Abstract

A general ray tracing algorithm for gradient-index media that treats various refractive index distributions in a unified manner has been developed by implementing the concept of isoindicial surfaces, position variables, and cubic splines. A novel and simpler algorithm for optical path length calculations is also presented.

© 1990 Optical Society of America

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References

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  1. A. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing Rays Through Graded-Index Media: a New Method,” Appl. Opt. 21, 984–987 (1982).
    [CrossRef] [PubMed]
  2. P. J. Sands, “Classification Scheme and Nomenclature for Refractive-Index Distributions,” Appl. Opt. 22, 430–431 (1983).
    [CrossRef] [PubMed]
  3. C. F. Gerald, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1980), pp. 474–482.
  4. S. Dorić, “Paraxial Ray Trace for Rotationally Symmetric Homogeneous and Inhomogeneous Media,” J. Opt. Soc. Am. A 1, 818–821 (1984).
    [CrossRef]
  5. A. Sharma, A. K. Ghatak, “Raytracing in Gradient Index Lenses,” in Technical Digest, Sixth Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985).
  6. M. P. Rimmer, “Ray Tracing in Inhomogeneous Media,” in Technical Digest, SPIE International Technical Conference, Geneva, Switzerland (1983).

1984 (1)

1983 (1)

1982 (1)

Doric, S.

Gerald, C. F.

C. F. Gerald, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1980), pp. 474–482.

Ghatak, A. K.

A. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing Rays Through Graded-Index Media: a New Method,” Appl. Opt. 21, 984–987 (1982).
[CrossRef] [PubMed]

A. Sharma, A. K. Ghatak, “Raytracing in Gradient Index Lenses,” in Technical Digest, Sixth Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985).

Kumar, D. V.

Rimmer, M. P.

M. P. Rimmer, “Ray Tracing in Inhomogeneous Media,” in Technical Digest, SPIE International Technical Conference, Geneva, Switzerland (1983).

Sands, P. J.

Sharma, A.

A. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing Rays Through Graded-Index Media: a New Method,” Appl. Opt. 21, 984–987 (1982).
[CrossRef] [PubMed]

A. Sharma, A. K. Ghatak, “Raytracing in Gradient Index Lenses,” in Technical Digest, Sixth Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985).

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Other (3)

A. Sharma, A. K. Ghatak, “Raytracing in Gradient Index Lenses,” in Technical Digest, Sixth Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985).

M. P. Rimmer, “Ray Tracing in Inhomogeneous Media,” in Technical Digest, SPIE International Technical Conference, Geneva, Switzerland (1983).

C. F. Gerald, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1980), pp. 474–482.

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Tables (1)

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Table I Typical Generic Distributions of Refractive Index

Equations (7)

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n d d s ( n d r d s ) = n n
d 2 r d t 2 = n n ,
n = ( n x , n y , n z )
n x = n p p x , n y = n p p y , n z = n p p z .
d 2 x d t 2 = n ( p ) n ( p ) p x , d 2 y d t 2 = n ( p ) n ( p ) p y , d 2 z d t 2 = n ( p ) n ( p ) p z .
n 2 = p · p + q · q + l · l .
OPL = i ( p i · p i + q i · q i + l i · l i ) Δ t i ,

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