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In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for instance, by acoustic or optical forces. Under the influence…
The aim of this paper is to propose an optimal control optimization algorithm for reconstructing admittivity distributions (i.e., both conductivity and permittivity) from multi-frequency micro-electrical impedance tomography. A convergent…
The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radiation diffusion and frequency-dependent diffusion equations…
This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
Reabsorption, the multiple scattering of spontaneously emitted photons in optically thick gases, is a major limitation to efficient optical pumping and laser cooling in ultracold gases. We report mitigation of reabsorption using spatial and…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to in-depth optical microscopy, as it causes a drastic degradation of contrast, resolution and…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature [5,6] certain simplifying…
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…
A computational model study for complete frequency redistribution linear incoherent two-level atomic radiation trapping in optically dense media using the multiple scattering representation is presented. This model study discuss at length…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…
There has been devoted significant mathematical research to model the light propagation in tissue and to recover the absorption and scattering coefficients after photoacoustic inversion. Typically, the basic light propagation models…
Optical coherence tomography (OCT) is a non-invasive, micrometer-scale imaging modality that has become a clinical standard in ophthalmology. By raster-scanning the retina, sequential cross-sectional image slices are acquired to generate…
Many applications seek to measure a sample's absorption coefficient spectrum to retrieve the chemical makeup. Many real world samples are optically turbid, causing scattering confounds which many commercial spectrometers cannot address.…