Equations

When a lens is used to form an image of some object, the distance from the object to the lens $u$, the distance from the lens to the image (i.e. film plane) $v$, and the focal length $f$ are related by: \[\frac {1}{f} = \frac{1}{u}+\frac{1}{v}\] which can be rewritten as e.g.: \[v=\frac{uf}{u-f}\] or \[v=\frac{uf}{u-f}\]

Jada jada…

\[N=\frac{f}{d}\]

The depth of field $d_F$ is simply the relative distance between the front and rear limits $d_f$ and $d_r$ respectively: \[d_F = d_r -d_f\]

\[d_f = \frac{uf^2}{f^2 + c^2N(u-f)}\] \[d_r = \frac{uf^2}{f^2 - c^2N(u-f)}\]

\[\text{DOF} \approx \frac{2u^{2}Nc}{f^{2}}\]

The depth of field, $D$, is directly related to the depth of focus, $\Delta d$, \[z=\frac{\Delta d}{2c}\]

fun = @(c, d) d ./ (2*c) c_normal = 0.089 c_critical = 0.030

A (view) camera is focused by

1. Set focus on the most distant object in the scene for which an acceptable sharpness is still required.
   • (This object will be at… $D_{far}$
   • Jada jada…using a caliper/ruler…$d_{far}$
   • Take note on how far the lens is extended from the
2. Set focus on the most nearby object in the scene for which an acceptable sharpness is required.
   • (This object will be at… $D_{close}$
   • Jada jada…$d_{close}$
3. Calculate, or measure, the depth of focus: \[\Delta d = d_{far} - d_{close}\]