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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 64, Iss. 6 — Jun. 1, 1974
  • pp: 850–856

Aberration expansion and evaluation of the quasi-gaussian beam by a set of orthogonal functions

Akira Arimoto  »View Author Affiliations


JOSA, Vol. 64, Issue 6, pp. 850-856 (1974)
http://dx.doi.org/10.1364/JOSA.64.000850


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Abstract

A set of orthogonal functions, convenient for the aberration analysis of the quasi-gaussian beams such as the laser TEM00 mode is derived. It is a set of hypergeometric functions. We can expand the aberration function of a quasi-gaussian beam in terms of it, and can calculate the diffraction patterns of aberrations. This set of functions has some characteristics of orthogonality to each other and relations to the Bessel functions. It bears a resemblance to the Zernike’s circle polynomials, but has some different characteristics. It is useful in holography, optical communications, and optical measurement.

Citation
Akira Arimoto, "Aberration expansion and evaluation of the quasi-gaussian beam by a set of orthogonal functions," J. Opt. Soc. Am. 64, 850-856 (1974)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-64-6-850


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References

  1. H. Kogelnik, Bell Syst. Tech. J. 43, 334 (1964).
  2. T. S. Chu, Bell Syst. Tech. J. 45, 287 (1966).
  3. F. Zernike, Physica 1, 689 (1934).
  4. D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).
  5. G. Boyd and J. Gordon, Bell Syst. Tech. J. 40, 489 (1961).
  6. H. Statz and C. Tang, J. Appl. Phys. 36, 1816 (1965).
  7. G. Szerö, Orthogonal Polynomials (American Mathematical Society, Providence, R. I., 1939), p. 62.
  8. E. Linfoot, Recent Advances in Optics (Clarendon, Oxford, 1955), p. 48.
  9. B. Nijboer, Thesis (Groningen University, 1942).

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