Three-dimensional optical tomography with the equation of radiative transfer

Gassan S. Abdoulaev, Andreas H. Hielscher

Research output: Contribution to journalArticlepeer-review


We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer (ERT) and allows for arbitrarily shaped medium boundaries and arbitrary spatial material distributions. The scheme builds on the concept of model-based iterative image reconstruction, in which a forward model provides prediction of detector readings, and a gradient-based updating scheme minimizes an appropriately defined objective function. The forward model is solved by using an even-parity formulation of the ERT, which lends itself to a finite-element discretization method. The finite-element technique provides the suitable framework for predicting light propagation in arbitrarily shaped three-dimensional media. For an efficient way of calculating the gradient of the objective function we have implemented an adjoint differentiation scheme. Initial reconstruction results using synthetic data from simple media and a three-dimensional mesh of the human forehead illustrate the performance of the code.

Original languageEnglish (US)
Pages (from-to)594-601
Number of pages8
JournalJournal of Electronic Imaging
Issue number4
StatePublished - Oct 2003

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Computer Science Applications
  • Electrical and Electronic Engineering


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