# Spatial frequency

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 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 $u$ is related to the wavelength $lambda$ by

:$u = \left\{ 1 over lambda \right\}$

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

:$k = 2 pi u = \left\{ 2 pi over lambda \right\}$

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.
Different spatial frequencies convey different information about the appearance of a stimulus. High spatial frequencies represent abrupt spatial changes in the image. such as edges, and generally correspond to configural information and fine detail. Low spatial frequencies, on the other hand, represent global information about the shape, such as general orientation and proportions. [ [http://www.nature.com/nrn/journal/v5/n8/box/nrn1476_BX2.html Box 2 : Visual objects in context : Nature Reviews Neuroscience ] ] In the general population of adults, the threshold for spatial frequency discrimination is about 7%. It is often poorer in dyslexic individuals [ [http://www.ncbi.nlm.nih.gov/pubmed/15031099?ordinalpos=4&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum Sequential spatial frequency discrimination is consistently impaired among adult dyslexics] ] .

References

ee also

*Fourier transform
*Fourier analysis

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Frequency — For other uses, see Frequency (disambiguation). Three cyclically flashing lights, from lowest frequency (top) to highest frequency (bottom). f is the frequency in hertz (Hz), meaning the number of cycles per second. T is the period in seconds (s) …   Wikipedia

• Spatial filter — A spatial filter is an optical device which uses the principles of Fourier optics to alter the structure of a beam of coherent light or other electromagnetic radiation. Spatial filtering is commonly used to clean up the output of lasers, removing …   Wikipedia

• Spatial disorientation — is a condition in which an aircraft pilot s perception of direction (proprioception) does not agree with reality. While it can be brought on by disturbances or disease within the vestibular system, it is more typically a temporary condition… …   Wikipedia

• Spatial capacity — is an indicator of data intensity in a transmission medium. It is usually used in conjunction with wireless transport mechanisms. This is analogous to the way that lumens per square meter determine illumination intensity. [citeweb|title=Ultra… …   Wikipedia

• Spatial anti-aliasing — In digital signal processing, spatial anti aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high resolution image at a lower resolution. Anti aliasing is used in digital photography, computer… …   Wikipedia

• Spatial cutoff frequency — In optics, spatial cutoff frequency is a precise way to quantify the smallest object resolvable by an optical system. Due to diffraction at the image plane, all optical systems act as low pass filters with a finite ability to resolve detail. If… …   Wikipedia

• Frequency distribution — In statistics, a frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and… …   Wikipedia

• Frequency (statistics) — In statistics the frequency of an event i is the number ni of times the event occurred in the experiment or the study. These frequencies are often graphically represented in histograms. We speak of absolute frequencies, when the counts ni… …   Wikipedia

• Frequency probability — Statistical probability redirects here. For the episode of Star Trek: Deep Space Nine, see Statistical Probabilities. John Venn Frequency probability is the interpretation of probability that defines an event s probability as the limit of its… …   Wikipedia

• Planck (télescope spatial) — Planck (satellite) Pour les articles homonymes, voir Planck. Planck Sa …   Wikipédia en Français