Page 203 - Modern Optical Engineering The Design of Optical Systems

186 Chapter Nine

Note that the preceding has been based on the assumption that the
pupil diameter is constant (with respect to ) and that is the angle
formed in image space (although it is often applied to the field angle in
object space). The “cosine fourth law” can be modified if the construc-
tion of the lens is such that the apparent size of the pupil increases for
off-axis points, or if a sufficiently large amount of barrel distortion is
introduced to hold to smaller values than one would expect from the
corresponding field angle in object space. Certain extreme wide-angle
camera lenses make use of these principles to increase off-axis illumi-
4
nation. The cos effect is in addition to any illumination reduction
caused by vignetting. It should be remembered that the cosine-fourth
effect is not a “law” but a collection of four cosine factors which may or
may not be present in a given situation.

9.8 Depth of Focus
The concept of depth of focus rests on the assumption that for a given
optical system, there exists a blur (due to defocusing) of small enough
size such that it will not adversely affect the performance of the system.
The depth of focus is the amount by which the image may be shifted
longitudinally with respect to some reference plane (e.g., film, reticle)
and which will introduce no more than the acceptable blur. The depth
of field is the amount by which the object may be shifted before the
acceptable blur is produced. The size of the acceptable blur may be
specified as the linear diameter of the blur spot (as is common in photo-
graphic applications) (Fig. 9.10) or as an angular blur, i.e., the angular
subtense of the blur spot from the lens. Thus, the linear and angular
blurs (B and , respectively and the distance S or S′ are related by
B B′
(9.6)
S S′

Figure 9.10 When an optical sys-
tem is defocused, the image of a
point becomes a blurred spot.
The size of the blur is deter-
mined by the relative aperture
of the system and the focus shift.