Riccardo Borghi

Università Degli Studi Roma Tre, Roma, Latium, Italy

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Publications (127)205.2 Total impact

  • Marco Lanucara, Riccardo Borghi
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    ABSTRACT: In Very Long Baseline Interferometry, signals from far radio sources are simultaneously recorded at different antennas, with the purpose of investigating their physical properties. The recorded signals are generally modeled as realizations of Gaussian processes, whose power is dominated by the system noise at the receiving antennas. The actual signal coming from the radio source can be detected only after cross-correlation of the various data-streams. The signals received at each antenna are digitized after low noise amplification and frequency down-conversion, in order to allow subsequent digital post-processing. The applied quantization is coarse, 1 or 2 bits being generally associated to the signal amplitude. In modern applications the sampling is typically performed at a high rate, and subchannels are then generated by filtering, followed by decimation and requantization of the signal streams. The redigitized streams are then cross-correlated to extract the physical observables. While the classical effect of quantization has widely been studied in the past, the decorrelation induced by the filtering and requantization process is still characterized experimentally, mainly due to its inherent mathematical complexity. In the present work we analyze the above problem, and provide algorithms and analytical formulas aimed at predicting the induced decorrelation for a wide class of quantization schemes, with the unique assumption of weakly correlated signals, typically fulfilled in VLBI and radio astronomy applications.
    Digital Signal Processing 03/2013; 23(2):522–529. · 1.92 Impact Factor
  • Marco Lanucara, Riccardo Borghi
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    ABSTRACT: We study the reconstruction of a Gaussian random signal, subject to extreme clipping. The reconstruction is achieved by adding a high frequency sinusoidal reference signal prior to the hard-limiter, and by low pass filtering the output. Such a scheme belongs to the area of signal reconstruction from Sine Wave Crossings (SWC). In the present paper we study in detail the effect of sampling in time domain on the reconstruction algorithm, and we carry out an analysis, valid for high sampling rates, leading to approximate analytical expressions of the cross-correlation coefficient between the signal and its reconstructed version. As a result of our analysis, the best achievable cross-correlation coefficient, together with the corresponding setting of the configuration parameters, i.e., the frequency and power of the reference signal, is obtained as a function of the sampling rate. Asymptotic closed form formulas are derived in the limit of very large sampling rates.
    Digital Signal Processing 12/2012; 22(6):1044–1055. · 1.92 Impact Factor
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    Riccardo Borghi
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    ABSTRACT: A didactical exposition of the classical problem of the trajectory determination of a body, subject to the gravity in a resistant medium, is proposed. Our revisitation is aimed at showing a derivation of the problem solution which should be as simple as possible from a technical point of view, in order to be grasped even by first-year undergraduates. A central role in our analysis is played by the so-called "chain rule" for derivatives, which is systematically used to remove the temporal variable from Newton's law to derive the differential equation of the Cartesian representation of the trajectory, with a considerable reduction of the overall mathematical complexity. In particular, for a resistant medium exerting a force quadratic with respect to the velocity our approach leads, in an elementary way, to the differential equation of the trajectory, which is subsequently solved by series expansion. A comparison of the polynomial approximants obtained by truncating such series with the solution recently proposed through a homotopy analysis is also presented.
    European Journal of Physics 11/2012; 34(2). · 0.64 Impact Factor
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    ABSTRACT: We show that the cross-spectral density in the far zone of a homogeneous spherical source can be described as a low-pass filtered version of that existing across the source surface. We prove that, to an excellent approximation, the corresponding filter with respect to a (normalized) spatial frequency ξ has a functional structure of the form √(1-ξ2), for 0≤ξ≤1. The cases of spatially incoherent and Lambertian sources are treated as significant examples.
    Optics Letters 08/2012; 37(15):3183-5. · 3.39 Impact Factor
  • Riccardo Borghi
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    ABSTRACT: A computational strategy, aimed at evaluating diffraction catastrophes belonging to the X(9) family is presented. The approach proposed is based on the use of power series expansions, suitably derived for giving meaningful representation of the whole (0)X(9) subfamily, jointly with a powerful sequence transformation algorithm, the so-called Weniger transformation. The convergence features of the above series expansions are investigated, and several numerical experiments are carried out to assess the effectiveness of the retrieving action of the Weniger transformation, as well as the ease of implementation of the whole approach.
    Physical Review E 04/2012; 85(4 Pt 2):046704. · 2.31 Impact Factor
