In optics and photography, hyperfocal distance is a distance from a lens beyond which all objects can be brought into an "acceptable" focus. As the hyperfocal distance is the focus distance giving the maximum depth of field, it is the most desirable distance to set the focus of a fixed-focus camera. The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable. The hyperfocal distance has a property called "consecutive depths of field", where a lens focused at an object whose distance from the lens is at the hyperfocal distance H will hold a depth of field from H/2 to infinity, if the lens is focused to H/2, the depth of field will be from H/3 to H; if the lens is then focused to H/3, the depth of field will be from H/4 to H/2, etc. Thomas Sutton and George Dawson first wrote about hyperfocal distance (or "focal range") in 1867. Louis Derr in 1906 may have been the first to derive a formula for hyperfocal distance. Rudolf Kingslake wrote in 1951 about the two methods of measuring hyperfocal distance. Some cameras have their hyperfocal distance marked on the focus dial. For example, on the Minox LX focusing dial there is a red dot between 2 m and infinity; when the lens is set at the red dot, that is, focused at the hyperfocal distance, the depth of field stretches from 2 m to infinity. Some lenses have markings indicating the hyperfocal range for specific f-stops, also called a depth-of-field scale.
Two definitions There are two common ways of defining and measuring hyperfocal distance, leading to values that differ only slightly. The distinction between the two meanings is rarely made, since they have almost identical values. The value computed according to the first definition exceeds that from the second by just one focal length.
Definition 1 The hyperfocal distance is the closest distance at which a lens can be focused while keeping objects at infinity acceptably sharp. When the lens is focused at this distance, all objects at distances from half of the hyperfocal distance out to infinity will be acceptably sharp. Definition 2 The hyperfocal distance is the distance beyond which all objects are acceptably sharp, for a lens focused at infinity.
Acceptable sharpness The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable. The criterion for the desired acceptable sharpness is specified through the circle of confusion (CoC) diameter limit. This criterion is the largest acceptable spot size diameter that an infinitesimal point is allowed to spread out to on the imaging medium (film, digital sensor, etc.).
Formula For the first definition,
H = f 2 N c + f {\displaystyle H={\frac {f^{2}}{Nc}}+f}
where
H is the hyperfocal distance; f is the focal length of the lens; N is f-number (f/D for aperture diameter D); and c is the circle of confusion limit. For any practical f-number, the added focal length is insignificant in comparison with the first term, so that
H ≈ f 2 N c . {\displaystyle H\approx {\frac {f^{2}}{Nc}}\,.}
This formula is exact for the second definition, if H is measured from a thin lens, or from the front principal plane of a complex lens; it is also exact for the first definition if H is measured from a point that is one focal length in front of the front principal plane. For practical purposes, there is little difference between the first and second definitions.
Derivation using geometric optics
The following derivations refer to the accompanying figures. For clarity, half the aperture and circle of confusion are indicated.
Definition 1 An object at distance H forms a sharp image at distance x (blue line). Here, objects at infinity have images with a circle of confusion indicated by the brown ellipse where the upper red ray through the focal point intersects the blue line. First using similar triangles hatched in green,
x − f c / 2 = f D / 2 ∴ x − f = c f D ∴ x = f + c f D {\displaystyle {\begin{array}{crcl}&{\dfrac {x-f}{c/2}}&=&{\dfrac {f}{D/2}}\\\therefore &x-f&=&{\dfrac {cf}{D}}\\\therefore &x&=&f+{\dfrac {cf}{D}}\end{array}}}
Then using similar triangles dotted in purple,
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