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A Monte Carlo (MC) method for modeling optical coherence tomography (OCT) measurements of a diffusely reflecting discontinuity embedded in a scattering medium is presented. For the first time to the authors' knowledge it is shown analytically that the applicability of an MC approach to this optical geometry is firmly justified, because, as we show, in the conjugate image plane the field reflected from the sample is delta-correlated from which it follows that the heterodyne signal is calculated from the intensity distribution only. This is not a trivial result because, in general, the light from the sample will have a finite spatial coherence that cannot be accounted for by MC simulation. To estimate this intensity distribution adequately we have developed a novel method for modeling a focused Gaussian beam in MC simulation. This approach is valid for a softly as well as for a strongly focused beam, and it is shown that in free space the full three-dimensional intensity distribution of a Gaussian beam is obtained. The OCT signal and the intensity distribution in a scattering medium have been obtained for several geometries with the suggested MC method; when this model and a recently published analytical model based on the extended Huygens-Fresnel principle are compared, excellent agreement is found. OCIS codes: 170.4500, 290.4210, 290.7050, 170.3660, 000.4430.

Finite difference time domain (FDTD) analysis has been successfully formulated for solving diffusion equation in biological tissues. Time-dependent diffusion equations are approximated by FDTD equations by assigning diffuse photon fluence rates and radiant flux defined in the diffusion equations to Yee meshes. At the boundary between scattering and no scattering material, FDTD equation including only fluence rate has been derived, which make it possible to calculate the fluence rate at the boundary. The formulation is useful to solve diffusion equations by iterative algebraic calculations in scattering media with inhomogeneous optical properties. The conditions to give stabilities for numerical solutions have been become clear in terms of scattering coefficients and mean cosine of scattering angles. Using the formulation, the reflectance of three-layered slabs containing a clear layer have been calculated. As a result, it has been found that absorption loss changes of the highly scattering medium beyond the clear layer are estimated from the time profiles of the reflectance. Index Terms--Diffusion equation, FDTD analysis, optical computer tomography, transmittance and reflectance.

We present an Abel-inversion algorithm to reconstruct mean and rms refractive-index profiles from spatially resolved statistical measurements of the beam-deflection angle in time-dependent, axisymmetric flows. An oscillating gas-jet diffusion flame was investigated as a test case for applying the algorithm. Experimental data were obtained across the whole field by a rainbow schlieren apparatus. Results show that simultaneous multipoint measurements are necessary to reconstruct the rms refractive index accurately.

A study on the use of the seismic transmission traveltime tomography technique proposes a reconstruction method to improve on the conventional singular value decomposition approaches by combining suitable weighing matrices and a variable regularization parameter. Experimental results indicate that the proposed reconstruction approach can strike a good balance between resolution and stability for an ill-posed problem without focusing too closely on the issue of parameter selection.

We present a three-dimensional (3D) image reconstruction scheme for optical near-infrared imaging of highly scattering material. The algorithm reconstructs the spatial distribution of the optical parameters of a volume [Omega] from transillumination measurements on the boundary of [Omega]. We test the performance of the method for a cylindrical object with embedded absorbing perturbation for a number of different source and detector arrangements. Furthermore, we investigate the effect of a mismatched reconstruction, using a two-dimensional (2D) reconstruction model to image a single plane of the object from 3D tomographic data obtained in a single plane. The motivation for the application of 2D models is their advantage in speed and memory requirements. We found that the difference in the measurement data between 2D and 3D models depends greatly on the measurement type used, giving a much better agreement for mean time-of-flight data than for dc intensity data. Image artifacts that are due to data model mismatches can therefore be significantly reduced by use of mean time data.