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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 7 — Jul. 1, 1994
  • pp: 1993–2003

Symmetry properties of aberrated point-spread functions

Virendra N. Mahajan  »View Author Affiliations

JOSA A, Vol. 11, Issue 7, pp. 1993-2003 (1994)

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The symmetry properties of point-spread functions of optical imaging systems with circular pupils aberrated by a Zernike-circle polynomial aberration were discussed by Nijboer [ “ The diffraction theory of aberrations,” Ph.D. dissertation ( University of Groningen, Groningen, The Netherlands, 1942)]. Although it was not pointed out by him, his analysis and some of his results are valid only for systems with large Fresnel numbers. The symmetry properties for systems with small and large Fresnel numbers are discussed. The analysis is extended to systems with annular pupils aberrated by a Zernike-annular polynomial aberration. This analysis is further extended to pupils with nonuniform but radially symmetric illumination such as Gaussian. It is shown, in particular, that whereas, for uniform pupils, the axial irradiance of the imaging-forming light cone for a primary spherical aberration is symmetric about the defocused point with respect to which the aberration variance is minimum, it is asymmetric for nonuniform pupils. The discussion is equally valid for focused beams of light. Computer-generated pictures of point-spread functions of systems with circular and annular pupils aberrated by primary aberrations illustrating their symmetry properties are given.

© 1994 Optical Society of America

Original Manuscript: September 17, 1993
Revised Manuscript: December 16, 1993
Manuscript Accepted: January 11, 1994
Published: July 1, 1994

Virendra N. Mahajan, "Symmetry properties of aberrated point-spread functions," J. Opt. Soc. Am. A 11, 1993-2003 (1994)

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  1. B. R. A. Nijboer, “The diffraction theory of aberrations,” Ph.D. dissertation (University of Groningen, Groningen, The Netherlands, 1942), pp. 44–51.
  2. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1986), Section 9.4.
  3. V. N. Mahajan, “Strehl ratio for primary aberrations: some analytical results for circular and annular pupils,” J. Opt. Soc. Am. 72, 1258–1266 (1982);errata, J. Opt. Soc. Am. A 10, 2092 (1993). [CrossRef]
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  5. K. Nienhuis, “On the influence of diffraction on image formation in the presence of aberrations,” Ph.D. dissertation (University of Groningen, The Netherlands, 1948);some discussion is also given in K. Nienhuis, B. R. A. Nijboer, “The diffraction theory of optical aberrations, Part II,” Physica (Utrecht) 14, 590–608 (1949). [CrossRef]
  6. R. Kingslake, “The diffraction structure of the elementary coma image,” Proc. Phys. Soc. London 61, 147–158 (1948). [CrossRef]
  7. E. Collett, E. Wolf, “Symmetry properties of focused fields,” Opt. Lett. 5, 264–266 (1980). [CrossRef] [PubMed]
  8. E. Wolf, “Phase conjugacy and symmetries in spatially band-limited wavefields containing no evanescent components,” J. Opt. Soc. Am. 70, 1311–1319 (1980). [CrossRef]
  9. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71, 75–85 (1981); errata 1408;J. Opt. Soc. Am. A 1, 685 (1984). [CrossRef]
  10. V. N. Mahajan, “Uniform versus Gaussian beams: a comparison of the effects of diffraction, obscuration, and aberrations,” J. Opt. Soc. Am. A 3, 470–485 (1986). [CrossRef]
  11. V. N. Mahajan, “Axial irradiance and optimum focusing of laser beams,” Appl. Opt. 22, 3042–3053 (1983). [CrossRef] [PubMed]

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