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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 10 — Oct. 1, 2013
  • pp: 2150–2161

Balanced diffraction aberrations, independent of the observation point: application to a tilted dielectric plate

Colin J. R. Sheppard  »View Author Affiliations

JOSA A, Vol. 30, Issue 10, pp. 2150-2161 (2013)

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Balancing of Zernike aberrations breaks down if the defocus term is large enough that the condition (z/λ)2/[π(NA)4] is not satisfied. A modified Zernike aberration expansion, based on the Zernike aberrations, is developed that accurately includes axial displacement as a low-order term, even for large displacements. This expansion can be used to analyze aberrations for on-axis illumination of a high numerical aperture system. But more importantly, for systems of moderate numerical aperture it allows balanced aberration coefficients to be determined independent of the assumption of a particular reference point. The approach is applied to the case of a tilted dielectric plate. An exact expression is given for the wave front aberration, valid for both large angles of tilt and high beam convergence angles, that is independent of observation distance. Analytical expressions for the third- and fifth-order aberration coefficients are derived. Expressions are given for expansion of multiple-angle power series terms into Zernike polynomials.

© 2013 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

Original Manuscript: June 13, 2013
Revised Manuscript: August 30, 2013
Manuscript Accepted: August 30, 2013
Published: September 30, 2013

Colin J. R. Sheppard, "Balanced diffraction aberrations, independent of the observation point: application to a tilted dielectric plate," J. Opt. Soc. Am. A 30, 2150-2161 (2013)

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