The receptive field of an individual sensory neuron is the particular part of the body surface in which a stimulus will trigger the firing of that neuron. This surface can be a hair in the cochlea or a piece of skin, retina, tongue or other part of an animal's body. Additionally, it can be the space surrounding an animal, such as an area of auditory space that is fixed in a reference system based on the ears but that moves with the animal as it moves (the space inside the ears), or in a fixed location in space that is largely independent of the animal's location (place cells). Receptive fields have been identified for neurons of the auditory system, the somatosensory system, and the visual system.
The term receptive field was first used by Sherrington (1906) to describe the area of skin from which a scratch reflex could be elicited in a dog. According to Alonso and Chen (2008)  it was Hartline (1938) who applied the terms to single neurons, in this case from the retina of a frog.
The concept of receptive fields can be extended further up to the neural system; if many sensory receptors all form synapses with a single cell further up, they collectively form the receptive field of that cell. For example, the receptive field of a ganglion cell in the retina of the eye is composed of input from all of the photoreceptors which synapse with it, and a group of ganglion cells in turn forms the receptive field for a cell in the brain. This process is called convergence.
In the auditory system, receptive fields can correspond to volumes in auditory space, or to regions of auditory frequencies. Researchers rarely equate auditory receptive fields to particular regions of the sensory epithelium such as, in the case of mammals, hair cells in the cochlea.
Large receptive fields allow the cell to detect changes over a wider area, but lead to a less precise perception. Thus, the fingers, which require the ability to detect fine detail, have many, densely packed (up to 500 per cubic cm) mechanoreceptors with small receptive fields (around 10 square mm), while the back and legs, for example, have fewer receptors with large receptive fields. Receptors with large receptive fields usually have a "hot spot", an area within the receptive field (usually in the center, directly over the receptor) where stimulation produces the most intense response.
Tactile-sense-related cortical neurons have receptive fields on the skin that can be modified by experience or by injury to sensory nerves resulting in changes in the field's size and position. In general these neurons have relatively large receptive fields (much larger than those of dorsal root ganglion cells). However, the neurons are able to discriminate fine detail due to patterns of excitation and inhibition relative to the field which leads to spatial resolution.
In the visual system, receptive fields are volumes in visual space. For example, the receptive field of a single photoreceptor is a cone-shaped volume comprising all the visual directions in which light will alter the firing of that cell. Its apex is located in the center of the lens and its base essentially at infinity in visual space. Traditionally, visual receptive fields were portrayed in two dimensions (e.g., as circles, squares, or rectangles), but these are simply slices, cut along the screen on which the researcher presented the stimulus, of the volume of space to which a particular cell will respond. In the case of binocular neurons in the visual cortex, receptive fields do not extend to optical infinity. Instead, they are restricted to a certain interval of distance from the animal, or from where the eyes are fixating (see Panum's area).
The receptive field is often identified as the region of the retina where the action of light alters the firing of the neuron. In retinal ganglion cells (see below), this area of the retina would encompass all the photoreceptors, all the rods and cones from one eye that are connected to this particular ganglion cell via bipolar cells, horizontal cells, and amacrine cells. In binocular neurons in the visual cortex, it is necessary to specify the corresponding area in both retinas (one in each eye). Although these can be mapped separately in each retina by shutting one or the other eye, the full influence on the neuron's firing is revealed only when both eyes are open.
Hubel and Wiesel (e.g., Hubel, 1963; Hubel-Wiesel, 1962) advanced the theory that receptive fields of cells at one level of the visual system are formed from input by cells at a lower level of the visual system. In this way, small, simple receptive fields could be combined to form large, complex receptive fields. Later theorists elaborated this simple, hierarchical arrangement by allowing cells at one level of the visual system to be influenced by feedback from higher levels. This hierarchy idea has inspired the deep (i.e., hierarchical) neural networks and deep learning recently. 
Receptive fields have been mapped for all levels of the visual system from photoreceptors, to retinal ganglion cells, to lateral geniculate nucleus cells, to visual cortex cells, to extrastriate cortical cells. Studies based on perception do not give the full picture of the understanding of visual phenomena, so the electrophysiological tools must be used, as the retina, after all, is an outgrowth of the brain.
Retinal ganglion cells
Each ganglion cell or optic nerve fiber bears a receptive field, increasing with intensifying light. In the largest field, the light has to be more intense at the periphery of the field than at the center, showing that some synaptic pathways are more preferred than others.
The organization of ganglion cells' receptive fields, composed of inputs from many rods and cones, provides a way of detecting contrast, and is used for detecting objects' edges. Each receptive field is arranged into a central disk, the "center", and a concentric ring, the "surround", each region responding oppositely to light. For example, light in the centre might increase the firing of a particular ganglion cell, whereas light in the surround would decrease the firing of that cell.
