Scatter Circle Size
A scatter spot (circle) is a distorted image of a point projected by a photographic lens onto the camera’s matrix or film. These distortions are caused, firstly, by structural factors, i.e. natural imperfection of optics and photosensitive material, and secondly, functional reasons, and above all – selective focus. An image of an infinitely small point can be a point only when it lies strictly in the plane of the matrix or film. If the image of the point is out of focus, the point turns into a blurry spot of rounded shape, the size of which increases with distance from the plane of the ideal focus (see also “Bokeh”).
Formation of a scattering circle.
Fortunately, the human eye is also not an ideal optical system and when viewing photographs it is not able to distinguish a tiny scattering circle from an infinitesimal point, since the size of the circle does not exceed a certain threshold value. When photographers talk about a circle of confusion, in most cases they mean nothing more than the maximum allowable size of the scattering spot, which is perceived as a dot in the photograph. This value is used primarily for calculating the hyperfocal distance and for calculating the depth of field.
The terms “scatter spot”, “scatter circle” and “blur circle” are used interchangeably and are commonly used synonymously. English literature uses the phrase “circle of confusion”.
How to determine the allowable size of the scattering circle? This question can be answered in different ways. For example, according to the Zeiss standard, the frame diagonal is taken as the basis of calculations. The formula is as follows:
z = d / 1500, where
z is the diameter of the scattering circle;
d is the diagonal of the frame.
So, for a frame of a 35 mm film or for a full-frame digital matrix with a diagonal of 43.3 mm, the admissible size of the scattering spot is 43.3 / 1500 ≈ 0.029 mm or 29 μm. It is this value that is usually used to calculate depth of field scales for photographic lenses, as well as most standard depth of field tables.
The trouble is that the practical use of outdated values of the permissible circle of confusion is meaningless if the image quality is of any importance to you. In the same case, if the quality did not matter to you, you would hardly have become interested in scattering circles and other similar things at all.
Why are the classic standards bad? And the fact that, given the size of the matrix, they completely do not take into account its resolution.
The maximum allowable scattering spot size of 29 microns suggests that smaller spots will be indistinguishable from a 29 micron spot. However, if the size of a single pixel of the photomatrix is, for example, 10 μm, then a circle with a diameter of 29 μm will capture more than a dozen pixels, which means that when viewing a photo at 100% magnification, such a circle can no longer pretend to be a dot. To look like a dot, the scattering spot should have a size close to the size of a pixel, otherwise pixel-by-pixel sharpness is out of the question.
Thus, if you plan to use the matrix of your camera in full force, then when calculating the allowable scattering spot, you should start not so much from the size of the matrix, but from the size of its single pixel.
In my humble opinion, the diameter of the scattering spot should not exceed the diagonal length of the matrix pixel, provided, of course, that the pixel has a nearly square shape. Such a circle completely covers only one pixel, and the neighboring pixels, although it captures it, are not so much as to prevent it from perceiving the circle of blur as a point.
How to find the diagonal of a pixel? Very simple if you know the length of its side. The diagonal of any square with a known side is calculated by multiplying its side by the square root of two, i.e. at 1.414. We get the formula:
z = n1414, where
z is the diameter of the scattering circle;
n is the pixel size.
The pixel size n for a particular camera can be calculated using one of the formulas given in the article “How to find out the pixel size of a matrix?” Or take the finished value from the table located there.
For example, the pixel size of the Canon EOS 7D Mark II is 4.1 microns. The diameter of the scattering circle will be equal to:
4.1 · 1.414 ≈ 5.8 μm
In order to make life easier for the reader, I took the liberty of personally calculating the size of the circles of confusion for the most popular digital formats. The calculation results are presented in the following table.
Allowable size of the scattering spot depending on the resolution of the camera and its crop factor, microns.
1 * 1.5 1.6 2 2.7
10 8.8 8.2 4.9
12 12 8 7.5 6
14 7.4 4.1
16 10 6.9 5.2
18 9.8 6.1 3.6
20 9.3 5.8 3.4
21 9.1 5.9
24 8.5 5.7 5.3