depth of field and Hyperfocal distance

[brett.cooper76@gmail.com]

Hello Everyone. thanks for all the help. I am close to getting it...

A simplified formula for the hyperfocal length is:

H=F^2/(d* f#)(1+d/D)

usually d/D is very small so

H=F^2/(d* f#)

d= diameter of accepted, maximum circle of confusion (set a priori)
F= focal length of positive lens
D=  lens diameter
f#= F/D


So, the hyperfocal length is farther out if the focal length increase and if the circle of (maximum) confusion is set to be small.
Let's do a numerical example:

F=2 cm
d= 1 mm=0.1 cm
f#= 3 (focal length is 3 times the lens diameter).

H= 4/ (.3)= 13.3 cm

So the DOF goes from  6.65cm  to "infinity". Infinity will include all those object distances where the objects are still imaged (not too small to be imaged as points). The circle of confusion at distance 6.65 cm is 1 mm. The circle of confusion at "infinity" is also 1 mm.
The circle of confusion at H=13.3 is 0mm (ignoring diffraction).

Now, focusing at infinity instead of focusing at H: the circle of at infinity is 0 mm. What distance can we call infinity in our example?  Let's call that distance INF.
As we move away from INF (back or forward) the circle of confusion grows, eventually reaching size 1 mm.

Brett