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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 9 — Sep. 1, 1980
  • pp: 1079–1084

Primary aberrations of thin planar surface lenses

Tomasz Jannson and Jacek Sochacki  »View Author Affiliations

JOSA, Vol. 70, Issue 9, pp. 1079-1084 (1980)

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By using the Rayleigh-Sommerfeld diffraction formula of the first kind for the two-dimensional case, the impulse response of a thin planar lens is given and the influence of primary aberrations is considered. Respective degrading factors are recognized and a two-dimensional diffraction theory of aberrations in the Seidel approximation is presented. The influence of the material parameters and the geometry of the thin planar lens on the respective aberrations is discussed. The authors show that in several cases, not only spherical aberration but also field curvature is of concern. The thin planar lens as an imaging system and as a Fourier transformer is considered and two apertures—rectangular and Gaussian—are compared.

© 1980 Optical Society of America

Tomasz Jannson and Jacek Sochacki, "Primary aberrations of thin planar surface lenses," J. Opt. Soc. Am. 70, 1079-1084 (1980)

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  1. G. C. Righini, V. Russo, S. Sottini, and G. Toraldo di Francia, "Geodesic Lenses for Guided Optical Waves," Appl. Opt. 12, 1477–1481 (1973).
  2. E. Spiller and J. S. Harper, "High Resolution Lenses for Optical Waveguides," Appl. Opt. 13, 2105–2108 (1974).
  3. C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).
  4. Van E. Wood, "Effect of edge-rounding on geodesic lenses," Appl. Opt. 15, 2817–2820 (1976).
  5. D. W. Vahey and V. E. Wood, "Focal Characteristics of Spheroidal Geodesic Lenses for Integrated Optical Processing," IEEE J. Quantum Electron. QE-13, 129–133 (1977).
  6. W. H. Southwell, "Inhomogeneous optical waveguide lens analysis," J. Opt. Soc. Am. 67, 1010–1014 (1977).
  7. W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1004–1009 (1977).
  8. D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical-Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–281 (1977).
  9. W. H. Southwell, "Geodesic optical waveguide lens analysis," J. Opt. Soc. Am. 67, 1293–1299 (1977).
  10. R. Shubert and J. H. Harris, "Optical guided-wave focusing and diffraction," J. Opt. Soc. Am. 61, 154–161 (1971).
  11. P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361–420 (1977).
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5, Sec. 3.
  13. See, for example, D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 8–9. Note that our case is slightly more general and leads to the one considered in Ref. 13, if β.r→ βz.
  14. The relation given in Ref. 10 is erroneous. This form is correct.
  15. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), Chaps. 5 and 9.
  16. The problem of field curvature for geodesic lenses was pointed out by G. C. Righini, V. Russo, and S. Sottini, "The family of perfect aspherical geodesic lenses for integrated optical circuits," IEEE J. Quantum Electron. QE-14, 1–3 (1978).
  17. J. R. Shewell and E. Wolf, "Inverse Diffraction and a New Reciprocity Theorem," J. Opt. Soc. Am. 58, 1596–1603 (1968).
  18. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 5, Sec. 4.

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