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    Weak convexity of Fisher information matrix and superresolved localization of blinking sources of light

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    A group of techniques known by the general name of single-molecule localization microscopy reaches a nanometer-scale spatial resolution of point light emitters, well below the diffraction limit of traditional microscopy. The key feature of these techniques is blinking, alternation of bright and dark states, of each emitter so that no more than one emitter is bright within the width of the point-spread function of the microscope during a time sufficient for its localization. We give a formulation of the optical part of these techniques in terms of quantum metrology, where the limit of precision is determined by the Fisher information on the emitters' positions contained in the measurement data. We show that the advantage in resolution provided by making the emitters blink is a consequence of the fundamental property of Fisher information, its convexity. In particular, we prove the weak matrix convexity and the trace convexity of the Fisher information matrix—two fundamental results in the multiparameter estimation theory. We show also that the advantage in information is inherent to the quantum state of light itself before the measurement and is related to the convexity of the quantum Fisher information matrix

    Reconstructing multiple initial pressure and speed of sound distributions simultaneously in photoacoustic tomography

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    Image reconstruction in photoacoustic tomography relies on an accurate knowledge of the speed of sound in the target. However, the speed of sound distribution is not generally known, which may result in artefacts in the reconstructed distribution of initial pressure. Therefore, reconstructing the speed of sound simultaneously with the initial pressure would be valuable for accurate imaging in photoacoustic tomography. Furthermore, the speed of sound distribution could provide additional valuable information about the imaged target. In this work, simultaneous reconstruction of initial pressure and speed of sound in photoacoustic tomography is studied. This inverse problem is known to be highly ill-posed. To overcome this, we study an approach where the ill-posedness is alleviated by utilising multiple photoacoustic data sets that are generated by different initial pressure distributions within the same imaged target. Then, these initial pressure distributions are reconstructed simultaneously with the speed of sound distribution. A methodology for solving this minimisation problem is formulated using a gradient-based iterative approach equipped with bound constraints and a multigrid approach. The methodology was evaluated with numerical simulations. Different approaches for generating multiple initial pressure distributions and their effect on the solution of the image reconstruction problem were studied. The results show that initial pressure and speed of sound can be simultaneously reconstructed from photoacoustic data. Furthermore, utilising multiple initial pressure distributions improves the reconstructions such that the locations of initial pressure and speed of sound inhomogeneities can be better distinguished and image artifacts are reduced

    Engineering THz components : synergy of geometry and material properties

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    The Impact of Teachers’ Attitudes on the Mathematics Self-Efficacy of Students with an Immigrant Background

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    Interpretation of three-dimensional polarization states through the smart decomposition of the polarization matrix

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    A complete description of a three-dimensional (3D) polarization state is provided by the two most12 significant eigenstates of the polarization matrix, together with the two indices of polarimetric purity. By means of13 the so-called smart decomposition, such information can be arranged to represent the state as a combination of two14 components, one partially polarized (active component) and one unpolarized. Contrary to what happens for two-15 dimensional (2D) polarization states (with the electric field fluctuating within a fixed plane), whose active component16 is constituted by a single totally polarized state, in the general case of 3D polarization states the active component is17 given by a weighted incoherent composition of the two above-mentioned eigenstates. We show that a detailed18 description of the intensity and spin anisotropies is encompassed by the active component of the state, which admits19 a simple interpretation and geometric representation. In addition, it is found that the degree of nonregularity can be20 viewed as a distance of the state to a regular state

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