Page 204 - Modern Optical Engineering The Design of Optical Systems

Stops, Apertures, Pupils and Diffraction 187

for a system in air, where the primed symbols refer to the image-side
quantities.
Since depth of focus ( ) and depth of field ( ′) are both longitudinal
distances (in image and object spaces respectively) they are related by
the longitudinal magnification, and

2

′ m m (9.7)
The hyperfocal distance of a system is the distance at which the sys-
tem must be focused so that the depth of field extends to infinity.
The idea of depth of focus was originally photographic, based on the
concept that a defocus blur which is smaller than a silver grain in the
film emulsion will not be noticeable. This concept also can be applied
to pixel size in, for example, a charge-coupled device (CCD). If the
acceptable blur diameter is B, then the depth of focus (at the image) is
simply (see Fig. 9.10).
′ B(f-number)

B
′ (9.8)
2NA
The corresponding depth of field (at the object) is from D near to D far ,
where

fD (A B)
D (9.9)
near
(fA DB)
fD (A B)
D (9.10)
far
(fA DB)
and the hyperfocal distance is simply

fA
D (9.11)
hyp
B
where D the nominal distance at which the system is focused (note
that, by our sign convention, D is normally negative)
A the diameter of the entrance pupil of the lens
f the focal length of the lens
B the acceptable blur diameter

Note that there are several false assumptions here. We assume that
the image is a perfect point, with no diffraction effects. We also assume
that the lens has no aberrations and that the blurring on both sides
of the focus is the same. None of these assumptions is correct, but
the equations above do give a usable model for the depth of focus. In