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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 × 10<sup>5</sup> 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

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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References

  1. N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Asymptotic methods for evaluation of diffractive lenses,” J. Pure Appl. Opt. 1, 552–559 (1999).
  2. N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
  3. J. J. Stamnes, B. Spjelkavik, and H. M. Pedersen, “Evaluation of diffraction integrals using local phase and amplitude approximations,” Opt. Acta 30, 207–222 (1983).
  4. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, UK, 1986), Sec. 7.2.
  5. P. Vahimaa, V. Kettunen, M. Kuittinen, J. Turunen, and A. T. Friberg, “Electromagnetic analysis of nonparaxial Bessel beams generated by diffractive axicons,” J. Opt. Soc. Am. A 14, 1817–1824 (1997).

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