Discussion of the finite element method in optical diffraction tomography

Julia Lobera; Jeremy Coupland

doi:10.1117/12.662102

27 April 2006 Discussion of the finite element method in optical diffraction tomography

Julia Lobera, Jeremy Coupland

Proceedings Volume 6188, Optical Micro- and Nanometrology in Microsystems Technology; 61880I (2006) https://doi.org/10.1117/12.662102
Event: SPIE Photonics Europe, 2006, Strasbourg, France

Abstract

In Optical Diffraction Tomography (ODT) the refractive index is reconstructed from images with different illuminating wavefronts. In most cases the Born approximation is assumed, although this limits the applicability of the technique to weak-scattering problems. In this work we examine the scattering problem from first principles beginning from the Helmholtz equation that governs scalar diffraction and wave propagation. We demonstrate the use of the Born approximation and show typical errors when it is applied in practice. Solution of the Helmholtz equation using a Finite Element Method (FEM) with an appropriate Absorbing Boundary Condition (ABC) is described, and a non-linear optimization technique, the Conjugate Gradient Method (CGM), previously proposed for microwave imaging, is applied to the inverse problem.

Citation Download Citation

Julia Lobera and Jeremy Coupland "Discussion of the finite element method in optical diffraction tomography", Proc. SPIE 6188, Optical Micro- and Nanometrology in Microsystems Technology, 61880I (27 April 2006); https://doi.org/10.1117/12.662102

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