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Depth of Field

I would like to know more about this circle of confusion which is controlled by the focal length of the lens and diameter. Also whether you are using large format, medium format or 35mm camera.

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February 03, 2000

Circle of Confusion:
Depth of Field is based on what appears to be in and out of focus to the average person at an average viewing distance from an image.

When you focus a rectilinear, flat field lens (nearly all lenses other than fisheyes are rectilinear) a flat plane in space perpendicular to the lens axis, and a specific distance from the lens, is in exact or "critical" focus on the film plane.

Anything not lying in this plane in space is out of focus. The farther from this plane, the more out of focus. A point in space not on the critical focus plane will form a "circle of confusion" on the film plane. The size of the circle depends on how far from the critical focus distance the point is in space.

If a circle of confusion is small enough in a print or projected slide at an average viewing distance, the average human eye cannot tell the difference between it and a point in critical focus. If it is big enough, it can be detected and is perceived as out of focus.
The maximum diameter a circle of confusion can have before being detected as a circle and not a point defines the Depth of Field. The figures given are for the maximum diameter on *film* not in the viewed image. This is a *subjective* measure, but is based on studies and experience over many decades of still photography. With a larger format of film, you can have a larger circle of confusion (on the film) because it will not be enlarged as much for the viewer to detect it.

Here are some generally accepted maximum diameters for various film formats; you may find some variation with other lists of these as they are a *subjective* measure:
Small Format
35mm: 0.025mm
Medium Format (120/220 roll film)
6x4.5cm: 0.050mm (aka 645)
6x6cm: 0.060mm (aka 2-1/4 x 2-1/4)
6x7cm: 0.065mm
6x9cm: 0.075mm
Large Format (sheet film)
4x5in: 0.150mm
5x7in: 0.200mm
8x10in: 0.300mm

The maximum diameter for a circle of confusion is used in computation of Depth of Field limits and this will be shown in a later posting.

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July 26, 2000

The hyperfocal distance is directly proportional to the square of the focal length and inversely proportional to the aperture setting and maximum circle of confusion allowed for the film format. If you double the focal length, the hyperfocal distance quadruples (4x); if you triple the focal length, the hyperfocal distance increases by 9 times; if the aperture f-number goes up, the hyperfocal distance goes down; the same for an increase in the max circle of confusion.

H = f^2 / (A * c)
H = hyperfocal distance
f = lens focal length
A = Aperture setting (f-number)
c = max circle of confusion for the film format

This equation is a very close approximation that works for nearly all photographic lenses. Once the hyperfocal distance is calculated you can use it to determine the depth of field for a different focus distance.

Remember! You must be consistent in units of distance (including lengths and diameters). If you use focal length in millimeters, you must use a circle of confusion in millimeters and the hyperfocal distance from this equation will be in millimeters.

Using hyperfocal distance to find DOF will be in the next posting.

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August 13, 2000

	Circle of Confusion Growth Behind Subject Shows how circle of confusion grows behind the subject for six focal lengths (keeping the subject the same size) John A. Lind
	Infinity Circle of Conf. for Different Focal Lengt Shows what happens to Circle of Confusion Size as focal length changes (keeping the subject the same size) John A. Lind
	DOF and Focal Length Shows what happens with DOF if we change focal length and keep the subject the same size by moving closer or farther John A. Lind

Now, the concept of magnification. As you move closer or farther from a subject, its size on the film changes. This is called the magnification. Obviously for most work, the film image is much smaller than the subject, so the magnification is much less than one. If you keep the same distance, but change focal length, it also changes. Longer focal length increases magnification and shorter focal length decreases it. For the purpose of comparing what happens with different focal lengths, this discussion will keep magnification constant. That is, the subject will be the same size on the film and in order to do so the distance will shift to keep it that way as the focal length changes.

Now the DOF equations using the hyperfocal distance (H) found in the last posting:
S = Subject (focus) distance
H = Hyperfocal Distance
f = Lens Focal length
Sn = Near edge of DOF
Sf = Far edge of DOF
The near edge of the DOF:
Sn = (H * S)/(H + (S - f))
The far edge of the DOF:
Sf = (H * S)/(H - (S - f))
As the focus distance grows, the far edge grows faster than the near edge.

Let us assume we will use an aperture of f/8, and a distance of 8 feet for the 50mm focal length. That means the distance will get shorter for shorter focal lengths and longer for longer focal lengths. The first chart shows two things for various focal lengths:
(a) The focus distance, the near edge, and the far edge for the DOF to keep the subject the same size as at 8 feet using a 50mm lens.
(b) The yellow line blows away a common myth about DOF. It is DOF = Sf - Sn, or the actual depth of the DOF. Notice that it remains very nearly constant (about four feet in this case) from 18mm through 600mm. What does this mean? If you change to a longer lens and move back to reframe thinking you will somehow reduce the DOF, you're wrong. It won't!

See this chart.

Why would we go longer and move back then? Because the circle of confusion can be made larger outside the DOF! The second chart shows the theoretical circle of confusion size at infinity for each focal length. Notice how it gets larger with a longer focal length (remember we're keeping magnification, or subject size the same).

See this second chart.

The third chart shows what happens to the circle of confusion from 1 - 50 feet behind the subject for six common focal lengths: 24, 35, 50, 85, 100 and 135mm. Note that its size grows faster with the longer focal length. This means for greater reduction of background clutter outside the DOF, go to a longer lens and move back.

See this third chart.

Hope this helps you understand DOF better and how to use it in for DOF control of distracting backgrounds. Keep in mind that a longer focal length will "flatten" and image and reduce perception of depth. A shorter focal length will increase it. This is always another aspect of (what Ansel Adams called) "image management."

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August 18, 2000