Hyperfocal distance
Encyclopedia
In optics
and photography
, hyperfocal distance is a distance beyond which all objects can be brought into an "acceptable" focus
. There are two commonly used definitions of hyperfocal distance, leading to values that differ only slightly:
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.
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
.
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
.
(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.).
where
is hyperfocal distance
is focal length
is f-number
(
for aperture diameter 
)
is the circle of confusion
limit
For any practical f-number, the focal length is insignificant in comparison
with the first term, so that
This formula is exact for the second definition, if
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 
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.
using a circle of confusion of 0.03 mm, which is a value typically used in 35 mm photography, the hyperfocal distance according to Definition 1,
If the lens is focused at a distance of 10.5 m, then everything from half that distance (5.2 m) to infinity will be acceptably sharp in our photograph. With the formula for the Definition 2, the result is 10417 mm, a difference of 0.48%.
Note that the second definition assumes that the depth of field is symmetric around H (which is roughly correct for normal lenses) and therefore assumes a setting in which only half the depth of field is utilized (i.e., for a lens focused at infinity, the depth of field is 10.4 m to infinity).
Piper 1901 calls this phenomenon "consecutive depths of field" and shows how to test the idea easily. This is also among the earliest of publications to use the word hyperfocal.
The figure on the right illustrates this phenomenon.
The concepts of the two definitions of hyperfocal distance have a long history, tied up with the terminology for depth of field, depth of focus, circle of confusion, etc. Here are some selected early quotations and interpretations on the topic.
Their focal range is about 1000 times their aperture diameter, so it makes sense as a hyperfocal distance with COC value of f/1000, or image format diagonal times 1/1000 assuming the lens is a “normal” lens. What is not clear, however, is whether the focal range they cite was computed, or empirical.
That is, a is the reciprocal of what we now call the f-number, and the answer is evidently in meters. His 0.41 should obviously be 0.40. Based on his formulae, and on the notion that the aperture ratio should be kept fixed in comparisons across formats, Abney says:
This formula implies a stricter COC criterion than we typically use today.
This "mathematically" observed relationship implies that he had a formula at hand, and a parameterization with the f-number or “intensity ratio” in it. To get an inverse-square relation to focal length, you have to assume that the COC limit is fixed and the aperture diameter scales with the focal length, giving a constant f-number.
It is unclear what distinction he means. Adjacent to Table I in his appendix, he further notes:
At this point we do not have evidence of the term hyperfocal before Piper, nor the hyphenated hyper-focal which he also used, but he obviously did not claim to coin this descriptor himself.
for hyperfocal distance, 
for aperture diameter, 
for the diameter that a circle of confusion shall not exceed, and 
for focal length, he derives:
http://books.google.com/books?id=AN6d4zTjquwC&pg=PA78
As the aperture diameter,
is the ratio of the focal length, 
to the numerical aperture, 
; and the diameter of the circle of confusion, 
, this gives the equation for the first definition above.
His drawing makes it clear that his e is the radius of the circle of confusion. He has clearly anticipated the need to tie it to format size or enlargement, but has not given a general scheme for choosing it.
Johnson's use of former and latter seem to be swapped; perhaps former was here meant to refer to the immediately preceding section title Depth of Focus, and latter to the current section title Depth of Field. Except for an obvious factor-of-2 error in using the ratio of stop diameter to COC radius, this definition is the same as Abney's hyperfocal distance.
Kingslake uses the simplest formulae for DOF near and far distances, which has the effect of making the two different definitions of hyperfocal distance give identical values.
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
and photography
Photography
Photography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...
, hyperfocal distance is a distance beyond which all objects can be brought into an "acceptable" focus
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
. There are two commonly used definitions of hyperfocal distance, leading to values that differ only slightly:
Definition 1: The hyperfocal distance is the closest distance at which a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
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.
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
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...
.
As the hyperfocal distance is the focus distance giving the maximum depth of field
Depth of field
In optics, particularly as it relates to film and photography, depth of field is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image...
, it is the most desirable distance to set the focus of a fixed-focus camera
Fixed focus lens
A photographic lens for which the focus is not adjustable is called a fixed-focus lens. The focus is set at the time of manufacture, and remains fixed...
.
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 confusionCircle of confusion
In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source...
(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.).
Formulae
For the first definition,where
is hyperfocal distance is focal lengthFocal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...
is f-numberF-number
In optics, the f-number of an optical system expresses the diameter of the entrance pupil in terms of the focal length of the lens; in simpler terms, the f-number is the focal length divided by the "effective" aperture diameter...
