Fourier Transform and Radiation Pattern

Cuthbert Nyack
The Radiation patterns of radiation sources are related to the Fourier Transform. From loudspeakers, loudspeaker arrays, diffraction horns, optical sources to microwave and radio antennas can all be treated by the Fourier Transform or its relatives.
At long distances the radiation pattern of a center fed line antenna with length of n half wavelenghts is determined by the Fourier Transform of the current distribution.
The applet below shows the pattern for different n. As n increases, the power radiated along the antenna increases while that perpendicular to the antenna reduces.

The analog of multiple slit diffraction is the antenna array. For antennas above the radiation is isotropic in a plane perpendicular to the antenna. The use of arrays can produce patterns which concentrate the power in a direction perdendicular to the array. In the applet below n is the number of elements in the array. Elements of the array are assumed to be half a wavelength apart.

The radiation pattern of an aperture is shown below.

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COPYRIGHT 2005 Cuthbert Nyack.