27 April 2006 Discussion of the finite element method in optical diffraction tomography
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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.
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Julia Lobera, Julia Lobera, Jeremy Coupland, 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); doi: 10.1117/12.662102; https://doi.org/10.1117/12.662102
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