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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 16 — Jun. 1, 2000
  • pp: 2539–2544

Diffracted-ray approach to the fast evaluation of diffractive lenses

Nickolai Sergienko and Jakob J. Stamnes  »View Author Affiliations


Applied Optics, Vol. 39, Issue 16, pp. 2539-2544 (2000)
http://dx.doi.org/10.1364/AO.39.002539


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Abstract

We employ a combination of asymptotic methods to speed up the computation of fields in the focal region of a diffractive lens (DL). The DL is treated locally as a linear grating with a slowly varying period and groove orientation. We employ rigorous electromagnetic diffraction theory locally to obtain the field just behind the DL. A simple diffracted-ray formula is derived for the field in the focal region of the DL at observation points that are not in the immediate vicinity of the optical axis. A careful study of the range of validity of this formula is made. For observation points that are not in the immediate vicinity of the optical axis the new algorithm is 3 × 105 times faster than the application of numerical integration to the double integrals involved and approximately 1000–1200 times faster than a recently published algorithm based on using asymptotic theory to replace the double integral with a single integral.

© 2000 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics

History
Original Manuscript: August 26, 1999
Revised Manuscript: January 24, 2000
Published: June 1, 2000

Citation
Nickolai Sergienko and Jakob J. Stamnes, "Diffracted-ray approach to the fast evaluation of diffractive lenses," Appl. Opt. 39, 2539-2544 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-16-2539

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