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
Original Manuscript: August 26, 1999
Revised Manuscript: January 24, 2000
Published: June 1, 2000
Nickolai Sergienko and Jakob J. Stamnes, "Diffracted-ray approach to the fast evaluation of diffractive lenses," Appl. Opt. 39, 2539-2544 (2000)