How phase and amplitude aberrations destabilize the phase singularities in the focal field of a lens

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 15, Issue 11, 1998, Pages 2862-2868

  Karman, G P ^a   Woerdman, J P ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001001596     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.15.002862     Document Type: Article

References (11)

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3. M. Born and E. Wolf, Principles of Optics, 6th ed. (Perga-mon, Oxford, UK, 1986), Subsec. 8.8.
4. J. F. Nye, “Unfolding of higher-order wave dislocations” J. Opt. Soc. Am. A 15, 1132–1138 (1998).
5. G. P. Karman, A. van Duijl, and J. P. Woerdman, “Unfolding of an unstable singularity point into a ring” Opt. Lett. 23, 403–405 (1998).
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7. M. V. Berry, “Wave dislocation reactions in nonparaxial Gaussian beams” J. Mod. Opt. 45 (to be published).
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10. E. Wolf and Y. Li, “Conditions for the validity of the Debye integral representation of focused fields” Opt. Commun. 39, 205–210 (1981).
11. Exact expressions for the roots of a polynomial of degree four exist, but they are involved. See, for instance, M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1970), p. 17.