Page 209 - Modern Optical Engineering The Design of Optical Systems

192 Chapter Nine

Figure 9.15 The distribution of illumination in the Airy
disk. The appearance of the Airy disk is shown in the upper
right.

The presence of aberrations will, of course, modify the distribution as
will any nonuniformity of transmission or wave-front amplitude (see,
for example, Sec. 9.11).

9.10 Resolution of Optical Systems
The diffraction pattern resulting from the finite aperture of an optical
system establishes a limit to the performance which we can expect
from even the best optical device. Consider an optical system which
images two equally bright point sources of light. Each point is imaged
as an Airy disk with the encircling rings, and if the points are close,
the diffraction patterns will overlap. When the separation is such that
it is just possible to determine that there are two points and not one,
the points are said to be resolved. Figure 9.16 indicates the summation
of the two diffraction patterns for various separations. When the
image points are closer than 0.5 /NA (NA is the numerical aperture of
the system and equals n′ sin U′), the central maxima of both patterns
blend into one and the combined patterns may appear to be due to a
single source. At a separation of 0.5 /NA the duplicity of the image
points is detectable, although there is no minimum between the maxima
from the two patterns. This is Sparrow’s criterion for resolution. When