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In optics, a circle of confusion, (also known as disk of confusion, circle of indistinctness, blur circle, etc.), 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.

Two important uses of this term and concept need to be distinguished:

1. To calculate a camera's depth of field, one needs to know how large a circle of confusion can be considered to be an acceptable focus. The maximum acceptable diameter of such a circle of confusion is known as the maximum permissible circle of confusion, the circle of confusion diameter limit, or the circle of confusion criterion, but is often incorrectly called simply the circle of confusion.

2. Recognizing that real lenses do not focus all rays perfectly under even the best of conditions, the circle of confusion of a lens is a characterization of its optical spot. The term circle of least confusion is often used for the smallest optical spot a lens can make, for example by picking a best focus position that makes a good compromise between the varying effective focal lengths of different lens zones due to spherical or other aberrations. Diffraction effects from wave optics and the finite aperture of a lens can be included in the circle of least confusion, or the term can be applied in pure ray (geometric) optics.

In idealized ray optics, where rays are assumed to converge to a point when perfectly focused, the shape of a mis-focused spot from a lens with a circular aperture is a hard-edged disk of light (that is, a hockey-puck shape when intensity is plotted as a function of x and y coordinates in the focal plane). A more general circle of confusion has soft edges due to diffraction and aberrations, and may be non-circular due to the aperture (diaphragm) shape. So the diameter concept needs to be carefully defined to be meaningful. The diameter of the smallest circle that can contain 90% of the optical energy is a typical suitable definition for the diameter of a circle of confusion; in the case of the ideal hockey-puck shape, it gives an answer about 5% less than the actual diameter.

Usefulness of Circle of Confusion Diameter Limit

The rest of this article is about only the first interpretation, where the circle of confusion diameter limit is a criterion used to describe how out of focus a point is allowed to be on film, on a print, or on an electronic sensor, before the fuzziness becomes unacceptable. In film photography, the circle of confusion criterion is sometimes defined as the largest circle of blur on a film negative that will still be perceived by the human eye as a clean point when printed at 30 cm diagonal size and viewed from a normal viewing distance of 50 cm (and variations thereon).

While this definition has its subjective aspects, photographers still find it very useful because it allows a mathematical treatment of image sharpness when the eye's resolution is specified numerically. It is, for instance, a part of the calculation of depth of field. The circle of confusion can be used to describe blur limitations in both digital and film cameras.

Film size is important because it relates to the amount of enlargement necessary to get to a 30 cm diagonal. The larger the film size, the less enlargement required and the larger the tolerable circle of confusion. A circle that is 0.03 mm on 35mm film when enlarged to the same size as a 6 x 4.5 cm (almost twice the size of the 35mm) will be about 0.05 mm.

The resolution of the eye is another factor in determining the area of the circle of confusion. A person with good vision can readily distinguish 5 lines per millimeter at a distance of 25 cm. Using this visual acuity, at a normal viewing distance for a 30 cm print, the maximum size for a point to still be regarded as a point is 1/5th of a mm. If the film negative was itself 8x10 size film, the enlargement ratio would be 1.0X and the circle of confusion would be 0.2 mm. Using the more common 35mm film size, however, the enlargement is 7X and thus the circle of confusion need be 7 times smaller, or 0.2 mm / 7 = 0.029 mm. That is, the optical sharpness demands on the optical system are more severe for smaller film formats, because the enlargement factor is bigger.

Using the so-called "Zeiss formula" the circle of confusion is calculated as d/1730 where "d" is the diagonal measure of the film. For 35mm film (24 mm x 36 mm, 43mm diagonal) this comes out to be 0.024 mm. A more widely used COC criterion is d/1500, or 0.029 mm for 24x36 format, which corresponds to resolving 5 lines per mm on a print of 30 cm diagonal. Values of 0.030 mm and 0.033 mm are also common for this format.

The circle of confusion of d/1500 is intended to represent "average" photographing, printing, and viewing conditions. If the photograph will be magnified to a larger size, or viewed more closely, or printed on photo printers which introduce additional blur, then a tighter circle of confusion will be required.

Accepted values for circle of confusion based on d/1500

History

An early precursor to DOF calculations is the 1866 calculation of a circle-of-confusion diameter from a subject distance, for a lens focused at infinity, in a one-page article "Long and Short Focus" by an anonymous T. H. (British Journal of Photography XIII p. 138; this article was pointed out by Moritz von Rohr in his 1899 book Photographische Objektive). The formula he comes up with for what he terms "the indistinctness" is equivalent to ${\displaystyle C=fd/S}$ for focal length ${\displaystyle f}$, aperture diameter d, and subject distance S. But he does not invert this to find the S corresponding to a given C criterion (i.e. he does not solve for the hyperfocal distance), nor does he consider focusing at any other distance than infinity. But he observes "long-focus lenses have usually a larger aperture than short ones, and on this account have less depth of focus" .

Thomas R. Dallmeyer's 1892 expanded re-publication of his father John Henry Dallmeyer's 1874 pamplet 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:

"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:

"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 on an inch at 12 to 15 inches is closer to two minutes of arc. This choice of COC limit remains (for a large print) the most widely used even today. Sir Abney, in his 1881 A Treatise on Photography, takes a similar approach based on a visual acuity of one minute of arc, and choose a circle of confusion of 0.025 cm for viewing at 40 to 50 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.

The common 1/100 inch value has been applied to blur other than mis-focus blur. For example, Edward John Wall, in his 1889 A Dictionary of Photography for the Amateur and Professional Photographer, says:

To find how quickly a shutter must act to take an object in motion that there may be a circle of confusion less than 1/100in. 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.

Trivia

The Circle of Confusion is a popular and often appropriate name for photography clubs.

See also

• Bokeh
• Depth of field
• Diffraction
• Hyperfocal distance

External links

• Depth of field and Circle of Confusion
• About the Circle of Confusion
• Circles of Confusion for digital cameras

Notes

Template:FnbThe frame size is an average of cameras that take photographs of this format. Not all 6x7 cameras (for example) take frames that are exactly 56mm x 69mm. Check with the specifications of a particular camera if this level of exactness is needed.

Template:FnbThis format is commonly found on digital SLRs.

• Photographic terms