HYPERFOCAL MATH

8/26/2005

All of these tables and formulas are derived from the formulas found in APPLIED DEPTH OF FIELD by Alfred Blaker, Focal Press, 1985, ISBN 0-240-51730-X

NOTE: all formulas assume metric and will use millimeters as the unit of measurement.

1) First we need to define the "circle of confusion":

Circle of Confusion = Effective Aperature X 0.001

where EA = distance from lens to film / size of the aperature

NOTE: this assumes no enlargement of the negative. The degree of sharpness on a final print needs to have this value multiplied by the degree of enlargement.

2) Assuming that the far focus limit is infinity the near focus limit is then [in mm]:

NFL = (focal length X focal length) / (f# X circle of confusion)

EX: so for a 4x5 camera with a f128 lens of 75mm focal length this becomes:

Circle = 128 * 0.001 or 0.128 mm

NFL = (75 X 75)/(128 X 0.128) = 343.3 mm [13.5 inches]

The camera is set at a focus of twice this distance or 686.6 mm [27 inches]

3) To find the lens to film distance: [NOT the same as focal length except in a pinhole camera]

d = 1 / ((1 / focal length) - (1 / film to subject distance))

EX: In the above the film to subject is the focus point or 687 mm, so

d = 1 / ((1 / 75) - (1 / 687)) = 1 / (0.0133 - 0.00146) = 1 / 0.01184 = 84.5 mm

The size of the f stop then becomes 84.5 / 128 or 0.66 mm

Now having said all that, here is an online calculator for the above: Hyperfocal Calculator

Tables: [4x5 camera][ALL units in mm]
[updated 8/26/2005]

This works great if you are building the entire camera, lens assembly and all, but what do you do if you already have the lens? The aperature values will be off. For instance, in the above, a 90mm focal length at F90, you would expect an aperature diameter of 1.000 mm, but the table shows 1.047, nearly a 5% change. Is this important? Probably not. Remember, F-stops are a 100% change (2x and 1/2x depending on direction). So, I would not sweat it.