(
for aperture diameter ) is the circle of confusionCircle of confusion
In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source...
limit
For any practical f-number, the focal length is insignificant in comparison
with the first term, so that
This formula is exact for the second definition, if
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 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.Example
As an example, for a 50 mm lens at using a circle of confusion of 0.03 mm, which is a value typically used in 35 mm photography, the hyperfocal distance according to Definition 1,If the lens is focused at a distance of 10.5 m, then everything from half that distance (5.2 m) to infinity will be acceptably sharp in our photograph. With the formula for the Definition 2, the result is 10417 mm, a difference of 0.48%.
Note that the second definition assumes that the depth of field is symmetric around H (which is roughly correct for normal lenses) and therefore assumes a setting in which only half the depth of field is utilized (i.e., for a lens focused at infinity, the depth of field is 10.4 m to infinity).
Mathematical phenomenon
The hyperfocal distance is a curious property: While a lens focused at 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 extend from H/3 to H; if the lens is then focused to H/3, the depth of field will extend from H/4 to H/2. This continues on through all successive 1/x values of the hyperfocal distance.Piper 1901 calls this phenomenon "consecutive depths of field" and shows how to test the idea easily. This is also among the earliest of publications to use the word hyperfocal.
The figure on the right illustrates this phenomenon.
History
Sutton and Dawson 1867
Thomas Sutton and George Dawson define focal range for what we now call hyperfocal distance:Their focal range is about 1000 times their aperture diameter, so it makes sense as a hyperfocal distance with COC value of f/1000, or image format diagonal times 1/1000 assuming the lens is a “normal” lens. What is not clear, however, is whether the focal range they cite was computed, or empirical.
Abney 1881
Sir William de Wivelesley Abney says:That is, a is the reciprocal of what we now call the f-number, and the answer is evidently in meters. His 0.41 should obviously be 0.40. Based on his formulae, and on the notion that the aperture ratio should be kept fixed in comparisons across formats, Abney says:
Taylor 1892
John Traill Taylor recalls this word formula for a sort of hyperfocal distance:This formula implies a stricter COC criterion than we typically use today.
Hodges 1895
John Hodges discusses depth of field without formulas but with some of these relationships:This "mathematically" observed relationship implies that he had a formula at hand, and a parameterization with the f-number or “intensity ratio” in it. To get an inverse-square relation to focal length, you have to assume that the COC limit is fixed and the aperture diameter scales with the focal length, giving a constant f-number.
Piper 1901
C. Welborne Piper may be the first to have published a clear distinction between Depth of Field in the modern sense and Depth of Definition in the focal plane, and implies that Depth of Focus and Depth of Distance are sometimes used for the former (in modern usage, Depth of Focus is usually reserved for the latter). He uses the term Depth Constant for H, and measures it from the front principal focus (i. e., he counts one focal length less than the distance from the lens to get the simpler formula), and even introduces the modern term:It is unclear what distinction he means. Adjacent to Table I in his appendix, he further notes:
At this point we do not have evidence of the term hyperfocal before Piper, nor the hyphenated hyper-focal which he also used, but he obviously did not claim to coin this descriptor himself.
Derr 1906
Louis Derr may be the first to clearly specify the first definition, which is considered to be the strictly correct one in modern times, and to derive the formula corresponding to it. Using for hyperfocal distance, for aperture diameter, for the diameter that a circle of confusion shall not exceed, and for focal length, he derives: http://books.google.com/books?id=AN6d4zTjquwC&pg=PA78As the aperture diameter,
is the ratio of the focal length, to the numerical aperture, ; and the diameter of the circle of confusion, , this gives the equation for the first definition above.Johnson 1909
George Lindsay Johnson uses the term Depth of Field for what Abney called Depth of Focus, and Depth of Focus in the modern sense (possibly for the first time), as the allowable distance error in the focal plane. His definitions include hyperfocal distance:His drawing makes it clear that his e is the radius of the circle of confusion. He has clearly anticipated the need to tie it to format size or enlargement, but has not given a general scheme for choosing it.
Johnson's use of former and latter seem to be swapped; perhaps former was here meant to refer to the immediately preceding section title Depth of Focus, and latter to the current section title Depth of Field. Except for an obvious factor-of-2 error in using the ratio of stop diameter to COC radius, this definition is the same as Abney's hyperfocal distance.
Others, early twentieth century
The term hyperfocal distance also appears in Cassell's Cyclopaedia of 1911, The Sinclair Handbook of Photography of 1913, and Bayley's The Complete Photographer of 1914.Kingslake 1951
Rudolf Kingslake is explicit about the two meanings:Kingslake uses the simplest formulae for DOF near and far distances, which has the effect of making the two different definitions of hyperfocal distance give identical values.
External links
- http://www.dofmaster.com/dofjs.html to calculate hyperfocal distance and depth of fieldDepth of fieldIn optics, particularly as it relates to film and photography, depth of field is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image...