8
Introduction: The optical nature of a charged particle beam
rays. As a result, the beam is not focused to a point, but rather
is blurred. This is readily apparent in Figure 1.3. Spherical aberration occurs in light optical lenses as well as charged particle
lenses. In light optics, it arises from the fact that ordinary lenses
have spherical surfaces, hence the name spherical aberration. It is
substantially corrected in light optics by grinding the lens surfaces
to a particular aspherical shape. It is not possible to shape the electric and magnetic fields of a charged particle lens in an analogous
way, because the fields always obey Maxwell’s equations. Significant progress has been made over the last two decades in correcting
the aberrations of charged particle lenses. The details are beyond
the scope of this study. The reader is referred to two excellent
references by Rose [75] and by Krivanek, et. al. [54] for precise
details. Indeed, it is hoped that the present study will provide the
background needed to approach this advanced topic expeditiously.
It is apparent from Figure 1.3 that the innermost rays close to
the central axis are less aberrated than the outermost rays. Selecting the inner rays and blocking the outer rays would improve
the quality of the focusing. This suggests a simple way of mitigating the effect of the spherical aberration for a given optical system,
namely, by using an aperture to admit the inner rays, while blocking the outer rays. Conceptually, one could add an aperture in the
lens plane of Figure 1.4, thus limiting the cone of rays. A convenient measure of the constriction is given by the index of refraction
times the sine of the angle which the extreme ray makes with the
central axis at an object point on the axis. This product is known
as the numerical aperture. The larger the aberration, the smaller
the numerical aperture must be to obtain the desired image quality. In fact, the size of the numerical aperture can be used as a
useful estimate of the quality of the optical system. In practice,
the numerical aperture is typically in the range of 0.3 to 1.3 for
light optical lenses, and 0.001 to 0.1 for charged particle lenses,
in order to achieve optimal imaging conditions. This expresses the
fact that charged particle lenses have significantly worse aberration than light optical lenses.
Introduction: The optical nature of a charged particle beam
rays. As a result, the beam is not focused to a point, but rather
is blurred. This is readily apparent in Figure 1.3. Spherical aberration occurs in light optical lenses as well as charged particle
lenses. In light optics, it arises from the fact that ordinary lenses
have spherical surfaces, hence the name spherical aberration. It is
substantially corrected in light optics by grinding the lens surfaces
to a particular aspherical shape. It is not possible to shape the electric and magnetic fields of a charged particle lens in an analogous
way, because the fields always obey Maxwell’s equations. Significant progress has been made over the last two decades in correcting
the aberrations of charged particle lenses. The details are beyond
the scope of this study. The reader is referred to two excellent
references by Rose [75] and by Krivanek, et. al. [54] for precise
details. Indeed, it is hoped that the present study will provide the
background needed to approach this advanced topic expeditiously.
It is apparent from Figure 1.3 that the innermost rays close to
the central axis are less aberrated than the outermost rays. Selecting the inner rays and blocking the outer rays would improve
the quality of the focusing. This suggests a simple way of mitigating the effect of the spherical aberration for a given optical system,
namely, by using an aperture to admit the inner rays, while blocking the outer rays. Conceptually, one could add an aperture in the
lens plane of Figure 1.4, thus limiting the cone of rays. A convenient measure of the constriction is given by the index of refraction
times the sine of the angle which the extreme ray makes with the
central axis at an object point on the axis. This product is known
as the numerical aperture. The larger the aberration, the smaller
the numerical aperture must be to obtain the desired image quality. In fact, the size of the numerical aperture can be used as a
useful estimate of the quality of the optical system. In practice,
the numerical aperture is typically in the range of 0.3 to 1.3 for
light optical lenses, and 0.001 to 0.1 for charged particle lenses,
in order to achieve optimal imaging conditions. This expresses the
fact that charged particle lenses have significantly worse aberration than light optical lenses.