# Spatial frequency

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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 the structure repeats per unit of distance. The SI unit of spatial frequency is cycles per meter. In image processing applications, the spatial frequency often is measured as lines per millimeter, which is 1000 times smaller than the SI unit.

In wave mechanics, the spatial frequency $\nu \$ is related to the wavelength $\lambda \$ by

$\nu \ = \ { 1 \over \lambda }$

Likewise, the wave number k is related to spatial frequency and wavelength by

$k \ = \ 2 \pi \nu \ = \ { 2 \pi \over \lambda }$

### Visual perception

In the study of visual perception, sinusoidal gratings are frequently used to probe the capabilities of the visual system. In these stimuli, spatial frequency is expressed as the number of cycles per degree of visual angle.