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:

Near distance of acceptable sharpness:

Far distance of acceptable sharpness:

where:
H^'	is the hyperfocal distance, mm
f	is the lens focal length, mm
s	is the focus distance
D_n^'	is the near distance for acceptable sharpness
D_f^'	is the far distance for acceptable sharpness
N	is the f-number
c	is the circle of confusion, mm

f-number is calculated by the definition N = 2^i/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:

Define H' as:

This can be stated as:

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:

With the far distance equation:

Rearrange the equation:

Substitute H' for (H - f):

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