The Mathematics of Depth of Field (DoF)

March 15, 2023  •  Leave a Comment

Depth of Field (DOF)

 

Depth of field is the distance between two planes, a closer one and a farther one, in which objects  can be positioned to have an "acceptably sharp" image formed in a camera.

There are two formulae for calculating Depth of Field (DOF), a simple one as described below which produces an approximate value and more a more complicated one which produces a more accurate value. The latter is not discussed in this document.

 

I will focus on the simple formula as below.

 

           DOF = (2 u2 N c)/f

 

Where:

  • C = circle of confusion*
  • F= focal length
  • U = distance to subject
  • N – F number

 

*circle of confusion has been defined as the largest blur circle that will be perceived by the human eye as a point when viewed at a distance of 25cm. Note there are more specific definitions but for the purposes of this document the above definition is considered sufficient.

The formula shows that DOF varies proportionally with the aperture, and with the square of the focal length and distance to subject.

Example: what is the DOF of a 50mm lens, when the circle of confusion is 0.029mm, f-stop is f/4 or 4 for the calculation, with a focus distance of 1200mm (1.2m)

Answer: square of u = 1200 * 1200 = 1,440,000

So DOF = 1,440,000*2*4*0.029 = 334,080 divided by square of focal length = 50 *50 = 2500

 

Ie 334,080/2500 = 133.632mm = 0.13m

 


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