Abstract

The caustic surface, which is the locus of the sagittal and tangential focal points for general skew rays, is shown to be given by the Coddington equations for the special case of meridional rays reflected or refracted by a spherical surface.

© 1976 Optical Society of America

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References

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  1. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), pp. 95, 149.
  2. D. L. Shealy and D. G. Burkhard, Optica Acta 22, 485 (1975).
    [Crossref]
  3. M. Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), p. 157.
  4. O. N. Stavroudis, Wavefront, Rays, and Caustics (Academic, New York, 1972), p. 157.
  5. D. L. Shealy and D. G. Burkhard, Optica Acta 20, 287 (1973).
    [Crossref]
  6. D. L. Shealy, “Analytical Illuminance and Caustic Surface Calculations in Geometrical Optics,” International Lens Design Conference, June 23–27, 1975, Haverford, PA.

1975 (1)

D. L. Shealy and D. G. Burkhard, Optica Acta 22, 485 (1975).
[Crossref]

1973 (1)

D. L. Shealy and D. G. Burkhard, Optica Acta 20, 287 (1973).
[Crossref]

Burkhard, D. G.

D. L. Shealy and D. G. Burkhard, Optica Acta 22, 485 (1975).
[Crossref]

D. L. Shealy and D. G. Burkhard, Optica Acta 20, 287 (1973).
[Crossref]

Herzberger, M.

M. Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), p. 157.

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), pp. 95, 149.

Shealy, D. L.

D. L. Shealy and D. G. Burkhard, Optica Acta 22, 485 (1975).
[Crossref]

D. L. Shealy and D. G. Burkhard, Optica Acta 20, 287 (1973).
[Crossref]

D. L. Shealy, “Analytical Illuminance and Caustic Surface Calculations in Geometrical Optics,” International Lens Design Conference, June 23–27, 1975, Haverford, PA.

Stavroudis, O. N.

O. N. Stavroudis, Wavefront, Rays, and Caustics (Academic, New York, 1972), p. 157.

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), pp. 95, 149.

Optica Acta (2)

D. L. Shealy and D. G. Burkhard, Optica Acta 22, 485 (1975).
[Crossref]

D. L. Shealy and D. G. Burkhard, Optica Acta 20, 287 (1973).
[Crossref]

Other (4)

D. L. Shealy, “Analytical Illuminance and Caustic Surface Calculations in Geometrical Optics,” International Lens Design Conference, June 23–27, 1975, Haverford, PA.

M. Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), p. 157.

O. N. Stavroudis, Wavefront, Rays, and Caustics (Academic, New York, 1972), p. 157.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), pp. 95, 149.

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Figures (1)

FIG. 1
FIG. 1

Point-source light reflected from or refracted by a spherical surface.

Equations (14)

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X = x ( i ) + r A ( i ) ,
I 0 ( i ) + r c I 1 ( i ) + r c 2 I 2 ( i ) = 0 ,
I 0 ( i ) = A ( i ) · x u i × x v i ,
I 1 ( i ) = A ( i ) · [ x u l × A v l ( i ) + A u l ( i ) × x v l ] ,
I 2 ( i ) = A ( i ) · A u i ( i ) × A v i ( i ) .
x c ( u i , v i ) = x ( u i , v i ) + r c ( u i , v i ) A ( u i , v i ) ,
r c = R r 1 { - R 2 + 3 R R 0 cos ξ + R 0 2 [ 1 - ( 1 + cos 2 ξ ) ± sin 2 ξ ] } - R 3 + 5 R 2 R 0 cos ξ - 2 ( 1 + 3 cos 2 ξ ) R R 0 2 + 4 R 0 3 cos ξ ,
r 1 = ( R 2 + R 0 2 - 2 R R 0 cos ξ ) 1 / 2 , cos ξ = sin θ sin θ 0 cos ( ϕ - ϕ 0 ) + cos θ cos θ 0 , cos ϕ i = ( R 0 cos ξ - R ) / r 1 .
1 r 1 + 1 r c ( + ) = - 2 R cos ϕ i ,
1 r 1 + 1 r c ( - ) = - 2 cos ϕ i R ,
r c = R r 1 { - [ r 1 Ω ( 1 + cos 2 ϕ s ) + R ( n 0 / n 1 ) ( cos 2 ϕ i + cos 2 ϕ s ) ] ± [ r 1 Ω sin 2 ϕ s + R ( n 0 / n 1 ) ( cos 2 ϕ i - cos 2 ϕ s ) ] } 2 [ r 1 2 Ω 2 + R r 1 Ω ( n 0 / n 1 ) ( 1 + cos 2 ϕ i ) + R 2 ( n 0 / n 1 ) 2 cos 2 ϕ i ] ,
Ω = ( n 0 / n 1 ) cos ϕ i + cos ϕ s , cos ϕ s = - [ 1 - ( n 0 / n 1 ) 2 sin 2 ϕ i ] 1 / 2 .
n 0 cos 2 ϕ i r 1 + n 1 cos 2 ϕ s r c ( + ) = - ( n 1 cos ϕ s + n 0 cos ϕ i ) R ,
n 0 r 1 + n 1 r c ( - ) = - ( n 1 cos ϕ s + n 0 cos ϕ i ) R ,