OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 48, Iss. 9 — Sep. 1, 1958
  • pp: 643–645

On the Axial Phase Anomaly for Microwave Lenses

G. W. FARNELL  »View Author Affiliations

JOSA, Vol. 48, Issue 9, pp. 643-645 (1958)

View Full Text Article

Acrobat PDF (506 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The behavior of the phase along the axis of aberration-free microwave lenses is shown by curves of the axial phase anomaly calculated from scalar Kirchhoff diffraction theory. These curves are drawn for three different wavelengths and two typical focal lengths. Also illustrated in the calculated results are the errors introduced by the use of certain geometrical approximations commonly employed in light optics.

Detailed experimental measurements have been made of the electric field along the axis in the point-source image produced by solid dielectric lenses at a wavelength of 3.2 cm. Despite the limited size of the exit pupil (radius approximately 8 wavelengths) the agreement between the measured values of the axial phase anomaly and those calculated from scalar theory is very good except within about one lens radius of the lens surface.

G. W. FARNELL, "On the Axial Phase Anomaly for Microwave Lenses," J. Opt. Soc. Am. 48, 643-645 (1958)

Sort:  Author  |  Journal  |  Reset


  1. L. G. Gouy, Comp. rend. acad. sci., Paris 110, 1251 (1890); ibid, Ann. chim. et phys. 24, 145 (1891).
  2. F. Reiche, Ann. Physik 29, 65 and 401 (1909).
  3. H. W. Breuniger, Ann. phys. 35, 228 (1939).
  4. E. H. Linfoot and E. Wolf, Proc. Phys. Soc. (London) A69, 823 (1956).
  5. P. Zeeman, Z. Physik 1, 542 (1899–1900).
  6. G. Sagnac, J. Phys. (Theoret. Inst.) 2, 721 (1903).
  7. G. Bekefi, Final Report to Air Force Cambridge Research Center on Contract AF19(122)-81, Eaton Laboratory, McGill University, ASTIA Doc. No. AD110152, 1957.
  8. T. J. F. Pavlasek, Ph.D. thesis, McGill University, 1958.
  9. M. P. Bachynski and G. Bekefi, J. Opt. Soc. Am. 47, 428 (1957).
  10. M. P. Bachynski and G. Bekefi, I.R.E. Trans. P.G.A.P., AP-4, 412 (1956).
  11. B. B. Baker and E. T. Copson, Mathematical Theory of Huygens Principle (Clarendon Press, Oxford, 1950), p. 74.
  12. A. Rubinowicz, Ann. Physik 53, 257 (1917); ibid, Phys. Rev. 54, 931 (1938).
  13. C. J. Bouwkamp, Physica 7, (1940), 485.
  14. F. Zernike and B. R. N. Nijboer, Contribution to "Theorie des Image Optiques," Rev. opt., (1949).
  15. E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, 1955), p. 35.
  16. E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).
  17. P. Debye, Ann. Physik (4) 30, 755 (1909).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited