Abstract

In this study we show that with minor modifications it is possible to adapt an existing optical design program to trace finite rays through a system containing Fresnel surfaces. Practical examples are given to illustrate the validity of our rather simple approach to this problem.

© 1983 Optical Society of America

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References

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  1. J. L. Chen, Appl. Opt. 22, 560 (1983).
    [CrossRef] [PubMed]
  2. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

1983 (1)

Chen, J. L.

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

Appl. Opt. (1)

Other (1)

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

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Figures (2)

Fig. 1
Fig. 1

Profile of a typical Fresnel lens.

Fig. 2
Fig. 2

Passage of a ray through a Fresnel lens.

Equations (9)

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1 l + 1 l = 1 f ,
sin ( θ + α ) = μ sin ( α i 3 ) .
sin θ cos α + cos θ sin α = μ sin α cos i 3 μ cos α sin i 3 .
tan α = sin [ tan 1 ( ρ / l ) ] + sin θ μ cos ( sin 1 { sin [ tan 1 ( ρ / l ) ] μ } ) cos θ .
Δ z Δ ρ = c ρ .
c = sin [ tan 1 ( ρ / l ) ] + sin θ ρ [ μ cos ( sin 1 { sin [ tan 1 ( ρ / l ) ] μ } ) cos θ ] .
c = sin [ tan 1 ( ρ / f ) ] ρ [ μ cos ( sin 1 { sin [ tan 1 ( ρ / f ) ] μ } ) 1 ] .
f x = c x / H , f y = c y / H , f z = [ 1 c ( 1 + Q ) ] / H , H = ( f x 2 + f y 2 + f z 2 ) 1 / 2 ,
f x = c x / ( 1 + c 2 ρ 2 ) , f y = c x / ( 1 + c 2 ρ 2 ) , f z = 1 / ( 1 + c 2 ρ 2 ) ,

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