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
Increase contrast by blocking scattered electrons
Decrease effects of
chromatic and spherical aberration by cutting off edges of a lens
Disadvantages
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
materia e
Primary electrons
X-rays Cathode
Luminescence Specimen
Transmitted electrons E
Secondary
Electrons (s.e.)
Backscattered Electrons (b.s.e.)
Auger-electrons
Absorbed Electrons
Electron-specimen Interactions
• Scanning Electron Microscope (SEM)
– Secondary Electrons
– Back-scattered Electrons – (X-rays)
• Transmission Electron Microscope (TEM)
– Transmitted Electrons
– (X-rays) Primary electrons
X-rays Cathode Luminescence Specimen
Transmitted electrons E
Secondary Electrons (s.e.)
Backscattered Electrons (b.s.e.)
Auger-electrons
Absorbed Electrons
Two Types of Electron Microscopes
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
Inelastic scattering
No energy is deposited, wavelength electron unaffected
Energy is deposited, inducing damage in the sample, wavelength electron increases
Atomic cross-section for carbon in biological specimens (barns = 10-24 cm2 )
Wavelength (Å)
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
Electrons (200 keV)
X-rays (1.5 Å) Inelastic / elastic
scattering events
3 10
Energy deposited per inelastic event
20 eV 8 keV Energy deposited
relative to electrons per elastic event
1 1300
Scattered photons
per scattered electron
1 106
Current resolution 6-8 Å < 1 Å
From Henderson (1995) Quart. Rev. Biophys. 28, 171
Comparing scattering of electrons & X-rays
focus diffraction
image
Optics of diffraction and imaging
object object
detector
lens
diffraction
Diffraction pattern
Apertures
Advantages
Increase contrast by blocking scattered electrons
Decrease effects of
chromatic and spherical aberration by cutting
off edges of a lens
Disadvantages
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
Defining apenture Strong
scatterer
lens
detector
