We present an approach to solving the radiative transport equation (RTE) for layered media in the spatial frequency domain (SFD) using Monte Carlo (MC) simulations. This is done by obtaining a complex photon weight from analysis of the Fourier transform of the RTE. We also develop a modified shortcut method that enables a single MC simulation to efficiently provide RTE solutions in the SFD for any number of spatial frequencies. We provide comparisons between the modified shortcut method and conventional discrete transform methods for SFD reflectance. Further results for oblique illumination illustrate the potential diagnostic utility of the SFD phase-shifts for analysis of layered media.

We examine the general problem of light transport initiated by oblique illumination of a turbid medium with a collimated beam. This situation has direct relevance to the analysis of cloudy atmospheres, terrestrial surfaces, soft condensed matter, and biological tissues. We introduce a solution approach to the equation of radiative transfer that governs this problem, and develop a comprehensive spherical harmonics expansion method utilizing Fourier decomposition (SHEFN). The SHEFN approach enables the solution of problems lacking azimuthal symmetry and provides both the spatial and directional dependence of the radiance. We also introduce the method of sequential-order smoothing that enables the calculation of accurate solutions from the results of two sequential low-order approximations. We apply the SHEFN approach to determine the spatial and angular dependence of both internal and boundary radiances from strongly and weakly scattering turbid media. These solutions are validated using more costly Monte Carlo simulations and reveal important insights regarding the evolution of the radiant field generated by oblique collimated beams spanning ballistic and diffusely scattering regimes.

We present a coupled forward-adjoint Monte Carlo (cFAMC) method to determine the spatially resolved sensitivity distributions produced by optical interrogation of three-dimensional (3-D) tissue volumes. We develop a general computational framework that computes the spatial and angular distributions of the forward-adjoint light fields to provide accurate computations in mesoscopic tissue volumes. We provide full computational details of the cFAMC method and provide results for low- and high-scattering tissues probed using a single pair of optical fibers. We examine the effects of source-detector separation and orientation on the sensitivity distributions and consider how the degree of angular discretization used in the 3-D tissue model impacts the accuracy of the resulting absorption sensitivity profiles. We discuss the value of such computations for optical imaging and the design of optical measurements.

A radiative transport method based on efficient coupled forward-adjoint Monte Carlo simulations is used for the analysis of diagnostic fiber optic probes. Results are shown for various probe geometries within a layered tissue model. © 2011 Optical Society of America.

We present a method to recover absorption and reduced scattering spectra for each layer of a two-layer turbid media from spatial frequency-domain spectroscopy data. We focus on systems in which the thickness of the top layer is less than the transport mean free path   (  0.1  -  0.8l  *    )  . We utilize an analytic forward solver, based upon the N'th-order spherical harmonic expansion with Fourier decomposition   (  SHEFN  )   method in conjunction with a multistage inverse solver. We test our method with data obtained using spatial frequency-domain spectroscopy with 32 evenly spaced wavelengths within λ  =  450 to 1000 nm on six-layered tissue phantoms with distinct optical properties. We demonstrate that this approach can recover absorption and reduced scattering coefficient spectra for both layers with accuracy comparable with current Monte Carlo methods but with lower computational cost and potential flexibility to easily handle variations in parameters such as the scattering phase function or material refractive index. To our knowledge, this approach utilizes the most accurate deterministic forward solver used in such problems and can successfully recover properties from a two-layer media with superficial layer thicknesses.