Spatial frequency

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 (as determined by the Fourier transform) 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 millimeter.

In wave mechanics, the spatial frequency is commonly denoted by ${\displaystyle \xi }$ or sometimes ${\displaystyle \nu }$, although the latter is also used to represent temporal frequency. It is related to the wavelength ${\displaystyle \lambda }$ by the formula

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