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In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components of the structure repeat per unit of distance. The SI unit of spatial frequency is cycles per meter. In image-processing applications, spatial frequency is often expressed in units of cycles per millimeter or equivalently line pairs per mm.
In wave propagation, the spatial frequency is also known as wavenumber. Ordinary wavenumber is defined as the reciprocal of wavelength λ {\displaystyle \lambda } and is commonly denoted by ξ {\displaystyle \xi } or sometimes ν {\displaystyle \nu } :
Angular wavenumber k {\displaystyle k} , expressed in rad per m, is related to ordinary wavenumber and wavelength by