Electromagnetic Lens
Pole Pieces of iron
Concentrate lines of
Magnetic force
Lens Defects
Since the focal length f of a lens is dependent
on the strength of the lens, if follows that different
wavelengths will be focused to different positions.
Chromatic aberration of a lens is seen as fringes
around the image due to a “zone” of focus.
Lens Defects
In light optics
chromatic aberration
can be corrected by
combining a
converging lens with
a diverging lens. This
is known as a
“doublet” lens
The simplest way to correct for chromatic aberration
is to use illumination of a single wavelength! This is
accomplished in an EM by having a very stable
acceleration voltage. If the e velocity is stable the
illumination source is monochromatic
Lens Defects
The fact that wavelengths enter and leave the lens
field at different angles results in a defect known as
spherical aberration. The result is similar to that of
chromatic aberration in that wavelengths are brought
to different focal points
Spherical aberrations are
worst at the periphery of
a lens so again a small
opening aperture that
cuts off the most
offensive part of the lens
is the best way to reduce
the effects of spherical
aberration
Diffraction
Diffraction occurs
when a wavefront
encounters an edge
of an object. This
results in the
establishment of
new wavefronts
Diffraction
When this occurs
at the edges of an
aperture the
diffracted waves
tend to spread out
the focus rather
than concentrate them. This results in a
decrease in resolution, the effect becoming
more pronounced with ever smaller apertures.
Apertures
Advantages
Disadvantages
Increase contrast by
blocking scattered
electrons
Decrease effects of
chromatic and spherical
aberration by cutting off
edges of a lens
Decrease resolution due to
effects of diffraction
Decrease resolution by
reducing half angle of
illumination
Decrease illumination by
blocking scattered
electrons
If a lens is not
completely
symmetrical
objects will be
focussed to
different focal
planes resulting
in an
astigmatic
image
The result is a
distorted image.
This can best be
prevented by
having as near to
perfect a lens as
possible but other
defects such as dirt
on an aperture etc. can cause an astigmatism
Astigmatism in light
optics is corrected by
making a lens with a
corresponding defect
to correct for the
defect in another lens
In EM it is corrected
using a stigmator
Which is a ring of electromagnets positioned
around the beam to “push” and “pull” the
beam to make it more perfectly circular
Interazioni tra elettroni
e
materia
Electron-specimen Interactions
Primary electrons
Secondary
Electrons (s.e.)‫‏‬
X-rays
Backscattered
Electrons (b.s.e.)‫‏‬
Cathode
Luminescence
Auger-electrons
Specimen
E
Transmitted electrons
Absorbed
Electrons
Two Types of Electron Microscopes
•  Scanning Electron Microscope (SEM)‫‏‬
–  Secondary Electrons
–  Back-scattered Electrons
–  (X-rays)‫‏‬
•  Transmission Electron Microscope (TEM)‫‏‬
–  Transmitted Electrons
–  (X-rays)‫‏‬
Primary electrons
Secondary
Electrons (s.e.)‫‏‬
X-rays
Backscattered
Electrons (b.s.e.)‫‏‬
Cathode
Luminescence
Auger-electrons
Specimen
E
Transmitted electrons
Absorbed
Electrons
The size and shape of the region of primary excitation can be
estimated by carrying out simulations that use Monte Carlo
calculations and take into account the composition of the specimen
An interaction
volume can also
be used to predict
the types of
signals that will
be produced and
the depth from
which they can
escape. Monte Carlo simulations of electron
trajectories are based on 1) the energy of the primary
beam electron, 2) the likelihood of an interaction, 3)
the change in direction and energy of the electron, 4)
the mean free path of the electron and 5) a “random”
factor for any given interaction.
Effects of Accelerating Voltage
Z = Atomic Weight
E = Energy of
primary beam
The angle at which the
beam strikes the
specimen and the
distance from the
surface are important
factors in how much
of signal escapes from
the specimen.
The probability of an elastic vs. an inelastic
collision is based primarily on the atomic weight
of the specimen.
Interactions of electrons with atoms
Elastic scattering
No energy is deposited,
wavelength electron
unaffected
Inelastic scattering
Energy is deposited,
inducing damage in the
sample, wavelength
electron increases
Atomic cross-section for carbon in
biological specimens (barns = 10-24 cm2)
Comparison of elastic and
inelastic interactions with
carbon of X-rays, neutrons and
electrons
•  Electrons interact far stronger
with matter than other
elementary particles, therefore
electrons can image very thin
objects better than other
particles
•  Electrons deposit far less
energy in a biological sample,
compared to X-rays, therefore
electrons are less damaging
Wavelength (Å)
Comparing scattering of electrons & X-rays
Electrons X-rays
(200 keV) (1.5 Å)
Inelastic / elastic
scattering events
3
10
Energy deposited per 20 eV
inelastic event
8 keV
Energy deposited
relative to electrons
per elastic event
1300
1
Scattered photons
1
per scattered electron
106
Current resolution
<1Å
6-8 Å
From Henderson (1995) Quart. Rev. Biophys. 28, 171
Optics of diffraction and imaging
detector
lens
object
object
diffraction
diffraction
image
focus
Diffraction
pattern
Apertures
Advantages
Disadvantages
Increase contrast by
blocking scattered
electrons
Decrease effects of
chromatic and spherical
aberration by cutting
off edges of a lens
Decrease resolution due to
effects of diffraction
Decrease resolution by
reducing half angle of
illumination
Decrease illumination by
blocking scattered
electrons
Phase contrast in the TEM
Contrast can arise from constructive and destructive
interference of “electron waves”.
Phase contrast in the TEM
Contrast in electron microscopy:
bright field
detector
Strong
scatterer
lens
Defining
apenture