Editing Circle of confusion (section)

==History==

===Henry Coddington 1829===
Before it was applied to photography, the concept of circle of confusion was applied to optical instruments such as telescopes. {{harvtxt|Coddington|1829|p=[https://books.google.com/books?id=WI45AAAAcAAJ&pg=PA54 54]}} quantifies both a ''circle of least confusion'' and a ''least circle of confusion'' for a spherical reflecting surface.

{{Blockquote|This we may consider as the nearest approach to a simple focus, and term the ''circle of least confusion''.}}

===Society for the Diffusion of Useful Knowledge 1832===
The {{harvtxt|Society for the Diffusion of Useful Knowledge|1832|p=[https://books.google.com/books?id=fxsAAAAAQAAJ&pg=RA1-PA11 11]}} applied it to third-order aberrations:

{{Blockquote|This spherical aberration produces an indistinctness of vision, by spreading out every mathematical point of the object into a small spot in its picture; which spots, by mixing with each other, confuse the whole. The diameter of this circle of confusion, at the focus of the central rays F, over which every point is spread, will be L K (fig. 17.); and when the aperture of the reflector is moderate it equals the cube of the aperture, divided by the square of the radius (...): this circle is called the aberration of latitude.}}

===T.H. 1866===
Circle-of-confusion calculations: An early precursor to [[depth of field]] calculations is the {{harvtxt|TH|1866|p=138}} calculation of a circle-of-confusion diameter from a subject distance, for a lens focused at infinity; this article was pointed out by {{harvtxt|von Rohr|1899}}. The formula he comes up with for what he terms "the indistinctness" is equivalent, in modern terms, to

<math display=block>c = {f A \over S}</math>

for focal length {{mvar|f}}, aperture diameter {{mvar|A}}, and subject distance {{mvar|S}}. But he does not invert this to find the {{mvar|S}} corresponding to a given {{mvar|c}} criterion (i.e. he does not solve for the [[hyperfocal distance]]), nor does he consider focusing at any other distance than infinity.

He finally observes "long-focus lenses have usually a larger aperture than short ones, and ''on this account'' have less depth of focus" [his italic emphasis].

===Dallmeyer and Abney===
{{harvtxt|Dallmeyer|1892|p=24}}, in an expanded re-publication of his father [[John Henry Dallmeyer]]'s 1874 {{harv|Dallmeyer|1874}} pamphlet ''On the Choice and Use of Photographic Lenses'' (in material that is not in the 1874 edition and appears to have been added from a paper by J.H.D. "On the Use of Diaphragms or Stops" of unknown date), says:

{{Blockquote|Thus every point in an object out of focus is represented in the picture by a disc, or circle of confusion, the size of which is proportionate to the aperture in relation to the focus of the lens employed. If a point in the object is 1/100 of an inch out of focus, it will be represented by a circle of confusion measuring but 1/100 part of the aperture of the lens.}}

This latter statement is clearly incorrect, or misstated, being off by a factor of focal distance (focal length). He goes on:

{{Blockquote|and when the circles of confusion are sufficiently small the eye fails to see them as such; they are then seen as points only, and the picture appears sharp. At the ordinary distance of vision, of from twelve to fifteen inches, circles of confusion are seen as points, if the angle subtended by them does not exceed one minute of arc, or roughly, if they do not exceed the 1/100 of an inch in diameter.}}

Numerically, 1/100&nbsp;inch at 12–15&nbsp;inches is closer to two minutes of arc. This choice of CoC limit remains (for a large print) the most widely used even today. {{harvtxt|Abney|1881|pp=[https://books.google.com/books?id=3QpNAAAAMAAJ&pg=PA208 207–08]}} takes a similar approach based on a visual acuity of one minute of arc, and chooses a circle of confusion of 0.025&nbsp;cm for viewing at 40–50&nbsp;cm, essentially making the same factor-of-two error in metric units. It is unclear whether Abney or Dallmeyer was earlier to set the CoC standard thereby.

===Wall 1889===
The common 1/100&nbsp;inch CoC limit has been applied to blur other than defocus blur. For example, {{harvtxt|Wall|1889|p= [https://books.google.com/books?id=AkTTOsZEGLMC&pg=PA92 92]}} says:

{{Blockquote|To find how quickly a shutter must act to take an object in motion that there may be a circle of confusion less than 1/100&nbsp;in. in diameter, divide the distance of the object by 100 times the focus of the lens, and divide the rapidity of motion of object in inches per second by the results, when you have the longest duration of exposure in fraction of a second.}}