7
Introduction: The optical nature of a charged particle beam
is undeflected. These two rays are depicted as bold lines in the
figure. They intersect in a distant plane located at z I , at a point
which is located at a distance r I from the central axis. In fact, all
rays emitted from this object point, regardless of their angle of
emission, are focused by the lens to the same image point. Since
all rays converge to a single point, it is apparent that a one-to-one
mapping of the object point into an image point exists. In order
for this to happen, each ray must experience a change in slope
which is proportional to the distance from the central axis. This
is the remarkable focusing action of an ideal lens.
Since this works for any point in the object plane z O , we deduce
that all object points are imaged simultaneously, each to a unique
point in the image plane. This is the mechanism by which a magnified image of an extended object is formed. The negative of the
ratio of r I to r O is called the magnification of the image relative
to the object. By convention, the magnification is negative in this
case, because the image is inverted relative to the object. By performing the construction in Figure 1.4 for multiple object points
r O , it is easy to convince oneself that this magnification is the
same for all object points. The magnification depends only on the
relative positions of the object plane z O and the lens plane z L , and
on the focal length f . The smaller the focal length f , the more the
rays are deflected, and the stronger is the lens. The focal length
is the same for all object points r O . For a charged particle beam,
the focal length also depends on the particle energy. The higher
the particle energy, the longer is the focal length. This is a direct
result of the fact that a faster particle spends less time in the lens
field, and is therefore deflected less than a slower particle.
The construction in Figure 1.4 works for both charged particles
and light. Many striking similarities exist between light optics and
charged particle optics. In both cases, no optical system is capable
of forming a perfect image. Blur and distortion are always present
to some degree. These imperfections are called aberrations. An
important example is the so-called spherical aberration, in which
the outermost rays are focused more strongly than the innermost
Introduction: The optical nature of a charged particle beam
is undeflected. These two rays are depicted as bold lines in the
figure. They intersect in a distant plane located at z I , at a point
which is located at a distance r I from the central axis. In fact, all
rays emitted from this object point, regardless of their angle of
emission, are focused by the lens to the same image point. Since
all rays converge to a single point, it is apparent that a one-to-one
mapping of the object point into an image point exists. In order
for this to happen, each ray must experience a change in slope
which is proportional to the distance from the central axis. This
is the remarkable focusing action of an ideal lens.
Since this works for any point in the object plane z O , we deduce
that all object points are imaged simultaneously, each to a unique
point in the image plane. This is the mechanism by which a magnified image of an extended object is formed. The negative of the
ratio of r I to r O is called the magnification of the image relative
to the object. By convention, the magnification is negative in this
case, because the image is inverted relative to the object. By performing the construction in Figure 1.4 for multiple object points
r O , it is easy to convince oneself that this magnification is the
same for all object points. The magnification depends only on the
relative positions of the object plane z O and the lens plane z L , and
on the focal length f . The smaller the focal length f , the more the
rays are deflected, and the stronger is the lens. The focal length
is the same for all object points r O . For a charged particle beam,
the focal length also depends on the particle energy. The higher
the particle energy, the longer is the focal length. This is a direct
result of the fact that a faster particle spends less time in the lens
field, and is therefore deflected less than a slower particle.
The construction in Figure 1.4 works for both charged particles
and light. Many striking similarities exist between light optics and
charged particle optics. In both cases, no optical system is capable
of forming a perfect image. Blur and distortion are always present
to some degree. These imperfections are called aberrations. An
important example is the so-called spherical aberration, in which
the outermost rays are focused more strongly than the innermost