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Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
We present a simple measurement and analysis technique to determine the fraction of optical loss due to both radiation (scattering) and linear absorption in microphotonic components. The method is generally applicable to optical materials…
Non-invasive and single-shot holographic imaging through complex media is technically challenging due to random light scattering which significantly scrambles optical information. Recently, several methods have been presented to address…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…
The traditional approaches to computerized tomography (CT) depend on the samples of Radon transform at multiple angles. In optics, the real time imaging requires the reconstruction of an object by the samples of Radon transform at a single…
Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption…
We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard…
Light scattering imposes a major obstacle for imaging objects seated deeply in turbid media, such as biological tissues and foggy air. Diffuse optical tomography (DOT) tackles scattering by volumetrically recovering the optical absorbance…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
The possibility of spatially resolving the optical properties of atomically thin materials is especially appealing as they can be modulated at the micro- and nanoscale by reducing their thickness, changing the doping level or applying a…
In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…
The resonant absorption of light by an ensemble of absorbers decreases when the resonance is inhomogeneously broadened, as only a fraction of the ensemble contributes to the absorption at any given optical frequency. Recovering the lost…
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…
We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the…
We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10^8 source-detector pairs, we demonstrate the…
Absorption imaging with quasi-resonant laser light is a commonly used technique to probe ultra-cold atomic gases in various geometries. Here we investigate some non-trivial aspects of this method when it is applied to in situ diagnosis of a…