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. In the current approaches to imaging, the intrinsic (related to the tissue) and extrinsic (related to the contrast agent) optical parameters are determined separately. This can result in errors, in particular, due to using simplified heuristic models for the spectral dependence of the optical parameters. Recently, we have developed the theory of non-reciprocal broken-ray tomography (NRBRT) for fluorescence imaging of weakly scattering systems. NRBRT enables simultaneous reconstruction of the fluorophore concentration as well as of the intrinsic optical attenuation coefficient at both the excitation and the emission wavelengths. Importantly, no assumption about the spectral dependence of the tissue optical properties is made in NRBRT. In this study, we perform numerical validation of NRBRT under realistic conditions using the Monte Carlo method to generate forward data. We demonstrate that NRBRT can be used for tomographic imaging of samples of up to four scattering lengths in size. The effects of physical characteristics of the detectors such as the area and the acceptance angle are also investigated.

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. In the case of x-ray imaging, problems with single Compton scattering also give rise to non-reciprocal BRTs. In this paper, we focus on tomographic optical fluorescence imaging and show that, by reversing the path of a photon and using the non-reciprocity of the data function, we can reconstruct simultaneously and independently all optical properties of the medium (the intrinsic attenuation coefficients at the excitation and the fluorescence frequency and the concentration of the contrast agent). Our results are also applicable to inverting BRTs that arise due to single Compton scattering.

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. The use of Cherenkov light measurements at the patient surface for molecular radiation therapy dosimetry is also addressed.

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. The forward data for these simulations were obtained by numerically solving the radiative transport equation without any approximations. Tomographic imaging in slabs of different widths was considered and it was shown that the technique can tolerate a maximum width that corresponds to approximately six scattering events. It is also shown that the use of broken rays does not result in additional ill posedness of the inverse problem in comparison to the classical problem of inverting the Radon transform. Applications to biomedical imaging are described.

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. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.

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. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.

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. Our model recaptures the effects of scatterers to narrow the emission spectral linewidth and to narrow the emitted pulse duration, at a specific threshold pump intensity. Our model also describes how this threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results.

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. That is, no physical mechanism for separating single-scattered photons from the rest of the multiply-scattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering.