Multiple passages of light through an absorption inhomogeneity of finite size deep within a turbid medium are analyzed for optical imaging by use of the self-energy diagram. The nonlinear correction becomes more important for an inhomogeneity of a larger size and with greater contrast in absorption with respect to the host background. The nonlinear correction factor agrees well with that from Monte Carlo simulations for cw light. The correction is approximately 50%-75% in the near infrared for an absorption inhomogeneity with the typical optical properties found in tissues and five times the size of the transport mean free path.

From the geometrical path statistics of rays in an anomalous-diffraction theory (ADT) Opt. Lett. 28 , 179 (2003) closed-form expressions for the geometrical path distribution of rays and analytical formulas for the optical efficiencies of finite circular cylinders oriented in an arbitrary direction with respect to the incident light are derived. The characteristics of the shapes of the cylinders produce unique features in the geometrical path distributions of the cylinders compared with spheroids. Gaussian ray approximations, which depend only on the mean and the mean-squared geometrical paths of rays, of the optical efficiencies of finite circular cylinders and spheroids are compared with the exact optical efficiencies in ADT. The influence of the difference in shape between cylinders and spheroids on the optical efficiencies in ADT is illustrated by their respective geometrical path distributions of rays.

The anomalous-diffraction theory (ADT) of extinction of light by soft particles is shown to be determined by a statistical distribution of the geometrical paths of individual rays inside the particles. Light extinction depends on the mean and the mean-squared geometrical paths of the rays. Analytical formulas for optical efficiencies from a Gaussian distribution of the geometrical paths of rays are derived. This Gaussian ray approximation reduces to the exact ADT in the intermediate case of light scattering for an arbitrary soft particle and describes well the extinction of light from a system of randomly oriented and (or) polydisperse particles. The implications for probing of the sizes and shapes of particles by light extinction are discussed.

The powerlaw patterns in Mie scattering (the normalized light intensity I()/I(0) vs. the dimensionless qR where is the magnitude of the wave vector transfer at the scattering angle for wavelength , and R is the radius of the nonabsorbing sphere with a relative refractive index m>1) are analyzed using the geometrical optics approximation for particles of a large size parameter. The (qR)?4 powerlaw regime is shown to be present only in Mie scattering of soft particles. The (qR)?2 powerlaw regime occurs at the scattering angles of the p=1 geometrical ray (refracted without internal reflections) from the portion of the incident beam with an incidence angle around /4 upon the particle. The (qR)?2 powerlaw regimes from particles sharing one common relative refractive index but differing in size parameters are collinear. Simple analytical expressions are derived to describe these powerlaw regimes of Mie scattering.

Light extinction and angular scattering measurements were performed on three species of bacteria with different sizes and shapes ( Pseudomonas aeruginosa, Staphylococcus aureus, and Bacillus subtilis). The Gaussian ray approximation of anomalous diffraction theory was used to determine the average bacteria size from transmission measurements. A rescaled spectra combining multiple angular data was analyzed in the framework of the Rayleigh-Gans theory of light scattering. Particle shape and size distribution is then obtained from the rescale spectra. Particle characteristics (size and/or shape) retrieved from both methods are in good agreement with size and shape measured under scanning electron microscopy. These results demonstrate that light scattering may be able to detect and identify microbial contamination in the environment.

The photon distribution, as a function of position, angle, and time, is computed using the analytical cumulant solution of the Boltzmann radiative transfer equation (RTE). A linear forward model for light propagation in turbid media for three-dimensional (3-D) optical tomography is formed based on this solution. The model can be used with time resolved, continuous wave (CW), and frequency-domain measurements in parallel geometries. This cumulant forward model (CFM) is more accurate than that based on the diffusion approximation of RTE. An inverse algorithm that incorporates this CFM is developed, based on a fast 3-D hybrid-dual-Fourier tomographic approach using multiple detectors and multiple sources in parallel geometries. The inverse algorithm can produce a 3-D image of a turbid medium with more than 20 000 voxels in 1-2 min using a personal computer. A 3-D image reconstructed from simulated data is presented.

A photon transport model for light migration in turbid media based on a cumulant approximation to radiative transfer is presented for image reconstruction inside an infinite medium or a bounded medium with a planar geometry. This model treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation and uses the second-order cumulant solution of photon density to the Boltzmann equation as the Green's function for the uniform background. It provides the correct behavior of photon migration at early times and reduces at long times to the center-moved diffusion approximation. At early times, it agrees much better with the result from the Monte Carlo simulation than the diffusion approximation. Both approximations agree well with the Monte Carlo simulation at later times. The weight function for image reconstruction under this proposed model is shown to have a strong dependence at both early and later times on absorption and/or scattering inhomogeneities located in the propagation direction of and close to the source, or in the field of view of and close to the detector. This effect originates from the initial ballistic motion of incident photons, which is substantially underestimated by the diffusion approximation.

Time-resolved Fourier optical diffuse tomography is a novel approach for imaging of objects in a highly scattering turbid medium with use of an incident (near) plane wave. The theory of the propagation of spatial Fourier components of the scattered wave field is presented, along with a fast algorithm for three-dimensional reconstruction in a parallel planar geometry. Examples of successful reconstructions of simulated hidden absorptive or scattering objects embedded inside a human-tissue-like semi-infinite turbid medium are provided.

A photon-transport forward model for image reconstruction in turbid media is derived that treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation. This model can conveniently replace the commonly used diffusion approximation in optical tomography. An analytical expression of the background Green's function is obtained from the cumulant solution of the Boltzmann equation. Our model provides the correct behavior of photon migration at early times and reduces at long times to the center-moved diffusion approximation. Numerical comparisons between this model and the standard and center-moved diffusion models are presented.

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.