Perceived visual angle
The visual angle, V degrees, subtended by a viewed object sometimes looks larger or smaller than its actual value, creating a visual angle illusion (V-illusion).
These V-illusions have been explicitly described by many vision researchers, including Joynson (1949), McCready (1963, 1965, 1985), Rock & McDermott (1964), Baird (1970), Ono (1970) , Roscoe (1985, 1989), Hershenson (1982, 1989), Reed (1984, 1989), Enright (1989), Plug & Ross (1989, 1994), Higashiyama & Shimono (1994), Gogel, & Eby (1997), Ross & Plug (2002), and Murray, Boyaci & Kersten (2006).
V-illusions are most obvious as relative V-illusions in which two objects that subtend the same visual angle appear different angular sizes; it is as if their equal-sized images on the retina were of different sizes.
Specifically, the researchers noted above have advocated the relatively new idea that many of the best-known "size" illusions see Note 3 clearly demonstrate that, for most observers, the (subjective) perceived visual angle, V' deg, can change for a viewed target that subtends a constant (physical) visual angle, V deg.
Indeed, various experiments have revealed most of the factors responsible for these V-illusions, and a few different explanations for them have been published (Baird, Wagner, & Fuld, 1990, Enright, 1987, 1989, Hershenson, 1982, 1989, Komoda & Ono, 1974, McCready, 1965, 1985, 1986, 1994, Ono, 1970, Oyama, 1977, Reed, 1984, 1989, Restle, 1970, Roscoe, 1985, 1989).
On the other hand, nearly all discussions (and explanations) of those classic "size" illusions found in textbooks, the popular media, and on the internet use, instead, a very old viewpoint (hypothesis) that the visual angle is not perceivable. That's why they do not (cannot) properly describe or explain the illusions that most people suffer.
In order to clarify the "new" idea paradigm which wholly replaces the old one, it helps to keep in mind that an angle is the difference between two directions from a common point (the vertex). Accordingly, as described below, the visual angle, V deg, is the difference between two real (optical) directions in the field of view , while the perceived visual angle, V' deg, is the difference by which the directions of two viewed points from oneself appear to differ in the visual field.
Consider some definitions.
The Physical Measures, S, D, V, R, and d.
Figure 1 illustrates an observer's eye looking at a frontal extent, AB, that has a linear size, S meters (also called its "metric size" or "tape-measure size"). The extent's lower endpoint at B lies D meters from point O, which for present purposes can represent the center of the eye's entrance pupil and the two nodal points (See visual angle)