On the singular spectrum of radiation operators in the non-reactive zone: the case of strip sources

In this work, the singular spectrum of radiation operators is studied for both magnetic and electric sources. The aim is to establish a theory that allow one to foresee the information content of the data as a function of the parameters of the radiation configuration. This is a classical problem and some results have been presented, mainly referring to the far-zone and the Fresnel paraxial zone. Here, we extend the previous studies by considering radiation configurations where no constraints on the source and observation domains are imposed as needed by the far-zone or the Fresnel paraxial zone approximation. However, it is assumed that evanescent waves are negligible. To keep the analysis simple, the case of strip currents is considered within a two-dimensional scalar geometry.

[1]  Hyunjoong Kim,et al.  Functional Analysis I , 2017 .

[2]  Francesco Soldovieri,et al.  On the information content of the radiated fields in the near zone over bounded domains , 1998 .

[3]  Giovanni Leone,et al.  Localizing a buried planar perfect electric conducting interface by multi-view data , 2008 .

[4]  M. Bertero Linear Inverse and III-Posed Problems , 1989 .

[5]  D. Jagerman $\varepsilon $-Entropy and Approximation of Bandlimited Functions , 1969 .

[6]  J. Goodman Introduction to Fourier optics , 1969 .

[7]  Miller,et al.  Electromagnetic degrees of freedom of an optical system , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  Enrico De Micheli,et al.  Fredholm Integral Equations of the First Kind and Topological Information Theory , 2016, ArXiv.

[9]  Raffaele Solimene,et al.  Role of diversity on the singular values of linear scattering operators: the case of strip objects. , 2013, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  D. Slepian,et al.  Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .

[11]  Raffaele Solimene,et al.  Number of degrees of freedom of the radiated field over multiple bounded domains. , 2007, Optics letters.

[12]  Loriano Bonora,et al.  String partition functions, Hilbert schemes and affine Lie algebra representations on homology groups , 2012, 1206.0664.

[13]  F. K. Gruber,et al.  New Aspects of Electromagnetic Information Theory for Wireless and Antenna Systems , 2008, IEEE Transactions on Antennas and Propagation.

[14]  Inverse Source Problem: a Comparison Between the Cases of Electric and Magnetic Sources , 2011 .

[15]  M. Menu,et al.  Effects of lens aberrations in some experiments of speckle interferometry , 1979 .

[16]  Giovanni Leone,et al.  Phase retrieval of radiated fields , 1995 .

[17]  Francis T. S. Yu,et al.  Light and information , 2015, Optical Memory and Neural Networks.

[18]  Raffaele Solimene,et al.  On the Singular Spectrum of the Radiation Operator for Multiple and Extended Observation Domains , 2013 .

[19]  A. Requicha,et al.  The zeros of entire functions: Theory and engineering applications , 1980, Proceedings of the IEEE.

[20]  E. Hille,et al.  On the characteristic values of linear integral equations , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[21]  G. D. Francia Degrees of Freedom of Image , 1969 .

[22]  Giovanni Leone,et al.  Information content of Born scattered fields: results in the circular cylindrical case , 1998 .

[23]  A Liseno,et al.  In-depth resolution for a strip source in the Fresnel zone. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  D. Miller,et al.  Communicating with waves between volumes: evaluating orthogonal spatial channels and limits on coupling strengths. , 2000, Applied optics.