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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1638–1640

Optimal apodizations for finite apertures

P. S. Carney and G. Gbur  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1638-1640 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001638


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Abstract

A method is presented for determining the aperture apodization functions needed to optimize any given product of powers of the even-order moments of the beam intensity in the near and far zones. The results are a generalization of previous work [Pure Appl. Opt. 7, 1221 (1998)] that dealt only with the far-zone moments. These methods are applied to the problem of optimizing the so-called beam propagation factor, MP2.

© 1999 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures

History
Original Manuscript: September 22, 1998
Revised Manuscript: February 8, 1999
Manuscript Accepted: February 8, 1999
Published: July 1, 1999

Citation
P. S. Carney and G. Gbur, "Optimal apodizations for finite apertures," J. Opt. Soc. Am. A 16, 1638-1640 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1638


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References

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  5. At the time this paper was written, A. E. Siegman maintained an extensive list of references on beam quality and characterization at the internet address http://www-ee.stanford.edu/~siegman/ .
  6. G. N. Lawrence, “Proposed international standard for laser-beam quality falls short,” Laser Focus World109–114 (July1994).
  7. R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995). [CrossRef]
  8. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964). See Sec. 50.
  9. G. Gbur, P. S. Carney, “Convergence criteria and optimization techniques for beam moments,” Pure Appl. Opt. 7, 1221–1230 (1998). [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996). See Secs. 4.2 and 4.3.
  11. Equation (9) reduces to the differential equation found in Ref. 9 when νl=0 for all l.
  12. N. N. Lebedev, Special Functions and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1965).
  13. C. Lanczos, The Variational Principles of Mechanics, 4th ed. (Dover, New York, 1986).

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