notes on depth of field
Depth of Field

When a camera lens is focussed on a subject, all points on the subject are focussed as points on the film plane. If the lens is focused in front of or behind the subject, points on the subject become rendered as circles, and the image of the subject becomes blurred. These 'circles of confusion' will grow in size as the focused distance of the lens departs from the subject distance, and the image of the subject appears more and more blurred. The rate at which these 'circles of confusion' expand as the focus is moved from the subject can be lowered by reducing the aperture of the lens.

If we can set a threshold for what is 'acceptably sharp', we can calculate the near and far subject distances that will appear 'acceptably sharp' for any given focus distance, lens focal length, and aperture (the 'near focus limit' and the 'far focus limit'). This span of these distances is known as the 'Depth of Field' (DoF).

DoF increases with smaller apertures as alluded to above, and also decreases with the magnification of the subject. The larger the subject in the frame, the less the DoF will be for any given aperture, and film format. It should be noted that focal length does not affect available DoF for a given subject magnification. For instance you are using a 35mm camera and compose a head and shoulders portrait shot using an aperture of f5.6 on a 50mm lens. You will have around 4 inches of DoF at the subject regardless of the focal length of the lens you are using. If you switch from a 50mm lens to a 28mm wide angle, you will initially have greater depth of field on the person, but it will be the same once you have moved closer to make the person the same size in the frame. The same logic applies in reverse when switching to a longer lens. You initially have less depth of field, but once you have retreated from the subject to restore the original size of the subject in the frame, DoF is the same as it was.

Magnification refers to the ratio of the actual size of the subject on the film to the actual subject size. Therefore for a given aperture and composition you have more depth of field available in smaller film formats than larger ones.

Hyperfocal Distance

When a lens is focused at the 'Hyperfocal Distance' the available depth of field is disposed so that the zone of acceptable sharpness runs from a distance equal to half the hyperfocal distance to infinity. For instance if the hyperfocal distance is calculated to be 10 feet, then focusing the lens at this distance will render everything from 5 feet to infinity as 'acceptably sharp'.

Circle of Confusion

How do we define what is 'acceptably sharp'? By defining the diameter of the maximum allowable circle of confusion at the film plane (i.e. on the negative).

Considering a 10" x 8" print, it is generally agreed that the image will appear acceptably sharp at a normal viewing distance (roughly the diagonal dimension of the print, or around 13 inches in this case), if it resolves detail to 5 lines per millimetre. If this print was made as a contact from a 10" x 8" negative, then we know that the largest 'circle of confusion' we can allow is 0.2mm in diameter. All circles of confusion smaller than this diameter will ensure each line isn't blurred into the next one, and this level of detail will be visible in the image.

The Effect of Different Formats

Consider that the 10"x8" print is to be made from a 5"x4" negative. We need twice the resolution on the negative to maintain the 5 lines/mm resolution in the print, as we have introduced an 'enlargement factor' of 2 (dividing the diagonal of the image on the print by the diagonal of the image on the negative). We therefore require resolution to 10 lines/mm on the negative, and need to reduce the maximum allowable size of our 'circle of confusion' to 0.1mm in diameter.

The Effect of Print Size

If you always view a print at a distance approximately equating to the diagonal measurement of the image, then no adjustment to the 'circle of confusion' is required. A 10" x 8" print from a given negative viewed from a distance of 12.8 inches, will appear equally as sharp as a 20" x 16" print from the same negative viewed at a distance of 25.6 inches.

I recommend you use 5 lines/mm on a 10"x8" print as your starting reference. This will give format specific CoC values which will generate DoF results consistent with the scales on most manufacturers lenses (jives with my Nikkors anyway).

However if you do need to derive a particular CoC that specifically gives you 3 lines/mm resolution on a 20"x16" print then you can set the CoC calculator to do this. This would give the same CoC result as using 6 lines/mm on a 10"x8" print.