Document Type
Conference Paper
Publication Date
2-2014
Publication Source
Proceedings of SPIE: Practical Holography XXVIII: Materials and Applications
Abstract
An analytic examination of 3D holography under a 90° recording geometry was carried out earlier in which 2D spatial Laplace transforms were introduced in order to develop transfer functions for the scattered outputs under readout [1,2].
Thereby, the resulting reconstructed output was obtained in the 2D Laplace domain whence the spatial information would be found only by performing a 2D Laplace inversion. Laplace inversion in 2D was attempted by testing a prototype function for which the analytic result was known using two known inversion algorithms, viz., the Brancik and the Abate [2]. The results indicated notable differences in the 3D plots between the algorithms and the analytic result, and hence were somewhat inconclusive. In this paper, we take a closer look at the Brancik algorithm in order to understand better the implications of the choices of key parameters such as the real and imaginary parts of the Bromwich contour and the grid sizes of the summation operations.
To assess the inversion findings, three prototype test cases are considered for which the analytic solutions are known. For specific choices of the algorithm parameters, optimal values are determined that minimize errors in general. It is found that even though errors accumulate near the edges of the grid, overall reasonably accurate inversions are possible to obtain with optimal parameter choices that are verifiable via cross-sectional views. Further work is ongoing whereby the optimized algorithm is to be applied to the 3D holography problem.
Inclusive pages
90060V-1 to 90060V-18
ISBN/ISSN
0277-786X
Document Version
Published Version
Copyright
Copyright © 2014, Society of Photo-optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited.
Publisher
Society of Photo-optical Instrumentation Engineers
Place of Publication
San Francisco, CA
Volume
9006
Peer Reviewed
yes
eCommons Citation
Chatterjee, Monish Ranjan and Feng, Le, "Numerical Inversion and Assessment of 2D Laplace Transforms using the Brancik Algorithm and its use in 3D Holography" (2014). Electrical and Computer Engineering Faculty Publications. 351.
https://ecommons.udayton.edu/ece_fac_pub/351
Included in
Computer Engineering Commons, Electrical and Electronics Commons, Electromagnetics and Photonics Commons, Optics Commons, Other Electrical and Computer Engineering Commons, Systems and Communications Commons
Comments
This document is provided for download in compliance with the publisher's policy on self-archiving. Permission documentation is on file.
DOI: http://dx.doi.org/10.1117/12.2053628