## Numerical solution of nonparaxial scalar diffraction integrals for focused fields |

JOSA A, Vol. 31, Issue 8, pp. 1832-1841 (2014)

http://dx.doi.org/10.1364/JOSAA.31.001832

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### Abstract

In this paper, we present sampling conditions for fast-Fourier-transform-based field propagations. The input field and the propagation kernel are analyzed in a combined manner to derive sampling criteria that guarantee accurate calculation results in the output plane. These sampling criteria are also applicable to the propagation of general fields. For focal field calculations, geometrical optics is used to obtain *a priori* knowledge about the input and output fields. This *a priori* knowledge is used to determine an optimum balance between computational load and calculation accuracy. In a numerical example, correct results are obtained even though both the input field and the propagation kernel are sampled below the Nyquist rate. Finally, we show how chirp

© 2014 Optical Society of America

**OCIS Codes**

(050.1960) Diffraction and gratings : Diffraction theory

(110.2990) Imaging systems : Image formation theory

(220.0220) Optical design and fabrication : Optical design and fabrication

(220.2560) Optical design and fabrication : Propagating methods

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: May 7, 2014

Revised Manuscript: June 27, 2014

Manuscript Accepted: June 27, 2014

Published: July 28, 2014

**Citation**

Matthias Hillenbrand, Damien P. Kelly, and Stefan Sinzinger, "Numerical solution of nonparaxial scalar diffraction integrals for focused fields," J. Opt. Soc. Am. A **31**, 1832-1841 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-8-1832

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