فاصله ابر کانونی
در علم اپتیک و عکاسی، فاصله ابر کانونی (به انگلیسی: Hyperfocal distance)، فاصلهای است که همه اشیاء در آن فاصله در میدان وضوح لنز قرار دارند. فاصله ابر کانونی، عمقی از زاویه دید لنز است (از نزدیکیهای لنز تا بینهایت) که آن محدوده، در میدان وضوح لنز قرار میگیرد. برای بدست آوردن این فاصله، ابتدا لنز در بازترین درجه دیافراگم، بر روی فاصله بینهایت تنظیم میکنیم، نزدیکترین نقطه فوکوس لنز، فاصله ابر کانونی لنز است. بهطور مثال اگر در این حالت نزدیکترین نقطه فوکوس فاصله ۷ متری از لنز دوربین است، فوکوس لنز را بر روی ۷ متر قرار داده و عکاسی میکنیم. در این حالت از نصف ۷ متری (از سه و نیم متری) دوربین الی بینهایت در میدان وضوح لنز قرار خواهند گرفت. البته درجه دیافراگم در این حالت حائز اهمیت است هر چه درجه دیافراگم بستهتر باشد، عمق میدان وضوح افزایش پیدا خواهد کرد.
In optics and photography, hyperfocal distance is a distance 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 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 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, 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.
There are two common methods 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.
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.).
For the first definition,
For any practical f-number, the added 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.
Derivation using geometric optics
The following derivations refer to the accompanying figures. For clarity, half the aperture and circle of confusion are indicated.
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,
Then using similar triangles dotted in purple,
Objects at infinity form sharp images at the focal length f (blue line). Here, an object at H forms an image with a circle of confusion indicated by the brown ellipse where the lower red ray converging to its sharp image intersects the blue line.
Using similar triangles shaded in yellow,
Depths of field of 3 ideal lenses of focal lengths, f1, f2 and f3, and f-numbers N1, N2 and N3 when focused at objects at different distances. H1, H2 and H3 denote their respective hyperfocal distances (using Definition 1 in that article) with a circle of confusion of 0.03 mm diameter. The darker bars show how that, for fixed subject distance, the depth of field is increased by using a shorter focal length or smaller aperture. The second topmost bar of each set illustrates the configuration for a fixed focus camera with the focus permanently set at the hyperfocal distance to maximise the depth of field.
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 is
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 0.5%.
Consecutive depths of field
The hyperfocal distance has 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.
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.
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.
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:
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.
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.
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.
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:
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.
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 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.