Page 106 - Modern Optical Engineering The Design of Optical Systems

The Primary Aberrations 89

f/10 (stop diameter of 10 mm) and covered a fixed field of 17° (field
diameter of 60 mm). It is often useful to know how the aberrations of
such a lens vary when the size of the aperture or field is changed.
Figure 5.16 lists the relationships between the primary aberrations
and the semi-aperture y (in column one) and the image height (or field
angle) h (in column two). To illustrate the use of this table, let us
assume that we have a lens the aberrations of which are known; we wish
to determine the size of the aberrations if the aperture diameter is
increased by 50 percent and the field coverage reduced by 50 percent.
The new y will be 1.5 times the original, and the new h will be 0.5 times
the original.
Since longitudinal spherical aberration is shown to vary with y , the
2
2
1.5 times increase in aperture will cause the spherical to be (1.5) , or
3
2.25, times as large. Similarly transverse spherical, which varies as y ,
will be (1.5) , or 3.375, times larger (as will the image blur due to
3
spherical).
2
Coma varies as y and h; thus, the coma will be (1.5) 0.5, or 1.125,
2
times as large. The Petzval curvature and astigmatism, which vary
2
2
with h , will be reduced to (0.5) , or 0.25, of their previous value, while
the blurs due to astigmatism or field curvature will be 1.5(0.5) , or
2
0.375, of their original size.
The aberrations of a lens also depend on the position of the object
and image. A lens which is well corrected for an infinitely distant
object, for example, may be very poorly corrected if used to image a
nearby object. This is because the ray paths and incidence angles
change as the object position changes.
It should be obvious that if all the dimensions of an optical system are
scaled up or down, the linear aberrations are also scaled in exactly

Figure 5.16 The variation of the primary aberrations with aperture and field.