TY - JOUR

T1 - Kirchhoff approximation for diffusive waves

AU - Ripoll, Jorge

AU - Ntziachristos, Vasilis

AU - Carminati, Remi

AU - Nieto-Vesperinas, Manuel

PY - 2001

Y1 - 2001

N2 - Quantitative measurements of diffuse media, in spectroscopic or imaging mode, rely on the generation of appropriate forward solutions, independently of the inversion scheme employed. For complex boundaries, the use of numerical methods is generally preferred due to implementation simplicity, but usually results in great computational needs, especially in three dimensions. Analytical expressions are available, but are limited to simple geometries such as a diffusive slab, a sphere or a cylinder. An analytical approximation, the Kirchhoff approximation, also called the tangent-plane method is presented for the case of diffuse light. Using this approximation, analytical solutions of the diffusion equation for arbitrary boundaries and volumes can be derived. Also, computation time is minimized since no matrix inversion is involved. The accuracy of this approximation is evaluated on comparison with results from a rigorous numerical technique calculated for an arbitrary geometry. Performance of the approximation as a function of the optical properties and the size of the medium is examined and it is demonstrated that the computation time of the direct scattering model is reduced at least by two orders of magnitude.

AB - Quantitative measurements of diffuse media, in spectroscopic or imaging mode, rely on the generation of appropriate forward solutions, independently of the inversion scheme employed. For complex boundaries, the use of numerical methods is generally preferred due to implementation simplicity, but usually results in great computational needs, especially in three dimensions. Analytical expressions are available, but are limited to simple geometries such as a diffusive slab, a sphere or a cylinder. An analytical approximation, the Kirchhoff approximation, also called the tangent-plane method is presented for the case of diffuse light. Using this approximation, analytical solutions of the diffusion equation for arbitrary boundaries and volumes can be derived. Also, computation time is minimized since no matrix inversion is involved. The accuracy of this approximation is evaluated on comparison with results from a rigorous numerical technique calculated for an arbitrary geometry. Performance of the approximation as a function of the optical properties and the size of the medium is examined and it is demonstrated that the computation time of the direct scattering model is reduced at least by two orders of magnitude.

UR - http://www.scopus.com/inward/record.url?scp=85035288796&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.64.051917

DO - 10.1103/PhysRevE.64.051917

M3 - Article

AN - SCOPUS:85035288796

SN - 1063-651X

VL - 64

SP - 8

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 5

ER -