The paper starts with a comparative discussion of features and limitations of the three types of recent approaches to reconstruction in thermoacoustic/photoacoustic tomography: backprojection formulae, eigenfunction expansions and time reversal. The latter method happens to be the least restrictive. It is then considered in more detail, e.g. its relation to trapping properties of the medium. The time reversal method is exact only in the case of a constant sound speed in odd dimension, due to validity of the Huygens' principle. The next best case is of non-trapping speed in odd dimensions. The authors provide 2D examples and discuss the features of numerical reconstructions for constant and variable (both non-trapping and trapping) speeds, showing that this technique works surprisingly well even under the most unfavorable circumstances (variable, and even trapping sound speed in 2D). In particular, a 'limited view' effect due to trapping is observed and explained. Finally, an initial consideration of the problem of sound speed recovery is also provided.

We report a simple fiber sensor for measurement of high temperature with high sensitivity. The sensing head is a multimode-single mode-multimode (MM-SM-MM) fiber configuration formed by splicing a section of uncoated single mode fiber (SMF) with two short sections of multimode fibers (MMF) whose core is composed of pure silica. Because of the mode-field mismatch at the splicing points of the SMF with 2 sections of MMFs, as well as index matching between the core of the MMF and the cladding of the SMF, optical power from the lead-in fiber can be partly coupled to the cladding modes of the SMF through the MMF. The cladding modes of the SMF then re-coupled to the lead-out fiber, in the same fashion. Due to the effective index difference between the core and cladding modes, an interference pattern in the transmission spectrum of the proposed device was obtained. The interference pattern was found to shift to the longer wavelength region with respect to temperature variation. The temperature sensor can measure temperature stably up to more than 900 degrees C with sensitivity of 0.088 nm/ degrees C.

We present a family of closed form inversion formulas in thermoacoustic tomography in the case of a constant sound speed. The formulas are presented in both time-domain and frequency-domain versions. As special cases, they imply most of the previously known filtered backprojection type formulas.1991 Mathematics Subject Classification. Primary: 92C55, 35L05, 35R30; Secondary: 44A99, 45Q05.

In this article, we revisit iterative methods for solving the inverse problem of photoacoustic tomography in free space. Recently, there have been interesting developments on explicit formulations of the adjoint operator, demonstrating that iterative methods is an attractive choice for photoacoustic image reconstruction. In this work, we propose several modifications of current formulations of the adjoint operator which help speed up the convergence and yield improved error estimates. We establish a stability analysis and show that, with our choices of the adjoint operator, the iterative methods can achieve a linear rate of convergence, in the L 2 -norm as well as in the H 1 -norm. In addition, we analyze the normal operator from the microlocal analysis point of view. This gives insight into the convergence speed of the iterative methods and choosing proper weights for the mapping spaces. Finally, we present numerical results using various iterative reconstruction methods for full as well as limited view data. Our results demonstrate that Nesterov's fast gradient and the CG methods converge faster than Landweber's and iterative time reversal methods in the visible as well as the invisible case.

Models of quantum gravity suggest that the vacuum should be regarded as a medium with quantum structure that may have non-trivial effects on photon propagation, including the violation of Lorentz invariance. Fermi Large Area Telescope (LAT) observations of gammaray bursts (GRBs) are sensitive probes of Lorentz invariance, via studies of energy-dependent timing shifts in their rapidly-varying photon emissions. In this paper we analyze the Fermi-LAT measurements of high-energy gamma rays from GRBs with known redshifts, allowing for the possibility of energy-dependent variations in emission times at the sources as well as a possible non-trivial refractive index in vacuo for photons. We use statistical estimators based on the irregularity, kurtosis and skewness of bursts that are relatively bright in the 100 MeV to multi-GeV energy band to constrain possible dispersion effects during propagation. We find that the energy scale characterizing a linear energy dependence of the refractive index should exceed a few ×10 17 GeV, and we estimate the sensitivity attainable with additional future sources to be detected by Fermi-LAT.