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    ABSTRACT: A general procedure is presented for the evaluation of the modes of a thin annular scalar source, whose angular mutual intensity is of the Schell-model type. Starting from the knowledge of the modes, the coherence properties of the field propagated from the source in paraxial conditions can be evaluated. When the propagated field is collimated by a suitable converging lens, presented results apply to the synthesis of propagation-invariant partially coherent beams.
    Journal of optics 01/2012; 14(3). · 2.01 Impact Factor
  • Riccardo Borghi
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    ABSTRACT: A didactical revisitation of the so-called tumbling toast problem is presented here. The numerical solution of the related Newton's equations has been found in the space domain, without resorting to the complete time-based law of motion, with a considerable reduction of the mathematical complexity of the problem. This could allow the effect of the different physical mechanisms ruling the overall dynamics to be appreciated in a more transparent way, even by undergraduates. Moreover, the availability from the literature of experimental investigations carried out on tumbling toast allows us to propose different theoretical models of growing complexity in order to show the corresponding improvement of the agreement between theory and observation.
    European Journal of Physics 01/2012; 33(5):1407-1420. · 0.64 Impact Factor
  • Riccardo Borghi
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    ABSTRACT: A theoretical analysis is proposed, aimed at investigating the character of those power series expansions recently considered for the evaluation of several types of diffraction catastrophes. A hyperlinear convergence is found to be the signature for such expansions, so that the results of the numerical experiments recently carried out find a meaningful interpretation in terms of the accelerating action operated by the Weniger transformation. As an important by-product of our analysis, simple criteria, aimed at numerically optimizing the diffraction catastrophe evaluations, are provided through analytical expressions.
    Optics Letters 11/2011; 36(22):4413-5. · 3.39 Impact Factor
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    Riccardo Borghi
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    ABSTRACT: The evaluation of the two diffraction catastrophes of codimension four, namely, the butterfly and the parabolic umbilic, is here proposed by means of a simple computational approach developed in the past to characterize the whole hierarchy of the structurally stable diffraction patterns produced by optical diffraction in three-dimensional space. In particular, after expanding the phase integral representations of butterfly and parabolic umbilic in terms of (slowly) convergent power series, the retrieving action of the Weniger transformation on them is investigated through several numerical experiments. We believe that the methodology and the results presented here could also be of help for the dissemination of catastrophe optics to the widest scientific audience.
    Journal of the Optical Society of America A 05/2011; 28(5):887-96. · 1.67 Impact Factor
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    ABSTRACT: A theoretical analysis aimed at investigating the divergent character of perturbative series involved in the study of free-space nonparaxial propagation of vectorial optical beams is proposed. Our analysis predicts a factorial divergence for such series and provides a theoretical framework within which the results of recently published numerical experiments concerning nonparaxial propagation of vectorial Gaussian beams find a meaningful interpretation in terms of the decoding operated on such series by the Weniger transformation.
    Optics Letters 03/2011; 36(6):963-5. · 3.39 Impact Factor
  • Riccardo Borghi
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    ABSTRACT: A simple computational approach is proposed for the evaluation of umbilic diffraction catastrophes which, together with cuspoids, describe the whole hierarchy of the structurally stable diffraction patterns that can be produced by optical diffraction. In this paper, after expanding the double integral representations of hyperbolic and elliptic umbilics as convergent power series, the action of the Weniger transformation on them is studied. Exact expressions for the "on-axis" umbilic field have also been found, which extend previously published results to complex values of the control parameter. Numerical experiments aimed at giving evidence of the effectiveness and implementative ease of the approach are eventually presented.
    Journal of the Optical Society of America A 07/2010; 27(7):1661-70. · 1.67 Impact Factor
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    ABSTRACT: We develop an electromagnetic analysis for partially correlated thin annular sources. The elements of the correlation matrix are assumed to depend only on the angular distance between two typical points. For any such source, we show how the modal expansion can be found. Correlation changes upon free propagation are discussed. Further, examples and possible synthesis schemes are presented.
    Journal of the Optical Society of America A 06/2010; 27(6):1450-6. · 1.67 Impact Factor
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    ABSTRACT: The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized.
    Journal of the Optical Society of America A 02/2010; 27(2):188-99. · 1.67 Impact Factor
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    ABSTRACT: The issue raised in this Letter is classical, not only in the sense of being nonquantum, but also in the sense of being quite ancient: which subset of 4x4 real matrices should be accepted as physical Mueller matrices in polarization optics? Nonquantum entanglement or inseparability between the polarization and spatial degrees of freedom of an electromagnetic beam whose polarization is not homogeneous is shown to provide the physical basis to resolve this issue in a definitive manner.
