## Fast nonparaxial scalar focal field calculations |

JOSA A, Vol. 31, Issue 6, pp. 1206-1214 (2014)

http://dx.doi.org/10.1364/JOSAA.31.001206

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### Abstract

An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first Rayleigh–Sommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately

© 2014 Optical Society of America

**OCIS Codes**

(050.1960) Diffraction and gratings : Diffraction theory

(110.2990) Imaging systems : Image formation theory

(220.2560) Optical design and fabrication : Propagating methods

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: February 18, 2014

Revised Manuscript: April 1, 2014

Manuscript Accepted: April 7, 2014

Published: May 12, 2014

**Citation**

Matthias Hillenbrand, Armin Hoffmann, Damien P. Kelly, and Stefan Sinzinger, "Fast nonparaxial scalar focal field calculations," J. Opt. Soc. Am. A **31**, 1206-1214 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-6-1206

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