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 $\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 (images containing bands of white and black in a regular pattern) 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. In the general population of adults, the threshold for spatial frequency discrimination is about 7%. It is often poorer in dyslexic individuals .

Sinusoidal gratings and Michelson equation (and its role in contrast)

There is an important quantitative concept related to spatial frequency, known as the Michelson equation, shown here:

${\frac {I_{\mathrm {max} }-I_{\mathrm {min} }}{I_{\mathrm {max} }+I_{\mathrm {min} }}},$

In layman's terms, this is the ratio of the crest-trough distance to the maximum thereof, which is twice the average. One degree on the visual field represents four cycles on the wave pattern.

See also

• Fourier transform
• Fourier analysis

External links

• Kalloniatis, Michael; Luu, Charles (2007). "Webvision: Part IX Psychophysics of Vision. 2 Visual Acuity, Contrast Sensitivity". University of Utah. Retrieved July 2009. {{cite web}}: Check date values in: |accessdate= (help)
• "The Contrast Sensitivity Function (CSF)". University of South Dakota Internet Psychology Laboratory. Retrieved July 2009. {{cite web}}: Check date values in: |accessdate= (help) (with on-line demonstration)