Spatial frequency

Green Sea Shell image

Spatial frequency representation of the Green Sea Shell image

Image and its spatial frequencies: Magnitude of frequency domain is logarithmically scaled, and zero frequency is in the center. Notable is the clustering of the content on the lower frequencies, a typical property of natural images.

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 the reciprocal metre (m⁻¹),^[1] although cycles per meter (c/m) is also common. In image-processing applications, spatial frequency is often expressed in units of cycles per millimeter (c/mm) or also line pairs per millimeter (LP/mm).

In wave propagation, the spatial frequency is also known as wavenumber. Ordinary wavenumber is defined as the reciprocal of wavelength ${\displaystyle \lambda }$ and is commonly denoted by ${\displaystyle \xi }$^[2] or sometimes ${\displaystyle \nu }$:^[3] $${\displaystyle \xi ={\frac {1}{\lambda }}.}$$ Angular wavenumber ${\displaystyle k}$, expressed in radian per metre (rad/m), is related to ordinary wavenumber and wavelength by $${\displaystyle k=2\pi \xi ={\frac {2\pi }{\lambda }}.}$$