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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 849–857

Extended Nijboer–Zernike approach for the computation of optical point-spread functions

Augustus J. E. M. Janssen  »View Author Affiliations

JOSA A, Vol. 19, Issue 5, pp. 849-857 (2002)

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New Bessel-series representations for the calculation of the diffraction integral are presented yielding the point-spread function of the optical system, as occurs in the Nijboer–Zernike theory of aberrations. In this analysis one can allow an arbitrary aberration and a defocus part. The representations are presented in full detail for the cases of coma and astigmatism. The analysis leads to stably converging results in the case of large aberration or defocus values, while the applicability of the original Nijboer–Zernike theory is limited mainly to wave-front deviations well below the value of one wavelength. Because of its intrinsic speed, the analysis is well suited to supplement or to replace numerical calculations that are currently used in the fields of (scanning) microscopy, lithography, and astronomy. In a companion paper [J. Opt. Soc. Am. A 19, 860 (2002)], physical interpretations and applications in a lithographic context are presented, a convergence analysis is given, and a comparison is made with results obtained by using a numerical package.

© 2002 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(070.2580) Fourier optics and signal processing : Paraxial wave optics

Original Manuscript: May 24, 2001
Revised Manuscript: October 1, 2001
Manuscript Accepted: October 2, 2001
Published: May 1, 2002

Augustus J. E. M. Janssen, "Extended Nijboer–Zernike approach for the computation of optical point-spread functions," J. Opt. Soc. Am. A 19, 849-857 (2002)

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