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

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

Related Journal Articles

• Calculation of diffraction effects on the average phase of an optical field (JOSAA)
• Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions (JOSAA)
• Extended Nijboer–Zernike representation of the vector field in the focal region of an aberrated high-aperture optical system (JOSAA)
• Diffraction corrections in radiometry: spectral and total power and asymptotic properties (JOSAA)
• Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula (AO)

Related Conference Papers

• Noisy Grovers searching algorithm
• Noisy Grovers searching algorithm
• Information gain and entropy change in generalized quantum measurements
• Information gain and entropy change in generalized quantum measurements
• Additivity for some product channels
• Additivity for some product channels
• The use of orbital angular momentum of light beams for super-high density optical data storage
• Complex pupil function reconstruction at high NA using the extended Nijboer-Zernike diffraction theory