The recent application of tomographic methods to three-dimensional imaging through tissue by use of light often requires modeling of geometrically complex diffuse–nondiffuse boundaries at the tissue–air interface. We have recently investigated analytical methods to model complex boundaries by means of the Kirchhoff approximation. We generalize this approach using an analytical approximation, the <i>N</i>-order diffuse-reflection boundary method, which considers higher orders of interaction between surface elements in an iterative manner. We present the general performance of the method and demonstrate that it can improve the accuracy in modeling complex boundaries compared with the Kirchhoff approximation in the cases of small diffuse volumes or low absorption. Our observations are also contrasted with exact solutions. We furthermore investigate optimal implementation parameters and show that a second-order approximation is appropriate for most <i>in vivo</i> investigations.
© 2003 Optical Society of America
(110.6960) Imaging systems : Tomography
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5270) Medical optics and biotechnology : Photon density waves
(170.5280) Medical optics and biotechnology : Photon migration
Jorge Ripoll and Vasilis Ntziachristos, "Iterative boundary method for diffuse optical tomography," J. Opt. Soc. Am. A 20, 1103-1110 (2003)