Depth of Field Approximations

The depth of field equations can be simplified when the focal length of the lens is much less than the focal distance. The approximations are:

Hyperfocal distance:

hyperfocal distance approximation

Near distance of acceptable sharpness:

near distance approximation

Far distance of acceptable sharpness:

far distance approximation



is the hyperfocal distance, mm


is the lens focal length, mm


is the focus distance


is the near distance for acceptable sharpness


is the far distance for acceptable sharpness


is the f-number


is the circle of confusion, mm

f-number is calculated by the definition N = 2i/2 , where i = 0, 1, 2, 3,... for f/1, f/1.4, f/2, f/2.8,...

Calculations using these equations must use consistent units. When focal length and circle of confusion have units of millimeters, the calculated hyperfocal distance will have units of millimeters. To convert to feet, divide H by 304.8. To convert to meters, divide H by 1000.

Derivation of Depth of Field Approximations

Begin with the hyperfocal distance equation:

hyperfocal distance equation

Define H' as:

hyperfocal distance approximation

This can be stated as:

hyperfocal distance approximation

H' is a good approximation of the hyperfocal distance, as the focal length f is always much less than the f2/Nc term in the hyperfocal distance equation.

With the near distance equation:

near distance equation

Rearrange the equation:

Substitute H' for (H - f):

As f is always much less than H' + s, the near distance approximation is:

near distance approximation

With the far distance equation:

far distance equation

Rearrange the equation:

Substitute H' for (H - f):

When f is much less than s, the far distance approximation is:

far distance approximation

© 2002 Don Fleming

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