Image reconstruction in non-reciprocal broken-ray tomography.

Optical methods of biomedical tomographic imaging are of considerable interest due to their non-invasive nature and sensitivity to physiologically important markers. Similarly to other imaging modalities, optical methods can be enhanced by utilizing extrinsic contrast agents. Typically, these are fluorescent molecules, which can aggregate in regions of interest due to various mechanisms.

Cherenkov light emission in molecular radiation therapy of the thyroid and its application to dosimetry.

Numerical experiments based on Monte Carlo simulations and clinical CT data are performed to investigate the spatial and spectral characteristics of Cherenkov light emission and the relationship between Cherenkov light intensity and deposited dose in molecular radiotherapy of hyperthyroidism and papillary thyroid carcinoma. It is found that Cherenkov light is emitted mostly in the treatment volume, the spatial distribution of Cherenkov light at the surface of the patient presents high-value regions at locations that depend on the symmetry and location of the treatment volume, and the surface light in the near-infrared spectral region originates from the treatment site. The effect of inter-patient variability in the tissue optical parameters and radioisotope uptake on the linear relationship between the dose absorbed by the treatment volume and Cherenkov light intensity at the surface of the patient is investigated, and measurements of surface light intensity for which this effect is minimal are identified.

Nonreciprocal broken ray transforms with applications to fluorescence imaging.

Broken ray transforms (BRTs) are typically considered to be reciprocal, meaning that the transform is independent of the direction in which a photon travels along a given broken ray. However, if the photon can change its energy (or be absorbed and re-radiated at a different frequency) at the vertex of the ray, then reciprocity is lost. In optics, non-reciprocal BRTs are applicable to imaging problems with fluorescent contrast agents.

Single-scattering optical tomography: simultaneous reconstruction of scattering and absorption.

We report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured.

Single-scattering optical tomography.

We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray transform. The technique can be used to recover the extinction coefficient of an inhomogeneous medium from angularly resolved measurements and is illustrated with numerical simulations.

Semiclassical model of stimulated Raman scattering in photonic crystals.

We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals.

Lasing in a random amplifying medium: spatiotemporal characteristics and nonadiabatic atomic dynamics.

We study the dynamics of lasing from photonic paints excited by short, localized, optical pulses, using a time-dependent diffusion model for light propagating in the medium containing active atoms. The full time-dependent, nonadiabatic nonlinear response of the atomic system to the local optical field intensity is described using the Einstein rate equations for absorption and emission of light. Solving the time-dependent diffusion equation for the light intensity in the medium with nonlinear gain and loss, we derive detailed information on the spectral, spatial, and temporal properties of the emitted laser light.

Theory of photon statistics and optical coherence in a multiple-scattering random-laser medium.

We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors.