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In this paper it is studied how the evanescent waves affect the achievable performance in linear inverse source problems. To this end, its impact on the Kolmogorov entropy measure is considered. In this way the metric information that can be conveyed back from data to the unknown can be estimated. For the sake of simplicity, the study deals with strip magnetic sources and both the cases of a single and double unbounded observation domain is considered.

In this paper, we address the problem of imaging "thin" metallic cylinders from the knowledge of the electric far-field scattered under the incidence of plane waves. A scattering model based on a multipole expansion accounting for the mutual scattering is introduced and then simplified under the single- and second-order scattering hypotheses. The locations of the unknown cylinders for the inverse problem are described in terms of support of /spl delta/-functions. The performances of a truncated singular value decomposition based linear inversion algorithm in the presence of model errors due to mutual scattering is investigated, by both analytical and numerical arguments, in three different measurement configurations: single-frequency/multiview, multifrequency/single-view, and multifrequency/multiview. The different effects of the angular and frequency diversities are pointed out.

This paper deals with the tomographic inversion of experimental data acquired by a stepped-frequency ground penetrating radar (SFGPR). The experimental SFGPR has been designed for archaeological prospecting and makes it possible to exploit a multi-view/multi-static/multi-frequency configuration. The tomographic algorithm is based on a linear model of the electromagnetic scattering to reconstruct the shape of strongly scattering targets. It has been already validated against experimental data for objects in free-space and synthetic data for buried scatterers. Here, we present experimental results for buried objects starting from measurements collected at two test-sites. The first one has been a dedicated outdoor test facility which has allowed to test the experimental setup and the inversion algorithm in controlled conditions; the second one has been an archeological test-site.

This paper deals with the reconstruction of the shape of unknown perfectly conducting objects from the knowledge of the scattered electric far field in a two-dimensional geometry. By adopting the Kirchhoff approximation, the problem is cast as a linear inverse one and is solved by resorting to the Singular Value Decomposition (SVD) approach. The finiteness of the available data along with the presence of the noise make undesired features on the reconstructed image arise. We here give some criteria for the choice of a threshold to cut them out from the reconstructions. Furthermore, we illustrate the processing of multi-view data.

The version of the “linear sampling” method introduced in D. Colton, A. Kirsch, Inverse Problems, 12 , 383, 1996, is analyzed. It consists into the attempt to recover a scatterer's contour by determining an indicator function from the knowledge of the scattered far field data. In particular, the indicator function is determined following the solution of a certain far field equation . We show that the far field equation to solve does not have (almost anywhere) a solution for two classes of objects: Perfectly conducting cylinders and homogeneous dielectric cylinders having circular cross section. It thus follows that the indicator function is “infinite” (almost) everywhere both inside and outside the scatterer and, consequently, does not represent the shape of the object.

In this paper an innovative procedure for the localization and reconstruction of objects composed of elementary shapes is described. Sparse backscattered multifrequency field data are assumed to be known. The strategy is based on two steps in order to decrease the computational costs and to allow the use of few measurement points (with respect of Number of Degrees of Freedom). At first an Interferometric-Migration (IM) strategy is introduced with the purpose of reducing the dimension of the solution space. The second step is founded on the assumption that the elementary shapes are known and their geometrical features can characterized by a small amount of parameters. Then an Interferometric-MUSIC (I-MUSIC) algorithm is applied by combining results at single frequency. The overall approach is numerically tested in a 2D geometry for electrically large objects and has been proved robust against uncertainties on data.

Cadmium is a heavy metal increasingly widespread in the environment that is associated with neurodegenerative disorders such as Parkinson's and Alzheimer's diseases. In the present work we analyzed the levels of accumulation of β-amyloid peptide and glutamate dehydrogenase in Zebrafish brain in order to verify possible alterations. β-amyloid peptide is between the major players in the pathology of Alzheimer's disease according to the amyloid cascade hypothesis; glutamate dehydrogenase is an important enzyme for many metabolic processes and for the functionality of neurotransmission. Adult specimens of Zebrafish were exposed for 16 days to 1.0 mg/l of CdCl2 and the brains were analyzed after 2, 7 and 16 days of exposure. By Western blotting experiments we have shown that the levels of β-amyloid peptide and glutamate dehydrogenase increased in a progressive manner in the course of treatment. In particular it has been found an increase in the levels of glutamate dehydrogenase of 2.5 times after 16 days, while for the β-amyloid peptide has been possible to observe a significant increase of its accumulation already after two days of exposure to the metal with a final increase of 4-fold major. By immunohistochemical analysis we verified the increase in signal intensity in the treated animals both for the β-amyloid peptide and for glutamate dehydrogenase. The first signal was in particular increased in the medulla oblongata, in the dorsal and the ventral telencephalon and at the level of the cerebellum in the area of Purkinje neurons; glutamate dehydrogenase was more immunorevealed in the hypothalamic area of diencephalon, in the area of Purkinje cells of cerebellum and in optic tectum and telencephalon. Our results confirm the toxic action performed by cadmium in the brain, highlighting in particular the effects on nerve cells. The data show a correlation between cadmium and alteration of the metabolism of β-amyloid peptide also in Zebrafish brain. In addition, the variation observed for glutamate dehydrogenase could attest an alteration in the metabolism of excitatory and inhibitory neurotransmitters, another characteristic of neurodegenerative diseases. Moreover these results validate zebrafish as a good experimental model in the studies on neurodegenerative diseases associated to heavy metals as cadmium.

In this paper the role of view and frequency diversities in linear inverse scattering problems is analyzed in terms of the singular values behavior of the pertinent scattering operators. In order to obtain analytical results, the analysis is developed within a two-dimensional scalar far-zone configuration. Moreover, the canonical case of strip scatterers is considered. © 2013 IEEE.

Background: Oculocutaneous albinism is a group of autosomal recessive disorders featuring hypopigmentation of the hair, skin and eyes. Ocular signs associated with the disease are nystagmus, decreased visual acuity, hypopigmentation of the retina, foveal hypoplasia, translucency of the iris, macular transparency, photophobia and abnormal decussation of nerve fibers at the chiasm. Case Report: An 8-year-old Caucasian girl presented to our clinic ‘Referral Center for Hereditary Retinopathies’ of the Second University of Naples with a diagnosis of Stargardt disease and a progressive reduction in visual acuity in both eyes. She underwent a complete ophthalmic examination including standard electroretinography and optical coherence tomography (OCT). A molecular analysis was also performed. Best-corrected visual acuity was 20/30 in the right eye and 20/40 in the left eye. Biomicroscopy of the anterior segment revealed a transparent cornea, in situ and transparent lens and normally pigmented iris. A mild diffuse depigmentation and macular dystrophy were observed at fundus examination. Standard electroretinography showed normal scotopic and photopic responses. OCT revealed high reflectivity across the fovea without depression. The typical OCT pattern led us to direct the molecular analysis towards the genes involved in oculocutaneous albinism. The molecular analysis identified mutations in the TYR gene. Conclusion: In this case, the role of OCT was crucial in guiding the molecular analysis for the diagnosis of albinism. OCT is therefore instrumental in similar cases that do not present typical characteristics of a disease. The case also proves the relevance of molecular analysis to confirm clinical diagnoses in hereditary retinal diseases. Background: Oculocutaneous albinism is a group of autosomal recessive disorders featuring hypopigmentation of the hair, skin and eyes. Ocular signs associated with the disease are nystagmus, decreased visual acuity, hypopigmentation of the retina, foveal hypoplasia, translucency of the iris, macular transparency, photophobia and abnormal decussation of nerve fibers at the chiasm. Case Report: An 8-year-old Caucasian girl presented to our clinic 'Referral Center for Hereditary Retinopathies' of the Second University of Naples with a diagnosis of Stargardt disease and a progressive reduction in visual acuity in both eyes. She underwent a complete ophthalmic examination including standard electroretinography and optical coherence tomography (OCT). A molecular analysis was also performed. Best-corrected visual acuity was 20/30 in the right eye and 20/40 in the left eye. Biomicroscopy of the anterior segment revealed a transparent cornea, in situ and transparent lens and normally pigmented iris. A mild diffuse depigmentation and macular dystrophy were observed at fundus examination. Standard electroretinography showed normal scotopic and photopic responses. OCT revealed high reflectivity across the fovea without depression. The typical OCT pattern led us to direct the molecular analysis towards the genes involved in oculocutaneous albinism. The molecular analysis identified mutations in the TYR gene. Conclusion: In this case, the role of OCT was crucial in guiding the molecular analysis for the diagnosis of albinism. OCT is therefore instrumental in similar cases that do not present typical characteristics of a disease. The case also proves the relevance of molecular analysis to confirm clinical diagnoses in hereditary retinal diseases. Copyright © 2012 S. Karger AG, Basel.

Il saggio prende in esame il legame di Marx con l'idealismo tedesco, in particolare con Fichte e con Hegel.

This paper deals with a procedure for retrieving the Fresnel reflection coefficients of a half-space medium starting from measurements collected under a reflection mode multistatic configuration. In particular, the procedure consists in inverting a linear integral operator which links the reflected field measurements and the Fresnel reflection coefficients. Some numerical results are presented to show the effectiveness of the proposed procedure.

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.

The second version of the "linear sampling" method is considered with reference to perfectly conducting cylinders and its performances analyzed. It is pointed out that, for nonconvex objects, the shape of the object under test is not retrieved, whereas in its place the convex hull is recovered. We also point out that in the case of aspect limited data neither the convex hull of the object is reconstructed.

A method is provided for reconstruction of the shape of perfectly conducting objects in a homogeneous space starting from knowledge of the scattered far field under the incidence of TE-polarized plane waves. The Kirchhoff model of scattering permits linearization of the inverse problem, which is further simplified by adopting an asymptotic approximation. Thus the problem is tackled with an approach based on singular-value decomposition already developed for the TM case.

