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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 5 — May. 1, 2008
  • pp: 1051–1063

Analytical optimal solution of the extension of the depth of field using cubic-phase wavefront coding. Part I. Reduced-complexity approximate representation of the modulation transfer function

Saeed Bagheri, Paulo E.X. Silveira, and Daniela Pucci de Farias  »View Author Affiliations


JOSA A, Vol. 25, Issue 5, pp. 1051-1063 (2008)
http://dx.doi.org/10.1364/JOSAA.25.001051


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Abstract

In this paper we derive an approximate analytical representation for the modulation transfer function (MTF) of an imaging system possessing a defocused cubic-phase pupil function. This expression is based on an approximation using the Arctan function and significantly reduces the computational time required to calculate the resulting MTF. We derive rigorous bounds on the minimum and average accuracy of our approximation. Using this approximate representation of the MTF, the analytical solution of the problem of calculating the extension of the depth of field for a circular aperture with a cubic phase mask becomes possible. We also comment on how one can modify our method to construct a lower-bound or an upper-bound approximate analytical expression for the MTF.

© 2008 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(080.3620) Geometric optics : Lens system design
(110.4100) Imaging systems : Modulation transfer function

ToC Category:
Imaging Systems

History
Original Manuscript: September 26, 2007
Revised Manuscript: January 27, 2008
Manuscript Accepted: January 31, 2008
Published: April 17, 2008

Citation
Saeed Bagheri, Paulo E. X. Silveira, and Daniela Pucci de Farias, "Analytical optimal solution of the extension of the depth of field using cubic-phase wavefront coding. Part I. Reduced-complexity approximate representation of the modulation transfer function," J. Opt. Soc. Am. A 25, 1051-1063 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-5-1051

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