The notion of Visual angle or apparent angle comes up frequently in physiological optics, including to characterize the resolving power of the eye (Visual acuity). The apparent Visual angle and angular size is used to free itself from the distance between the eye and the observed target: a diameter of 1 cm at a distance of 1 meter will be imaged on the retina with a same size of a piece of a diameter of 2 cm at a distance of 2 metres.
The apparent angle integrates in a same size distance and size of the object. It can be used to quantify the power of eye resolution, which corresponds to the minimum angle below which we cannot separate two distinct point light sources (example: a pair of double stars). The term is also used of "resolving power.
Visual angle: units
The apparent Visual angle is expressed in different units: radians (for calculations), ('big' angles) degrees, or minutes and seconds of arc ('small ' angles). Fortunately, there are conversion formulas that allow to move from one unit to the other.
By following the path of a 'unit' (of RADIUS 1) circle, a 360 ° rotation is needed to achieve a full turn. The perimeter of this circle worth 2 Pi, we easily get the value in radians of an angle expressed in degrees: A (rad) = Pix (deg) / 180.
A radian value matches the angle which is formed by an arc of the same length as the RADIUS that generates it. When an object is part of an angle small (ex: 1 °, area of study of the OPD, or PI/180 = 0.017 radians), one can calculate the actual size of an object which we know the distance to the eye by multiplying it by the angle in radians (figure).
A degree is divided into 60 minutes of arc; each arc minute is divided into 60 seconds of arc.
The measurement of Visual acuity is based partly on the resolving power of the eye, which allows him to see distinct two points separated by a Visual angle which cannot be reduced under sentence to "confuse" the images (which are more separated).
Visual acuity is defined as the inverse of the value of the minimum angle of resolution expressed in minutes of arc, often referred to by the acronym MAR (Minimum Resolution Angle).
A resolution of 1 minute of arc power corresponds to be able to see two points as "distinct" that under tend an angle of 1/60e degree. It is a theoretical acuity of 1/1 = 10/10. A resolving power of 1.2 minutes of arc is a Visual acuity of 1 / 1.25 = 8/10, and 2 minutes of arc to a Visual acuity of 1/2 = 5/10.
Logically, more market increases, more Visual acuity decreases, and vice versa.
The visual angle of the lunar disk is half a degree, approximately 30 minutes of arc. This is approximately the angle under which the nail of an index saw elongated arm. The apparent diameter of Jupiter seen from Earth is close to 30 seconds of Arc, the SCNV resolution limit of the human eye; To the naked eye, Jupiter actually appears as a record and not a point for an observer with a good visual acuity.
Visual angle and cycles
The splitter power of the eye can also be expressed as the amount of "details" that it is able to "solve" when they are enrolled in a given angle (eg: 1 °). For example, an elemental detail consists of a "cycle", which connects two different luminance ranges (see also: spatial frequencies). The smaller the cycle, the more you can repeat it in a degree of angle (the cycles are all the more "fine" they are many). The resolution capacity of an eye can be quantified by the number of cycles it is able to discern in an apparent degree of visual angle. The contrast within each cycle, i.e. the difference between the minimum and maximum luminances, obviously plays an important role in this capacity. A visual acuity of 10/10 is equivalent to the power to discern 30 cycles (maximum contrast) per degree. A sharpness of 20/10 allows to solve 60 cycles per degree.