The problem of determining the shape of perfectly conducting objects from knowledge of the scattered electric field is considered. The formulation of the problem accommodates the nature of the distribution of the induced surface current density. Thus, as the unknown representing the object’s contour, a single layer distribution is chosen so that the contour of the scatterer is described by its support. The nonlinear unknown-data mapping is then linearized by means of the Kirchhoff approximation, and the problem is recast as the inversion of a linear operator acting on a distribution space. An extension of the singular value decomposition approach to solve the linearized problem is provided and numerical results are presented.

The achievable depth resolution in reconstructing the permittivity profile of a dielectric strip under the Born approximation when data are collected in the Fresnel zone is studied. We consider a rectilinear measurement aperture and an orthogonal and centered rectilinear investigation domain. The roles of the aperture extent and frequency diversity are highlighted.

Deals with the reconstruction of the contrast function of a dielectric cylinder with rectangular cross section starting from the knowledge of the electric scattered far field produced under the incidence of plane waves. We analyze the set of the reconstructable Fourier harmonics of the unknown permittivity contrast function with linear and quadratic approaches. This set depends on the ranges of the wavenumbers /spl beta/, of the angles of incidence /spl theta//sub i/ of the impinging plane waves, and of the observation angles /spl theta//sub o/. We discuss a simple way to describe such a dependence, which allows us to find out that the set of the retrievable harmonics for the quadratic approach contains that for the linear one. Moreover, our investigation points out how increasing the amount of independent data through a multifrequency/multiview measurement scheme allows us to enlarge the set of the retrievable unknown harmonics with respect to a multifrequency/single-view one. Our analysis is confirmed by numerical results. Memory storage requirements and processing time consumption for the quadratic approach are greatly reduced thanks to the massive use of the fast Fourier transform algorithm.

This paper deals with the problem of determining the shape of unknown perfectly conducting infinitely long cylinders; starting from the knowledge of the scattered electric far field under the incidence of plane waves with a fixed angle of incidence and varying frequency. The problem is formulated as a nonlinear inverse one by searching for a compact support distribution accounting for the objects contour. The nonlinear unknown to data mapping is then linearized by means of the Kirchhoff approximation, which reduces it into a Fourier transform relationship. Then, the Fourier transform inversion from incomplete data is dealt with by means of the singular value decomposition (SVD) approach and the features of the reconstructable unknowns are investigated. Finally, numerical results confirm the performed analysis.

The problem of determining the achievable resolution limits in the reconstruction of a current distribution is considered. The analysis refers to the one-dimensional, scalar case of a rectilinear, bounded electric current distribution when data are collected by measurement of the radiated field over a finite rectilinear observation domain located in the Fresnel zone, orthogonal and centered with respect to the source. The investigation is carried out by means of analytical singular-value decomposition of the radiation operator connecting data and unknown, which is made possible by the introduction of suitable scalar products in both the unknown and data spaces. This strategy permits the use of the results concerning prolate spheroidal wave functions described by B. R. Frieden [Progress in Optics Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam 1971), p. 311.] For values of the space-bandwidth product much larger than 1, the steplike behavior of the singular values reveals that the inverse problem is severely ill posed. This, in turn, makes it mandatory to use regularization to obtain a stable solution and suggests a regularization scheme based on a truncated singular-value decomposition. The task of determining the depth-resolving power is accomplished with resort to Rayleigh's criterion, and the effect of the geometrical parameters of the measurement configuration is also discussed.

The information content of radiated fields and the achievable resolution limits in the reconstruction of a bounded current distribution are dealt with. The analysis refers to the scalar and one dimensional case of a rectilinear and bounded electric current distribution when data are collected over a segment location in the Fresnel or near zone, orthogonal and centered with respect to the source. In the Fresnel zone, the investigation is carried out by means of the analytical Singular Value Decomposition (SVD) of the radiation operator providing the unknown-data mapping. This has been made possible thanks to the introduction of suitable weighted scalar products both in the unknown and data spaces. In the near zone, a numerical approach based on the SVD of the radiation operator has been followed. The effect of the geometrical parameters of the measurement configuration on depth resolving power is also discussed.

We have developed a numerical code that, starting from far-field intensity measurements, is able to evaluate the excitation coefficients of the transverse modes in a laser system.Both the coherent and incoherent mode cases are addressed, and, while the incoherent case is shown to be equivalent to a linear problem, the coherent case is discussed through its equivalence to the phase-retrieval problem. Problems arising from both ill posedness and the nonlinearity are discussed in detail.The validity of our approach is confirmed by several numerical simulations and some experimental results on the characterization of a Q-switched Nd:YAG laser.

A new method for the estimation of the far field from two amplitude distributions in near zone is presented. The crucial point of the proposed approach relies on the choice of an appropriate function of the data, which is minimised in order to find the solution. It turns out that, although the problem is nonlinear, the global minimum can be found efficiently by a Newton-like minimisation procedure.

The newly developed pseudo-sampling representation is applied for computing the far field of an offset parabolic reflector with a cluster feed illumination. A new comb-type fast Fourier transform (FFT) algorithm is used in a computer program. Both precision and computational time are analyzed, demonstrating the excellent performance of the method.