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Concept# Spatial frequency

Summary

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 (m). In applications, spatial frequency is often expressed in units of cycles per millimeter (mm) or equivalently per mm.
In wave propagation, the spatial frequency is also known as wavenumber. Ordinary wavenumber is defined as the reciprocal of wavelength and is commonly denoted by or sometimes :
Angular wavenumber , expressed in rad per m, is related to ordinary wavenumber and wavelength by
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. Sine-wave gratings also differ from one another in amplitude (the magnitude of difference in intensity between light and dark stripes), and angle.
The spatial-frequency theory refers to the theory that the visual cortex operates on a code of spatial frequency, not on the code of straight edges and lines hypothesised by Hubel and Wiesel on the basis of early experiments on V1 neurons in the cat. In support of this theory is the experimental observation that the visual cortex neurons respond even more robustly to sine-wave gratings that are placed at specific angles in their receptive fields than they do to edges or bars. Most neurons in the primary visual cortex respond best when a sine-wave grating of a particular frequency is presented at a particular angle in a particular location in the visual field. (However, as noted by Teller (1984), it is probably not wise to treat the highest firing rate of a particular neuron as having a special significance with respect to its role in the perception of a particular stimulus, given that the neural code is known to be linked to relative firing rates.

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Planck constant

The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by . The reduced Planck constant, or Dirac constant, equal to divided by , is denoted by .

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