Journal ArticleDOI
Extended Nijboer-Zernike approach for the computation of optical point-spread functions
TLDR
In this article, 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.Abstract:
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.read more
Citations
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Journal ArticleDOI
Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions
TL;DR: These new series representations of diffraction integrals yield a flexible means to compute optical point-spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases of practical interest.
Journal ArticleDOI
Extended Nijboer–Zernike representation of the vector field in the focal region of an aberrated high-aperture optical system
TL;DR: In this article, the authors present expressions for the electric field components in the focal region in the case of a high-numerical-aperture optical system, where the transmission function, the aberrations, and the spatially varying state of polarization of the wave exiting the optical system are represented in terms of a Zernike polynomial expansion over the exit pupil of the system.
Book ChapterDOI
Assessment of optical systems by means of point-spread functions
TL;DR: In this paper, the authors presented the computation of the point-spread function of optical imaging systems and the characterization of these systems by means of the measured three-dimensional structure of the PFF, which is a nonlinear function of the basic electromagnetic field components in the focal region.
Journal ArticleDOI
Extracting density–density correlations from in situ images of atomic quantum gases
TL;DR: In this article, the static structure factor of a 2D quantum gas was derived from in situ imaging using a complete recipe to extract the density-density correlations and the static structural factor.
Journal ArticleDOI
On the computation of the Nijboer-Zernike aberration integrals at arbitrary defocus
TL;DR: In this article, the authors present a new computation scheme for the integral expressions describing the contributions of single aberrations to the diffraction integral in the context of an extended Nijboer-Zernike approach.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Principles of Optics
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Principles of Optics
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Journal ArticleDOI
Zernike polynomials and atmospheric turbulence
TL;DR: In this paper, a Zernike representation of the Kolmogoroff spectrum of turbulence is given that provides a complete analytical description of the number of independent corrections required in a wave-front compensation system.
Journal ArticleDOI
Wave-front interpretation with Zernike polynomials
Jon Y. Wang,D. E. Silva +1 more
TL;DR: Contrary to the traditional understanding, the classical least-squares method of determining the Zernike coefficients from a sampled wave front with measurement noise has been found numerically stable.