Abstract

In this paper we report studies on imaging through a defocusing gradient-index rod. We have obtained analytic expressions for the third-order aberration of this system and compared it with the total aberration obtained by numerical ray tracing. Our studies show that the rod length can be critically optimized for low aberrations depending on the numerical aperture requirement. Further, a value of the fourth-order grading parameter exists for which the aberration can be reduced to a minimum for fixed values of other parameters.

© 1983 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. D. Forer, S. N. Houde-Walter, J. J. Miceli, D. T. Moore, M. J. Nadeau, D. P. Ryan, J. M. Stagaman, N. J. Sullo, Appl. Opt. 22, 407 (1983).
    [CrossRef] [PubMed]
  2. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, Appl. Opt. 21, 3456 (1982).
    [CrossRef] [PubMed]
  3. K. Thyagarajan, A. Rohra, A. K. Ghatak, Appl. Opt. 19, 1061 (1980).
    [CrossRef] [PubMed]
  4. M. Kawazu, Y. Ogura, Appl. Opt. 19, 1105 (1980).
    [CrossRef] [PubMed]
  5. W. J. Tomlinson, Appl. Opt. 19, 1127 (1980).
    [CrossRef] [PubMed]
  6. Y. Ohtsuka, K. Maeda, Appl. Opt. 20, 3562 (1981).
    [CrossRef] [PubMed]
  7. K. Thyagarajan, A. K. Ghatak, Optik 44, 329 (1976).
  8. A. Gupta, K. Thyagarajan, I. C. Goyal, A. K. Ghatak, J. Opt. Soc. Am. 66, 1320 (1976).
    [CrossRef]
  9. See, e.g., A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).
  10. We have given these equations here for the sake of completeness; a detailed discussion of the derivation of third-order aberration coefficients using this approach can be found in Ref. 9 or in R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1964).
  11. Since the system is rotationally symmetric we assume y0 = 0 without any loss of generality.
  12. Since the direction cosines of the ray at the object plane are given by (dx/ds)z=0 = sinγ cosψ, (dy/ds)z=0 = sinγ sinψ, and (dz/ds)z=0 = cosγ, where γ is the angle which the ray makes with the z axis and ψ is the angle which the projection of the ray on the x-y plane makes with the x axis, meridional rays correspond to ψ = 0 and skew rays correspond to ψ = π/2.
  13. We have considered rays launched within γ = ±10°.

1983 (1)

1982 (1)

1981 (1)

1980 (3)

1976 (2)

Banno, J.

Forer, J. D.

Ghatak, A. K.

K. Thyagarajan, A. Rohra, A. K. Ghatak, Appl. Opt. 19, 1061 (1980).
[CrossRef] [PubMed]

K. Thyagarajan, A. K. Ghatak, Optik 44, 329 (1976).

A. Gupta, K. Thyagarajan, I. C. Goyal, A. K. Ghatak, J. Opt. Soc. Am. 66, 1320 (1976).
[CrossRef]

See, e.g., A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).

Goyal, I. C.

Gupta, A.

Houde-Walter, S. N.

Iga, K.

Kawazu, M.

Kokubun, Y.

Luneburg, R. K.

We have given these equations here for the sake of completeness; a detailed discussion of the derivation of third-order aberration coefficients using this approach can be found in Ref. 9 or in R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1964).

Maeda, K.

Miceli, J. J.

Misawa, S.

Moore, D. T.

Nadeau, M. J.

Ogura, Y.

Ohtsuka, Y.

Oikawa, M.

Rohra, A.

Ryan, D. P.

Stagaman, J. M.

Sullo, N. J.

Thyagarajan, K.

K. Thyagarajan, A. Rohra, A. K. Ghatak, Appl. Opt. 19, 1061 (1980).
[CrossRef] [PubMed]

K. Thyagarajan, A. K. Ghatak, Optik 44, 329 (1976).

A. Gupta, K. Thyagarajan, I. C. Goyal, A. K. Ghatak, J. Opt. Soc. Am. 66, 1320 (1976).
[CrossRef]

See, e.g., A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).

Tomlinson, W. J.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Optik (1)

K. Thyagarajan, A. K. Ghatak, Optik 44, 329 (1976).

Other (5)

See, e.g., A. K. Ghatak, K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).

We have given these equations here for the sake of completeness; a detailed discussion of the derivation of third-order aberration coefficients using this approach can be found in Ref. 9 or in R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1964).

Since the system is rotationally symmetric we assume y0 = 0 without any loss of generality.

Since the direction cosines of the ray at the object plane are given by (dx/ds)z=0 = sinγ cosψ, (dy/ds)z=0 = sinγ sinψ, and (dz/ds)z=0 = cosγ, where γ is the angle which the ray makes with the z axis and ψ is the angle which the projection of the ray on the x-y plane makes with the x axis, meridional rays correspond to ψ = 0 and skew rays correspond to ψ = π/2.

We have considered rays launched within γ = ±10°.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics