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

Augustus J. E. M. Janssen
2002 Optical Society of America. Journal A: Optics, Image Science, and Vision  
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
more » ... e 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.
doi:10.1364/josaa.19.000849 pmid:11999961 fatcat:foajodtq5vdirj3eh5jlzg64ue