Regular papers

Effective and flexible modeling approach to investigate various 3D Talbot carpets from a spatial finite mask

¹ Carl Zeiss Jena GmbH, Carl-Zeiss-Promenade 10, 07745 Jena, Germany
² University of Applied Sciences “Hochschule Hamm-Lippstadt”, Marker Allee 76-78, 59063 Hamm, Germany
³ University of Applied Sciences “Ernst-Abbe-Fachhochschule Jena”, Carl-Zeiss-Promenade 2, 07745 Jena, Germany

^* maass@zeiss.de

Received: 17 September 2012

Abstract

We present an effective modeling approach for a fast calculation of the Talbot carpet from an initially 2-dimensional mask pattern. The introduced numerical algorithm is based on a modified angular-spectrum method, in which it is possible to consider the border effects of the Talbot region from a mask with a finite aperture. The Bluestein’s fast Fourier transform (FFT) algorithm is applied to speed up the calculation. This approach allows as well to decouple the sampling points in the real space and the spatial frequency domain so that both parameters can be chosen independently. As a result an extended three-dimensional Talbot-carpet can be calculated with a minimized number of numerical steps and computation time, but still with high accuracy. The algorithm was applied to various 2-dimensional mask patterns and illumination setups. The influence of specific mask patterns to the resulting field intensity distribution is discussed.