Foveal, para-foveal and peripheral vision work together to produce our entire visual perception, but each has distinct characteristics that are significant when discussing vision and lighting.
The fovea is the central area of the retina, also called the macula, extending about one degree out from the center of the eye (i.e. two degrees across). When we are "looking at" something, we are directing our eyes so the image is projected onto the fovea. This central area is filled with cone photoreceptors although the fovea contains fewer short (blue) cones and no rods at all. Foveal vision uses this area of the retina, and the response to radiation is described by the photopic sensitivity function, which is also the basis for the unit of "lumen" used throughout lighting calculations. An approximation of the two degree foveal visual field is the circle of a US penny held at (an adult's) arm's length.
Para-foveal describes the region surrounding the fovea, corresponding to the retinal area from two to ten degrees off-center. The response of the combined foveal and para-foveal regions to radiation is described by the variant of the photopic sensitivity function known as the CIE Supplementary Observer. This region of the retina has a mix of photoreceptors, with all three types of cones and rods present. An approximation of the ten degree para-foveal visual field is a circle with a four-inch diameter - like the top to a 1 lb coffee can - held at (an adult's) arm's length.
Peripheral refers to the region of the retina outside the central ten degree area. The periphery of the retina has a low density of cones of all three types, but is dominated by rods. The highest density of rods is between 10 and 30 degrees out, peaking at 20 degrees. This is the reason that dark-adapted astronomical observers "look away" from what they are observing (see a discussion of scotopic vision here). Since the ganglion connections between rods are more dense than between cones, this rod-dominance in the periphery corresponds to an increased sensitivity to motion detection too.
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