    Physical Review Letters 01/2010; 104(2):023901. · 7.73 Impact Factor
  • Riccardo Borghi, Franco Gori, Sergey A Ponomarenko
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    ABSTRACT: We present a general theory of electromagnetic diffraction-free beams composed of uncorrelated Bessel modes. Our approach is based on the direct application of the nonnegativity constraint to the cross-spectral density tensor describing the electromagnetic field distribution. The field correlation properties are most conveniently derived in the spatial frequency domain, where the angular spectrum takes on the form of an infinitely thin ring. We also present several examples, including a vector generalization of the recently introduced dark and antidark diffraction-free beams.
    Journal of the Optical Society of America A 11/2009; 26(11):2275-81. · 1.67 Impact Factor
  • Riccardo Borghi, Miguel A Alonso
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    ABSTRACT: A systematic procedure for deriving the complete asymptotic series in inverse powers of the distance from the origin of free-space 2D and 3D, scalar and vectorial, monochromatic electromagnetic fields is derived here. Each term of the series is expressed in closed form through the use of a differential operator acting on the angular spectrum. A simple recursive routine for computing the derivatives is provided. Examples of application are also given.
    Journal of the Optical Society of America A 11/2009; 26(11):2410-7. · 1.67 Impact Factor
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    Riccardo Borghi
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    ABSTRACT: The use of hyperasymptotics (H) and the Weniger transformation (WT) has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals evaluated across Stokes sets [R. Borghi, Phys. Rev. E 78, 026703 (2008)]. In the present sequel, the full development of the hyperasymptotic-Weniger transformation (H-WT) up to the second order in H is derived. Numerical experiments, carried out on several classes of saddle-point integrals, including the swallowtail diffraction catastrophe, show the effectiveness of the second-level H-WT, in particular when the integrals are evaluated beyond the asymptotic realm.
    Physical Review E 08/2009; 80(1 Pt 2):016704. · 2.31 Impact Factor
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    Riccardo Borghi
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    ABSTRACT: A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse powers and in inverse rising factorials of $n$, are obtained. It is found that the corresponding expanding coefficients are expressed, in closed form, in terms of exponential polynomials, well known in combinatorics, and in terms of associated Laguerre polynomials, respectively. A study of the divergence and/or of the convergence of the above expansions is also carried out for positive values of the Euler series argument.
    Applied Numerical Mathematics 07/2009; · 1.15 Impact Factor
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    ABSTRACT: A procedure for the synthesis of the most general electromagnetic Schell-model light source is proposed. It makes use of the generalized van Cittert-Zernike theorem to produce the electromagnetic source starting from a primary spatially incoherent source, characterized by a suitable position-dependent polarization matrix. By resorting to the spectral decomposition of the polarization matrix, it is shown how such an incoherent source can be synthesized by using a Mach-Zehnder interferometer, with suitable amplitude transmittances placed in its arms, fed by two mutually uncorrelated laser beams. Examples are given for the case of electromagnetic Gaussian Schell-model sources.
    Journal of the Optical Society of America A 07/2009; 26(6):1437-43. · 1.67 Impact Factor
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    ABSTRACT: The Mueller-Stokes formalism which governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could demand of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller matrix of some physical system is that $M$ should map $\Omega^{({\rm pol})}$, the positive cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability or non-quantum entanglement brings in additional constraints that a pre-Mueller matrix $M$ mapping $\Omega^{({\rm pol})}$ into itself needs to meet in order that it is an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. Comment: 16 pages. Talk presented at the Koli Workhsop on `Partial Electromagnetic Coherence and 3D Polarization'
    06/2009;

Publication Stats

1k Citations
205.20 Total Impact Points

Institutions

  • 1998–2013
    • Università Degli Studi Roma Tre
      • • Department of Applied Electronics
      • • Department of Mathematics and Physics
      • • Department of Electronic Engineering
      Roma, Latium, Italy
  • 2009
    • Consorzio Nazionale Interuniversitario per le Scienze del Mare
      Roma, Latium, Italy
  • 2006
    • University of Rochester
      • Institute of Optics
      Rochester, NY, United States
  • 1995–2002
    • Sapienza University of Rome
      • • Department of Astronautics, Electrical and Energetics Engineering DIAEE
      • • Department of Physics
      Roma, Latium, Italy
  • 2001
    • Complutense University of Madrid
      • Departamento de Óptica
      Madrid, Madrid, Spain
  • 2000–2001
    • Universidad Politécnica de Madrid
      • Departamento de Matemática Aplicada (ETSI de Sistemas Informaticos)
      Madrid, Madrid, Spain
  • 1996–2000
    • The American University of Rome
      Roma, Latium, Italy