Bayesian Tomography for Projections With an Arbitrary Transmission Function With an Application in Electron Microscopy

Published

December 1, 2006

Author(s)

Zachary H. Levine, Anthony J. Kearsley, John G. Hagedorn

Abstract

The vast majority of the developments in tomography assume that the transmission of the probe trhought he sample follows Beer s Law, i.e., the rule of exponential attenuation. However, for transmission electron microscopy of samples a few times their mean free path, Beer s Law is no longer an accurate description of the transmission of the probe as a function of the sample thickness. Recent simulations have demonstrated accounting ofrthe correct transmission function leads to superior tomographic reconstructions for a photonic band gap sample 8000 nm square. A previous paper assumed 180 degree data was available. Here we consider a more realistic case in which only 140 degree data is available. To treat the limited angle problem, the Bayesian formalism of Bouman and Sauer is generalized to allow an arbitrary transmission function. The new formalism is identical to that of Bouman and Sauer when the transmission function obeys Beer s Law. The examples suggest that using the physical transmission function is a requirement for performing limited angle reconstructions.

Citation

Journal of Research (NIST JRES) -

Volume

111 No. 6

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

Bayesian tomography, Beer's Law, maximum likelihood, multiple scattering, photonic band gap, Physical transmission function, transmission electron microscope, transmission-thickness relation

Citation

Levine, Z. , Kearsley, A. and Hagedorn, J. (2006), Bayesian Tomography for Projections With an Arbitrary Transmission Function With an Application in Electron Microscopy, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed October 13, 2025)