Hyperfocal distance

[1] The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable.

Thomas Sutton and George Dawson first wrote about hyperfocal distance (or "focal range") in 1867.

Rudolf Kingslake wrote in 1951 about the two methods of measuring hyperfocal distance.

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.

[3] There are two common methods of defining and measuring hyperfocal distance, leading to values that differ only slightly.

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.).

where For any practical f-number, the added focal length is insignificant in comparison with the first term, so that

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.

Objects at infinity form sharp images at the focal length f (blue line).

This continues on through all successive neighboring terms in the harmonic series (1/x) values of the hyperfocal distance.

C. Welborne Piper calls this phenomenon "consecutive depths of field" and shows how to test the idea easily.

stop (apertal ratio one-twenty-fourth), all objects situated at distances lying between 20 feet from the lens and an infinite distance from it (a fixed star, for instance) are in equally good focus.

The terms 'apertal ratio' and 'focal range' have not come into general use, but it is very desirable that they should, in order to prevent ambiguity and circumlocution when treating of the properties of photographic lenses.

Sir William de Wivelesley Abney says:[6] The annexed formula will approximately give the nearest point p which will appear in focus when the distance is accurately focussed, supposing the admissible disc of confusion to be 0.025 cm:

Based on his formulae, and on the notion that the aperture ratio should be kept fixed in comparisons across formats, Abney says: It can be shown that an enlargement from a small negative is better than a picture of the same size taken direct as regards sharpness of detail.

... Care must be taken to distinguish between the advantages to be gained in enlargement by the use of a smaller lens, with the disadvantages that ensue from the deterioration in the relative values of light and shade.John Traill Taylor recalls this word formula for a sort of hyperfocal distance:[7] We have seen it laid down as an approximative rule by some writers on optics (Thomas Sutton, if we remember aright), that if the diameter of the stop be a fortieth part of the focus of the lens, the depth of focus will range between infinity and a distance equal to four times as many feet as there are inches in the focus of the lens.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:[8] There is a point, however, beyond which everything will be in pictorially good definition, but the longer the focus of the lens used, the further will the point beyond which everything is in sharp focus be removed from the camera.

Mathematically speaking, the amount of depth possessed by a lens varies inversely as the square of its focus.This "mathematically" observed relationship implies that he had a formula at hand, and a parameterization with the f-number or "intensity ratio" in it.

Louis Derr may be the first to clearly specify the first definition,[9] which is considered to be the strictly correct one in modern times, and to derive the formula corresponding to it.

His definitions include hyperfocal distance: Depth of Focus is a convenient, but not strictly accurate term, used to describe the amount of racking movement (forwards or backwards) which can be given to the screen without the image becoming sensibly blurred, i.e. without any blurring in the image exceeding 1/100 in., or in the case of negatives to be enlarged or scientific work, the 1/10 or 1/100 mm.

Then the breadth of a point of light, which, of course, causes blurring on both sides, i.e. {{{1}}} (or {{{1}}}).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.

d being the diameter of the stop, ...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.

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.

Rudolf Kingslake is explicit about the two meanings:[1] if the camera is focused on a distance s equal to 1000 times the diameter of the lens aperture, then the far depth D1 becomes infinite.

It is worth noting, too, that if a camera is focused on s = ∞, the closest acceptable object is at L2 = sh/(h + s) = h/(h/s + 1) = h (by equation 21).