OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 3, Iss. 4 — Apr. 1, 1986
  • pp: 508–522

Gabor representation and aperture theory

P. D. Einziger, S. Raz, and M. Shapira  »View Author Affiliations


JOSA A, Vol. 3, Issue 4, pp. 508-522 (1986)
http://dx.doi.org/10.1364/JOSAA.3.000508


View Full Text Article

Enhanced HTML    Acrobat PDF (1576 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The analytical properties and computational implications of the Gabor representation are investigated within the context of aperture theory. The radiation field in the pertinent half-space is represented by a discrete set of linearly shifted and spatially rotated elementary beams that fall into two distinct categories, the propagating (characterized by real rotation angles) and evanescent beams. The representation may be considered a generalization in the sense that both the classical plane wave and Kirchhoff’s spatial-convolution forms are directly recoverable as limiting cases. The choice of a specific window function [w(x)] and the corresponding characteristic width (L) are, expectedly, cardinal decisions affecting the analytical complexity and the convergence rate of the Gabor series. The significant spectral compression achievable by an appropriate selection of w(x) and L is demonstrated numerically, and simple selection guidelines are derived. Two specific window functions possessing opposite characteristics are considered, the uniformly pulsed and the Gaussian distributions. These are studied analytically and numerically, highlighting several outstanding advantages of the latter. Consequently, the primary attention is focused on Gaussian elementary beams in their paraxial and their far-field estimates. Although the main effort is devoted to aperture analysis, demonstrating the advantages and limitations of the proposed approach, reference is also made to its potential when applied to aperture-synthesis and spatial-filtering problems. The quantitative effects of basic filtering in the discrete Gabor space are depicted.

© 1986 Optical Society of America

History
Original Manuscript: January 28, 1985
Manuscript Accepted: August 12, 1985
Published: April 1, 1986

Citation
P. D. Einziger, S. Raz, and M. Shapira, "Gabor representation and aperture theory," J. Opt. Soc. Am. A 3, 508-522 (1986)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-3-4-508


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Gabor, “Theory of communication,”J. Inst. Elec. Eng. (London) 93III, 429–457 (1946).
  2. M. J. Bastiaans, “Gabor’s expansion of a signal into Gaussian elementary signals,” Proc. IEEE 68, 538–539 (1980). [CrossRef]
  3. M. J. Bastiaans, “Sampling theorem for the complex spectrogram, and Gabor’s expansion of a signal in Gaussian elementary signals,” Soc. Photo-Opt. Instrum. Eng. International Opt. Comput. Conf. 231, 274–279 (1980).
  4. M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” Optik 57, 95–101 (1980).
  5. A. J. E. M. Janssen, “Gabor representation of generalized functions,”J. Math. Anal. Appl. 83, 377–394 (1981). [CrossRef]
  6. G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971). [CrossRef]
  7. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, New York, 1966).
  8. P. D. Einziger, L. B. Felsen, “Evansecent waves and complex rays,”IEEE Trans. Antennas Propag. AP-30, 594–605 (1982). [CrossRef]
  9. A. Papoulis, The Fourier Integral and Its Application (McGraw-Hill, New York, 1962), p. 62.
  10. M. Abramovitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970), p. 590.
  11. N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Holt, New York, 1975).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. III.
  13. J. B. Keller, W. Streifer, “Complex ray with an application to Gaussian beams,”J. Opt. Soc. Am. 61, 40–43 (1971). [CrossRef]
  14. P. D. Einziger, Y. Haramaty, L. B. Felsen, “Radiation from planar aperture distributions by evanescent wave and complex ray analysis,” in Proceedings of the 13th Convention of IEEE in Israel (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 2.1.2.1–2.1.2.3.

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