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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 12 — Dec. 1, 2010
  • pp: 2563–2573

Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration

Aleksey N. Simonov and Michiel C. Rombach  »View Author Affiliations

JOSA A, Vol. 27, Issue 12, pp. 2563-2573 (2010)

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Asymptotic expressions are derived for the two-dimensional incoherent optical transfer function (OTF) of an optical system with defocus and spherical aberration. The two-dimensional stationary phase method is used to evaluate the aberrated OTF at large and moderately large defocus and spherical aberration. For small aberrations, the OTF is approximated by a power series in the aberration coefficients. An accurate approximation (in elementary functions) to the OTF is obtained for a defocused optical system with a circular pupil. We experimentally demonstrate the validity of the OTF approximations in sharp-focus image restoration from two defocused images. A digital focusing method is presented.

© 2010 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(110.0110) Imaging systems : Imaging systems
(110.4850) Imaging systems : Optical transfer functions

ToC Category:
Imaging Systems

Original Manuscript: June 1, 2010
Revised Manuscript: October 9, 2010
Manuscript Accepted: October 9, 2010
Published: November 10, 2010

Aleksey N. Simonov and Michiel C. Rombach, "Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration," J. Opt. Soc. Am. A 27, 2563-2573 (2010)

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