scholarly journals Coherent electromagnetic field imaging through Fourier transform heterodyne

1998 ◽  
Author(s):  
B.J. Cooke ◽  
B.E. Laubscher ◽  
N.L. Olivas ◽  
R.M. Goeller ◽  
M. Cafferty ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Fourier Transform ◽  
Field Imaging

Field of a Uniformly Moving Charge in an Anisotropic Dispersive Medium

1973 ◽  
Vol 28 (6) ◽  
pp. 907-910
Author(s):  
S. Datta Majumdar ◽  
G. P. Sastry
Keyword(s):  
Electromagnetic Field ◽  
Fourier Transform ◽  
Point Charge ◽  
Rest Frame ◽  
Dispersive Medium ◽  
Scalar Potential ◽  
Fourier Integral ◽  
The Third ◽  
Dispersion Formula ◽  
The Fourier Transform

The electromagnetic field of a point charge moving uniformly in a uniaxial dispersive medium is studied in the rest frame of the charge. It is shown that the Fourier integral for the scalar potential breaks up into three integrals, two of which are formally identical to the isotropic integral and yield the ordinary and extraordinary cones. Using the convolution theorem of the Fourier transform, the third integral is reduced to an integral over the isotropic field. Dispersion is explicitly introduced into the problem and the isotropic field is evaluated on the basis of a simplified dispersion formula. The effect of dispersion on the field cone is studied as a function of the cut-off frequency.

scholarly journals МАТЕМАТИЧЕСКОЕ ОПИСАНИЕ ПРОЦЕДУР ПОСТРОЕНИЯ КОГЕРЕНТНЫХ ИЗОБРАЖЕНИЙ ПРИРОДНЫХ СРЕД В ЗОНЕ ФРАУНГОФЕРА МНОГОКАНАЛЬНЫМИ РАДИОТЕХНИЧЕСКИМИ СИСТЕМАМИ

2018 ◽  
pp. 92-97
Author(s):  
Валерий Константинович Волосюк ◽  
Семён Сергеевич Жила ◽  
Эдуард Алексеевич Цернэ ◽  
Александр Иванович Стороженко
Keyword(s):  
Electromagnetic Field ◽  
Fourier Transform ◽  
Spectral Component ◽  
Delta Function ◽  
Resonance Scattering ◽  
Ambiguity Function ◽  
Inverse Transformation ◽  
Basic Operation ◽  
Full Spectrum ◽  
Coherent Image

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

scholarly journals Laser field imaging through Fourier transform heterodyne

1999 ◽  
Author(s):  
Bradly J. Cooke ◽  
Amy E. Galbraith ◽  
Bryan E. Laubscher ◽  
Charlie E. M. Strauss ◽  
Nicholas L. Olivas ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Laser Field ◽  
Field Imaging

High Resolution Transmission Electron Microscopy

MRS Bulletin ◽  
1991 ◽  
Vol 16 (3) ◽  
pp. 27-33 ◽  
Author(s):  
J.M. Gibson
Keyword(s):  
Fourier Transform ◽  
Focal Plane ◽  
Materials Science ◽  
Image Plane ◽  
Real Space ◽  
Dark Field ◽  
Dark Field Imaging ◽  
Wave Nature ◽  
Transmission Electron ◽  
Field Imaging

The transmission electron microscope (TEM) has had a major impact on materials science in the last five decades, despite the fact that it is necessary to prepare thin samples in order to use the technique. The primary reason for this effectiveness is the ability to access both real space and diffraction data in the same instrument, and to filter in one and observe the effect in the other. This is possible because of the wave nature of electrons and the existence of effective magnetic lenses for focusing. Abbe showed that any lens has the ability to Fourier transform its input wavefield in its focal plane, and to provide a second Fourier transform in the image plane. This is schematically shown in Figure 1. A crystalline object will diffract only in certain directions, with Bragg angles (θB) depending on the inverse of the interplanar spacing. The diffraction pattern is a series of spots in the Fourier, or focal, plane of the lens. A filter placed in the focal plane serves to limit the resolution by limiting the bandwidth of the image, but it also can serve to select certain parts of the Fourier spectrum in the image. The simplest examples of this, as used in optical microscopy, are bright-field and dark-field imaging. In the former the un-scattered beam is allowed to reach the image, in the latter it is not.

scholarly journals Toward quantitative electromagnetic field imaging by differential-phase-contrast scanning transmission electron microscopy

Microscopy ◽  
2020 ◽  
Author(s):  
Takehito Seki ◽  
Yuichi Ikuhara ◽  
Naoya Shibata
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Electromagnetic Field ◽  
Scanning Transmission Electron Microscopy ◽  
Phase Contrast ◽  
Differential Phase ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Differential Phase Contrast ◽  
Field Imaging

Abstract Differential-phase-contrast scanning transmission electron microscopy (DPC STEM) is a technique to directly visualize local electromagnetic field distribution inside materials and devices at very high spatial resolution. Owing to the recent progress in the development of high-speed segmented and pixelated detectors, DPC STEM now constitutes one of the major imaging modes in modern aberration-corrected STEM. While qualitative imaging of electromagnetic fields by DPC STEM is readily possible, quantitative imaging by DPC STEM is still under development because of the several fundamental issues inherent in the technique. In this report, we review the current status and future prospects of DPC STEM for quantitative electromagnetic field imaging from atomic scale to mesoscopic scale.

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