Standard Linear Array
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In the context of
phased array In antenna theory, a phased array usually means an electronically scanned array, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving th ...
s, a standard linear array (SLA) is a
uniform linear array A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...
(ULA) of interconnected transducer elements, e.g. microphones or antennas, where the individual elements are arranged in a straight line spaced at one half of the smallest wavelength of the intended signal to be received and/or transmitted. Therefore, an SLA is a subset of the ULA category. The reason for this spacing is that it prevents
grating lobes For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, a spatial aliasing effect allows plane waves incident to the array from visible angles other than the desired direction to be coh ...
in the
visible region The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
of the array. Intuitively one can think of a ULA as spatial sampling of a signal in the same sense as time sampling of a signal. Grating lobes are identical to aliasing that occurs in time series analysis for an under-sampled signal. Per Shannon's
sampling theorem Sampling may refer to: *Sampling (signal processing), converting a continuous signal into a discrete signal * Sampling (graphics), converting continuous colors into discrete color components *Sampling (music), the reuse of a sound recording in ano ...
, the sampling rate must be at least twice the highest frequency of the desired signal in order to preclude spectral aliasing. Because the beam pattern (or
array factor An array is simply a group of objects, and the array factor is a measure of how much a specific characteristic changes because of the grouping. This phenomenon is observed when antennas are grouped together. The radiation (or reception) pattern of ...
) of a linear array is the Fourier transform of the element pattern, the sampling theorem directly applies, but in the spatial instead of spectral domain. The
discrete-time Fourier transform In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the ...
(DTFT) of a sampled signal is always periodic, producing "copies" of the spectrum at intervals of the sampling frequency. In the spatial domain, these copies are the grating lobes. The analog of radian frequency in the time domain is
wavenumber In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
, k = \frac radians per meter, in the spatial domain. Therefore the spatial sampling rate, in samples per meter, must be \geq 2 \frac \times \frac. The sampling interval, which is the inverse of the sampling rate, in meters per sample, must be \leq \frac.


References

{{Reflist Antennas (radio) Phased array radar