176
An Introduction to Beam Physics
mirror symmetric about the degrader and forms a dispersive image at that
point. The matrices of the two parts are
ˆ
M 1 =
⎛
⎝
M 1
0
D 1
(a|x) 1 1/M 1 0
0
0
1
⎞
⎠ ,
ˆ
M 2 =
⎛
⎝
1/M 1 0
−D 1 /M 1
(a|x) 1 M 1 −(a|x) 1 D 1
0
0
1
⎞
⎠ .
From eq. (7.2), the achromatic condition for the fragment separator is
D 1 (δ|x) d + (δ|δ) d = 1.
Therefore the shape of the degrader can be decided, which is a wedge with
the slope
∂d
∂x
=
γd 0
D 1
.
It is straightforward to verify that the system with the degrader is indeed
achromatic
ˆ
M = ˆ
M 2 · ˆ
M d · ˆ
M 1 =
⎛
⎜
⎝
(δ|δ) d
0 0
M 1 (a|x) 1 (2 − (δ|x) d D 1 ) 1 0
M 1 (δ|x) d
0 1
⎞
⎟
⎠ .
7.4 *Electron Microscopes and Their Correction
The field of electron optics is one of the oldest branches of beam physics,
which is a direct descendant of light optics. Recently, it is also one of the most
active branches due to the advancement of aberration correction in electron
microscopes. In the past decade, the TEAM project (Transmission Electron
Aberration-corrected Microscope) has been developing the next generation of
electron microscopes. Initial experiments using the latest aberration-corrected
scanning transmission electron microscope (STEM) demonstrated the scientific potential of aberration-corrected electron microscopes.
Since their invention in the early 1930s, electron microscopes have been used
in various areas ranging from scientific research to industrial production, and
various different types of microscopes were developed for the specific needs
of those applications. The main variants are the transmission electron microscope (TEM), the scanning transmission electron microscope (STEM), the
photoemission electron microscope (PEEM), the low energy electron microscope (LEEM) and the scanning electron microscope (SEM).
Among them, TEM and STEM are used mainly to study the bulk properties of materials with electron energy ranges from 100 keV to 1 MeV. PEEM,
LEEM and SEM are used to study surface properties of materials with electron energy below 30 keV. In a PEEM, secondary electrons generated by
An Introduction to Beam Physics
mirror symmetric about the degrader and forms a dispersive image at that
point. The matrices of the two parts are
ˆ
M 1 =
⎛
⎝
M 1
0
D 1
(a|x) 1 1/M 1 0
0
0
1
⎞
⎠ ,
ˆ
M 2 =
⎛
⎝
1/M 1 0
−D 1 /M 1
(a|x) 1 M 1 −(a|x) 1 D 1
0
0
1
⎞
⎠ .
From eq. (7.2), the achromatic condition for the fragment separator is
D 1 (δ|x) d + (δ|δ) d = 1.
Therefore the shape of the degrader can be decided, which is a wedge with
the slope
∂d
∂x
=
γd 0
D 1
.
It is straightforward to verify that the system with the degrader is indeed
achromatic
ˆ
M = ˆ
M 2 · ˆ
M d · ˆ
M 1 =
⎛
⎜
⎝
(δ|δ) d
0 0
M 1 (a|x) 1 (2 − (δ|x) d D 1 ) 1 0
M 1 (δ|x) d
0 1
⎞
⎟
⎠ .
7.4 *Electron Microscopes and Their Correction
The field of electron optics is one of the oldest branches of beam physics,
which is a direct descendant of light optics. Recently, it is also one of the most
active branches due to the advancement of aberration correction in electron
microscopes. In the past decade, the TEAM project (Transmission Electron
Aberration-corrected Microscope) has been developing the next generation of
electron microscopes. Initial experiments using the latest aberration-corrected
scanning transmission electron microscope (STEM) demonstrated the scientific potential of aberration-corrected electron microscopes.
Since their invention in the early 1930s, electron microscopes have been used
in various areas ranging from scientific research to industrial production, and
various different types of microscopes were developed for the specific needs
of those applications. The main variants are the transmission electron microscope (TEM), the scanning transmission electron microscope (STEM), the
photoemission electron microscope (PEEM), the low energy electron microscope (LEEM) and the scanning electron microscope (SEM).
Among them, TEM and STEM are used mainly to study the bulk properties of materials with electron energy ranges from 100 keV to 1 MeV. PEEM,
LEEM and SEM are used to study surface properties of materials with electron energy below 30 keV. In a PEEM, secondary electrons generated by