Abstract

In this study based on an original program of aberration calculations and automated optical lens design we try to increase ray tracing of a Fresnel system so that the original program not only contains the initial functions but also satisfies the calculations of a Fresnel or mixed system (both general and Fresnel lenses).

© 1983 Optical Society of America

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References

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  1. E. Delano, J. Opt. Soc. Am. 64, 459 (1974).
    [CrossRef]
  2. E. Delano, J. Opt. Soc. Am. 66, 1317 (1976).
    [CrossRef]
  3. E. Delano, J. Opt. Soc. Am. 68, 1306 (1978).
    [CrossRef]
  4. E. Delano, Appl. Opt. 18, 4187 (1979).
    [CrossRef] [PubMed]

1979 (1)

1978 (1)

1976 (1)

1974 (1)

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Figures (3)

Fig. 1
Fig. 1

Flat Fresnel surface.

Fig. 2
Fig. 2

Curved Fresnel surface.

Fig. 3
Fig. 3

Incident ray of the Fresnel surface.

Equations (8)

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Z = C S 2 1 + 1 C 2 S 2 + a 4 S 4 + a 6 S 6 + a 8 S 8 + a 10 S 10 ·
x F = x 0 + L N ( d z 0 ) , y F = y 0 + M N ( d z 0 ) , z F = 0.
F = C 0 ( x F 2 + y F 2 ) , G = N C 0 ( L x F + M y F ) , cos I = G 2 C 0 F , Δ = F / ( G + cos I ) , x 2 = x F + L Δ , y 2 = y F + M Δ , z 2 = N Δ ,
Z 2 = C S 1 + 1 + 1 C 2 S 2 + a 4 S 4 + a 6 S 6 + a 8 S 8 + a 10 S 10 ,
F ( z , y , z ) = Z C S 2 1 + 1 C 2 s 2 a 4 S 4 a 6 S 6 a 8 S 8 a 10 S 10 ·
F z = 1 , F y = y ( c 1 C 2 S 2 + 4 a 4 S 2 + 6 a 6 S 4 + 8 a 8 S 6 + 10 a 10 S 8 ) , F x = x ( c 1 C 2 S 2 + 4 a 4 S 2 + 6 a 6 S 4 + 8 a 8 S 6 + 10 a 10 S 8 ) ,
α = F x / T , β = F y / T , γ = F z / T , T = ( F x ) 2 + ( F y ) 2 + ( F z ) 2 ·
cos i = α L + β M + γ N , cos i = 1 ( n n ) 2 ( 1 cos 2 I ) , g = n C 0 n I n C 0 n I , L = 1 n ( n L + g α ) , M = 1 n ( n M + g β ) , N = 1 n ( n M + g γ ) ,

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