table 1 Optical Properties of Two Selfoc Lenses

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Table 2 Buchdahl Dispersion Constants of the Two Selfoc Lenses (λ0 = 0.574 μm)

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Table 3 Comparison of Estimating Function ΔP/P for Two Lenses

Equations (22)

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n λ ( r ) = n λ ( 0 ) ( 1 A 2 r 2 ) ,
Δ P P = 1 2 Δ A A = Δ A A = 1 2 n λ ( 0 ) Δ n ( r 0 ) n λ ( r 0 ) Δ n ( 0 ) [ n λ ( 0 ) n λ ( r 0 ) ] n λ ( 0 ) ,
n ( r , ω λ ) = n 0 ( ω λ ) + n 1 ( ω λ ) r 2 + ,
n 0 ( ω λ ) = n 00 λ0 + ν 01 ω λ + ν 02 ω λ 2 + , n 1 ( ω λ ) = n 10 λ0 + ν 11 ω λ + ν 12 ω λ 2 + ,
n λ ( 0 ) = n ( 0 , ω λ ) = n 0 ( ω λ ) = n 00 λ0 + ν 01 ω λ + ν 02 ω λ 2 + , n λ ( r 0 ) = n ( r 0 , ω λ ) = n 0 ( ω λ ) + n 1 ( ω λ ) r 0 2 = ( n 00 λ0 + n 10 λ0 r 0 2 ) + ( ν 01 + ν 11 r 0 2 ) ω λ + ( ν 02 + ν 12 r 0 2 ) ω λ 2 + .
Δ n ( 0 ) = n ( 0 , ω F ) n ( 0 , ω C ) = ν 01 ( ω F ω C ) + ν 02 ( ω F 2 ω C 2 ) , Δ n ( r 0 ) = n ( r 0 , ω F ) n ( r 0 , ω C ) , = ( ν 01 + ν 11 r 0 2 ) ( ω F ω C ) + ( ν 02 + ν 12 r 0 2 ) ( ω F 2 ω C 2 ) ,
Δ P P = 1 2 { [ ν 11 n 1 ( ω λ ) ν 01 n 0 ( ω λ ) ] ( ω F ω C ) + [ ν 12 n 1 ( ω λ ) ν 02 n 0 ( ω λ ) ] ( ω F 2 ω C 2 ) } .
Δ P P = 1 2 [ ψ 1 ( ω F ω C ) + ψ 2 ( ω F 2 ω C 2 ) ] ,
ψ 1 = ( ν 11 n 10 λ0 ν 01 n 00 λ0 ) ,  ψ 2 = ( ν 12 n 10 λ0 ν 02 n 00 λ0 ) .
f = 1 n λ ( 0 ) A sin ( A Z ) ,
l = 1 n λ ( 0 ) A tan ( A Z ) ,
Δ f f = [ 1 + A Z cot ( A Z ) ] Δ P P Δ n 0 n 0 ,
Δ l l = [ 1 + A Z 1 sin ( A Z ) cos ( A Z ) ] Δ P P Δ n 0 n 0 .
n 00 λ0 = N 0 ,     ν 01 = N 0 1 V 0 ( ω F ω C ) , n 10 λ0 = N r 0 N 0 r 0 2 , ν 11 = ( N r 0 1 ) / [ V r 0 ( ω F ω C ) ] ν 01 r 0 2 ,
n 10 λ0 = ( A n 00 λ0 ) / 2 , r 0 = { [ n λ ( r 0 ) n λ ( 0 ) ] / n 10 λ0 } 1 / 2 .
ψ 1 = v 11 n 10 λ0 v 01 n 00 λ0 = 0.7825 , Δ P P = 1 2 ψ 1 ( ω F ω C ) = 0.0708.
ψ 1 ( model ) = ψ 1 , K T1 + ψ 1 , K Na, = ( ν 1 I , K T1 ν I λ0 , K T1 ν 01 n 00 λ0 ) + ( ν 1 I , K Na ν I λ0 , K Na ν 01 n 00 λ0 ) , = 0.3857153 + 0.0135403 , = 0.372175.
ψ 1 = 0.0213 , Δ P / P = 0.0019 , Δ l = 0.1749  mm, L c h C = 0.1772  mm,
ψ 1 ( model ) = ψ 1 ,K Cs + ψ 1 ,K Na = 0.004857 + 0.0045368 , = 0.0093938 , Δ P / P ( model ) = 0.0008495.
ψ 1 = ν 1 I n I λ0 ν 01 n 00λ0 = 1.8 × 10 3 , Δ P / P = 0.5 ψ 1 ( ω F ω C ) = 1.628 × 10 4 .
A = c 0 + c 1 λ 2 + c 2 λ 4 , n λ = b 0 + b 1 λ 2 ,
n λ ( r , ω λ ) = n 0 ( ω λ ) + n 1 ( ω λ ) r 2 = ( n 00 λ0 + ν 01 ω λ + ν 02 ω λ 2 ) + ( n 10 λ0 + ν 11 ω λ + ν 12 ω λ 2 ) r 2 .

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