Circle Of Confusion In Optics A Circle Of Confusion

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

Circle of confusion
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.

The depth of field is the region where the size of the circle of
confusion is less than the resolution of the human eye.
Circles with a diameter less than the circle of confusion
will appear to be in focus.
Two uses
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 35 mm film when enlarged to the
same size as a 6x4.5 cm (almost twice the size in each direction of
the 35 mm) 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 one-fifth
of a millimeter. If the film negative was itself 8x10 inch size film,
the enlargement ratio would be 1.0X and the circle of confusion would
be 0.2 mm. Using the more common 35 mm 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 35 mm film (24 mm x 36 mm, 43 mm diagonal) this comes out to be
0.024 mm. A more widely used COC criterion is d/1500, or 0.029 mm for
24x36 inch format, which corresponds to resolving 5 lines per
millimeter 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
Film format
Frame size[1]
CoC
Small Format
APS-C[2]
22.5 mm x 15.0 mm
0.018 mm
35 mm
36 mm x 24 mm
0.029 mm
Medium Format
645 (6x4.5)
56 mm x 42 mm
0.047 mm
6x6
56 mm x 56 mm
0.053 mm
6x7
56 mm x 69 mm
0.059 mm
6x9
56 mm x 84 mm
0.067 mm
6x12
56 mm x 112 mm
0.083 mm
6x17
56 mm x 168 mm
0.12 mm
Large Format
4x5
102 mm x 127 mm
0.11 mm
5x7
127 mm x 178 mm
0.15 mm
8x10
203 mm x 254 mm
0.22 mm