Delta‐function identities and electromagnetic field singularities

1989 ◽  
Vol 57 (5) ◽  
pp. 455-456 ◽  
Author(s):  
Werner Weiglhofer
2018 ◽  
pp. 97-102
Author(s):  
Валерий Константинович Волосюк ◽  
Семён Сергеевич Жила ◽  
Глеб Сергеевич Черепнин ◽  
Эдуард Алексеевич Цернэ

The generalized structure of the electromagnetic field in the registration area is considered in the case of the solution of problems of remote sensing of the underlying surfaces. Examples of the existing radar and optical coherent devices are given. Analytical expressions for the electromagnetic field in the reception area when sounding is carried out in a near-field Fresnel region, in the assumption that the size of the field of registration and radiation is considerably less than a distance between them, are concretized. It is shown the main operations that are necessary for the recovery of coherent images in a near-field Fresnel region by the methods of multichannel signal processing. Research shows that as the amplitude-phase distribution of the registration field is necessary to choose the classical basic function of Fresnel transformation with the reversed sign in the exponent power. Formally, in an infinite range, the Fresnel transform is invertible, i.e. in the ideal case, the function can be completely restored. However physically to Fresnel's region satisfies area with finite sizes. From the analysis of the obtained operations over the received field, it follows that the radar or optical system forms an estimate of the coherent image in the form of a convolution of a true image of the underlying surface with an ambiguity function. Generally, this function contains two multipliers, one of which determines the resolution of recovery of the coherent image. In that specific case, when the linear sizes of the field of registration go to infinity, ambiguity function takes a form of delta function and the required image can be restored without distortions. It is offered to determine resolution by the width between first zeros of ambiguity function. For rectangular area ambiguity function has the form of two sinc functions which width is directly proportional to wavelength, to the height of sounding and is inversely proportional to the linear sizes of receiving area on the corresponding coordinates. Finally, it is mentioned that for the higher-quality coherent imaging with good resolution by the same receiving area it is necessary to perform scanning and movement in space


2018 ◽  
pp. 92-97
Author(s):  
Валерий Константинович Волосюк ◽  
Семён Сергеевич Жила ◽  
Эдуард Алексеевич Цернэ ◽  
Александр Иванович Стороженко

The structure of the electromagnetic field in the domain of its registration is considered in the case of the solution of problems of remote sensing of the underlying surfaces on the basis of the phenomenological approach. This approach is mainly based on the theory of ray optics and the Huygens-Fresnel principle. It allows to determine the radiated and scattered fields for complex types of surfaces. Analysis of the structure of the electromagnetic field shows that it can be regarded as a mathematical transformation over the true image of the surface. In this case, the basic procedures for the coherent imaging in the far-field Fraunhofer region by multichannel radio-engineering systems should be based on the inverse transformation. For incomplete restoration of the desired image, without the phase and attenuation due to propagation, the basic operation is the inverse Fourier transform on the angular coordinates. The quality of the imaging in the Fraunhofer zone is determined by the ambiguity function. In a simple case of a rectangular receiving domain, ambiguity function has the form of two sinc functions which width is proportional to wavelength, to height of sounding and the linear sizes of receiving domain. If the distance to each point of the surface is known, then it is possible to completely reconstruct the coherent image. In this case, it is necessary to apply sliding short-scale Fourier transform to the received electromagnetic field. Obtained results correspond to the classical theory of resonance scattering. While ambiguity function is constant in the infinite limits of integration for a specific fixed value of the direction, only one spectral component (spatial harmonic) can be extracted from the desired image.  it Is possible to allocate an ever wider range of spatial frequencies with the narrowing of the ambiguity function. In the limit, when the ambiguity function is a delta function, the full spectrum of frequencies of the desired image can be extracted, i.e. this function can be completely restored. If it is not possible to create a system with narrow ambiguity function then the higher-quality coherent image can be obtained by the same receiving domain by scanning or movement in space


1993 ◽  
Vol 3 (3) ◽  
pp. 363-371 ◽  
Author(s):  
A. Konrad ◽  
I. A. Tsukerman

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.


Author(s):  
Leemon B. McHenry

What kinds of things are events? Battles, explosions, accidents, crashes, rock concerts would be typical examples of events and these would be reinforced in the way we speak about the world. Events or actions function linguistically as verbs and adverbs. Philosophers following Aristotle have claimed that events are dependent on substances such as physical objects and persons. But with the advances of modern physics, some philosophers and physicists have argued that events are the basic entities of reality and what we perceive as physical bodies are just very long events spread out in space-time. In other words, everything turns out to be events. This view, no doubt, radically revises our ordinary common sense view of reality, but as our event theorists argue common sense is out of touch with advancing science. In The Event Universe: The Revisionary Metaphysics of Alfred North Whitehead, Leemon McHenry argues that Whitehead's metaphysics provides a more adequate basis for achieving a unification of physical theory than a traditional substance metaphysics. He investigates the influence of Maxwell's electromagnetic field, Einstein's theory of relativity and quantum mechanics on the development of the ontology of events and compares Whitehead’s theory to his contemporaries, C. D. Broad and Bertrand Russell, as well as another key proponent of this theory, W. V. Quine. In this manner, McHenry defends the naturalized and speculative approach to metaphysics as opposed to analytical and linguistic methods that arose in the 20th century.


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