There are two types of retinal ganglion cells: "on-center" and "off-center". An on-center cell is stimulated when the center of its receptive field is exposed to light, and is inhibited when the surround is exposed to light. Off-center cells have just the opposite reaction. On the edge between the two, in mammals, an on-off effect (i.e., discharging at switching on or off but not at a duration of either state) is present. Stimulation of the center of an on-center cell's receptive field produces depolarization and an increase in the firing of the ganglion cell, stimulation of the surround produces a Hyperpolarization and a decrease in the firing of the cell, and stimulation of both the center and surround produces only a mild response (due to mutual inhibition of center and surround). An off-center cell is stimulated by activation of the surround and inhibited by stimulation of the center (see figure).
Photoreceptors that are part of the receptive fields of more than one ganglion cell are able to excite or inhibit postsynaptic neurons because they release the neurotransmitter glutamate at their synapses, which can act to depolarize or to hyperpolarize a cell, depending on whether there is a metabotropic or ionotropic receptor on that cell.
The center-surround receptive field organization allows ganglion cells to transmit information not merely about whether photoreceptor cells are exposed to light, but also about the differences in firing rates of cells in the center and surround. This allows them to transmit information about contrast. The size of the receptive field governs the spatial frequency of the information: small receptive fields are stimulated by high spatial frequencies, fine detail; large receptive fields are stimulated by low spatial frequencies, coarse detail. Retinal ganglion cell receptive fields convey information about discontinuities in the distribution of light falling on the retina; these often specify the edges of objects. In dark adaptation, the peripheral opposite activity zone becomes inactive, but, since it is a diminishing of inhibition between center and periphery, the active field can actually increase, allowing more area for summation.
The receptive field tends to favor movement (such as a light or dark spot moving over the field, as in center-to-periphery (or vice versa)), as well as contours (due to their nonuniformity in the receptive fields). The center of the visual field has as much diameter as its dendrite spread, so the periphery is founded by amacrine cells connecting a wide area of bipolars to the ganglion. These amacrine cells can also inhibit signals of the periphery from being transmitted to the ganglion, thus rendering it on-center, off-periphery. In the rabbit, one direction, the "preferred," of a moving patch of light will excite a ganglion cell, whereas the opposite ("null") direction will not, also inhibiting spontaneous activity. Thus, there may be a linear nature of photoreceptors, one inhibiting its following neighbor when moving in the null direction, but arriving too late at the adjacent cell when traveling in the preferred direction.
Lateral geniculate nucleus
Further along in the visual system, groups of ganglion cells form the receptive fields of cells in the lateral geniculate nucleus. Receptive fields are similar to those of ganglion cells, with an antagonistic center-surround system and cells that are either on- or off center.
Receptive fields of cells in the visual cortex are larger and have more-complex stimulus requirements than retinal ganglion cells or lateral geniculate nucleus cells. Hubel and Wiesel (e.g., Hubel, 1963; Hubel-Wiesel 1959) classified receptive fields of cells in the visual cortex into simple cells, complex cells, and hypercomplex cells. Simple cell receptive fields are elongated, for example with an excitatory central oval, and an inhibitory surrounding region, or approximately rectangular, with one long side being excitatory and the other being inhibitory. Images for these receptive fields need to have a particular orientation in order to excite the cell. For complex-cell receptive fields, a correctly oriented bar of light might need to move in a particular direction in order to excite the cell. For hypercomplex receptive fields, the bar might also need to be of a particular length.
|Simple||orientation, position||Brodmann area 17|
|Complex||orientation, motion, direction||Brodmann area 17 and 18|
|Hypercomplex||orientation, motion, direction, length||Brodmann areas 18 and 19|
Extrastriate visual areas
In extrastriate visual areas, cells can have very large receptive fields requiring very complex images to excite the cell. For example in the inferotemporal cortex, receptive fields cross the midline of visual space and require images such as radial gratings or hands. It is also believed that in the fusiform face area, images of faces excite the cortex more than other images. This property was one of the earliest major results obtained through fMRI (Kanwisher, McDermott and Chun, 1997); the finding was confirmed later at the neuronal level (Tsao, Freiwald, Tootell and Livingstone, 2006). In a similar vein, people have looked for other category-specific areas and found evidence for regions representing views of places (parahippocampal place area) and the body (Extrastriate body area). However, more recent research has suggested that the fusiform face area is specialised not just for faces, but also for any discrete, within-category discrimination. 
Computational theory of visual receptive fields
Idealized models of visual receptive fields similar to those found in the retina, lateral geniculate nucleus and the primary visual cortex of higher mammals can be derived in an axiomatic way from structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. Such receptive fields can be shown to enable computation of invariant visual representations under natural image transformations. By these results, the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, can be seen as well adapted to structure of the physical world and be explained from the requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.
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An open-access, refereed article on receptive fields: Alonso, J.-M., & Chen, Y. (2008). Receptive field. Scholarpedia, 4(1), 5393. doi: 10.4249/scholarpedia.5393