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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. more...

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Two uses

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

1. To calculate a camera's depth of field (“DoF�), 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.

Basis for circle of confusion diameter limit

In photography, the circle of confusion diameter limit (“CoCâ€�) is sometimes defined as the largest blur circle that will still be perceived by the human eye as a point when viewed at a distance of 25 cm (and variations thereon).

With this definition, the CoC in the original image depends on three factors:

Visual acuity. For most people, the closest comfortable viewing distance, termed the near distance for distinct vision (Ray 2002, 216), is approximately 25 cm. At this distance , a person with good vision can usually distinguish an image resolution of 5 line pairs per millimeter (lp/mm), equivalent to a CoC of 0.2 mm in the final image.; Viewing conditions. If the final image is viewed at approximately 25 cm, a final-image CoC of 0.2 mm often is appropriate. A comfortable viewing distance is also one at which the angle of view is approximately 60° (Ray 2002, 216); at a distance of 25 cm, this corresponds to about 30 cm, approximately the diagonal of an 8×10 inch image. It often may be reasonable to assume that, for whole-image viewing, an image larger than 8×10 will be viewed at a distance greater than 25 cm, for which a larger CoC may be acceptable.; Enlargement from the original image (the focal plane image on the film or image sensor) to the final image (print, usually). If an 8×10 inch original image is contact printed, there is no enlargement, and the CoC for the original image is the same as that in the final image. However, if the long dimension of a 35 mm image is enlarged to approximately 25 cm (10 inches), the enlargement is approximately 7×, and the CoC for the original image is 0.2 mm/7, or 0.029 mm.;

All three factors are accommodated with this formula:

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