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Whole course about Electron Microscopy and Diffraction
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Electron Microscopy Electron Microscopy and Diffractionand Diffraction
3. Electron optics, Lenses and Apertures3. Electron optics, Lenses and Apertures
Do Minh NghiepMaterials Science Center
Part of the figures, texts are quoted from internet resources. All the copyrights belong to the original authors.
All the references made here are for educational purpose only.
ContentContent
Image formation System of optical, electrostatic and
electromagnetic lensses Aperture system Optical aberrations and its corrections
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ImagingImaging
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Light and electron opticsLight and electron optics
TEM
Illumination Illumination sourcesource
Condense lens
Condenser lens
Objective lens 1
Objective lens 2
Specimen Objective
lens
Projection lens
Image plane
Fluorescent screenEye
Specimen
Detector
SEMOM
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Electron path and signals used in EMsElectron path and signals used in EMs
Sample
SEM
STEM
TEM
Imaging principleImaging principle
TEM Optical instrument in that it uses a lens to form an image SEM- Not an optical instrument (no image-forming lens). - But it uses electron optics: probe forming-signal detecting devices.
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Refraction by lensRefraction by lens
Refraction or bending of a illumination beam is caused when the wave enters a medium of a different optical density.
Medium 1:
lower density
Medium 2: higher density
Incident beam
Refracted beam
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Refraction in OMsRefraction in OMs
In light optics this is accomplished when a light moves from air into glass.
In EM there is only a vacuum with an optical density of 1.0 (whereas glass has much higher).01/01/2009 8Handouts-MSE4346-K51KHVL
Refraction in EMsRefraction in EMs
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In electron optics we cannot bend the beam by a conventional (glass) lens of a different optical density.
Instead a “force” must be applied that has the same effect causing the beam of illumination to bend. It is Electromagnetic or Electrostatic force.
Classic optics: The refractive index changes abruptly at a surface and is constant between the surfaces. The refraction of light at surfaces, separating media of different refractive indices, makes it possible to construct imaging lenses. Glass surfaces can be shaped. Electron optics: Here, changes in the refractive index are gradual, so rays are continuous curves rather than broken straight lines. Refraction of electrons must be accomplished by fields in space around charged electrodes or solenoids, and these fields can assume only certain distributions consistent with field theory.
Light optics vs electron opticsLight optics vs electron optics
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LensesLenses
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Converging (positive) lens (convex glass):
Bends rays toward the axis.
It has a positive focal length.
Forms a real inverted image of an object placed to the left of the first focal point and an erect virtual image of an object placed between the first focal point and the lens.
Glass lensesGlass lenses
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Diverging (negative) lens (concave glass):
Bends the light rays away from the axis.
It has a negative focal length.
An object placed anywhere to the left of a diverging lens results in an erect virtual image.
It is not possible to construct a negative magnetic lens although negative electrostatic lenses can be made.
Glass lensesGlass lenses
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Electrostatic lensElectrostatic lens
Must have very clean and high vacuum environment to avoid arcing across plates.
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Converging lens
Diverging lens
Electrostatic lens vs glass lensElectrostatic lens vs glass lens
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Passing through a single coil of wire a
current will produce a strong magnetic field
in the center of the coil
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Electromagnetic lens: principleElectromagnetic lens: principle
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Electromagnetic lens: constructionElectromagnetic lens: construction
Pole pieces of iron concentrate lines of magnetic force.
CoilPole pieces
Magnetic force lines
Electromagnetic lens: Electromagnetic lens: lines of magnetic forcelines of magnetic force
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Electromagnetic lens: Electromagnetic lens: magnetic forcesmagnetic forces
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Two force vectors:
one in the direction of the electron trajectory
the other perpendicular to it
they cause the electrons to move through the magnetic field in a helical manner.
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Electromagnetic Electromagnetic lens: spiralling lens: spiralling
mouving of electron mouving of electron
`̀The strength of the magnetic
field is determined by: the number of wraps of the
wire and the amount of current
passing through the wire.
A value of zero current (weak lens) would have an infinitely long focal length
A large amount of current (strong lens) would have a short focal length.
Two types of electromagnetic lensTwo types of electromagnetic lens
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Aperture systemAperture system
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A TEM image contrast is made up of:
nonscattered electrons (which strike the screen: bright area)
scattered electrons (which do not: dark area)
therefore appear as a shadow on the screen (contrast : intensity defference)
TEM contrast imageTEM contrast image
Scattered beam
Transmitted beam
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Some of the electrons will only be partially scattered and thus will reach the screen in an inappropriate position, giving a false signal and thus contributing to a degradation of the image.
These forward scattered electrons can be eliminated by placing an aperture beneath the specimen.
Aperture increasesAperture increases image qualityimage quality
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The design of an electromagnetic lens results in a very strong lens with a very short focal length, thus requiring that the specimen lie within the lens itself along with an aperture to stop the highly scattered electrons.
Objective aperture
Sample grid
Scattered electron
Transmitted electron
Aperture is followed by lensAperture is followed by lens
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Sample
Aperture
Upper pole piece
Lower pole piece
Both the specimen rod and the aperture rod assembly have to be inserted into the lens.
They are made of nonmagnetic metals such as copper (Cu), brass (Cu-Zn) and platinum (Pt)
Aperture location and materialsAperture location and materials
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While a small opening objective aperture has the advantage of stopping scattered electrons and thus increasing image contrast
It also dramatically reduces the half angle of illumination for the projection lenses and thus decreases image resolution
Aperture - contrast - resolutionAperture - contrast - resolution
Small aperture increases contrast Large aperture increases resolution
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Narrow aperture generatesNarrow aperture generates diffractiondiffraction
Diffraction occurs when a wavefront encounters an edge of an object. This results in the establishment of new wavefronts.
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Narrow aperture reduces resolution Narrow aperture reduces resolution due to diffractiondue to diffraction
Diffraction occurs at the edges of an aperture.
The diffracted waves spread out the focus rather than concentrate them.
This results in a decreasing resolution, (more pronounced with ever smaller apertures).
Aperture corrects optic defects
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Edges beam
Narrow aperture
Many focal planes
One focal plane
Chromatic aberration
Edges beam
Narrow apertureOne focal plane
Many focal planesSpherical aberration
Pros and cons of aperturePros and cons of aperture
AdvantagesAdvantages
Increase contrast by blocking scattered electrons
Decrease effects of chromatic and spherical aberration by cutting off edges of a lens
DisadvantagesDisadvantages
Decrease resolution due to effects of diffraction
Decrease resolution by reducing half angle of illumination
Decrease illumination by blocking scattered electrons
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Lens defects and Lens defects and its corrections its corrections
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Chromatic aberrationChromatic aberration
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The focal length f of a lens is dependent on the strength of the lens and energy of beam.
Therefore different wavelengths will be focused to different positions.
ChromaticChromatic aberration (CA) of a lens is seen as fringes around the image due to a “zone” of focus.
In light optics wavelengths of higher energy (blue) are bent more strongly
and have a shorter focal length.
In the electron microscope the exact
opposite is true in that higher energy
wavelengths are less effected and have a
longer focal length.
Chromatic aberration in OM and EMChromatic aberration in OM and EM
OM
EM
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In light optics chromatic aberration can be corrected by combining a converging lens with a diverging lens.
This is known as a “doublet” lens.
Correction of CA in OM Correction of CA in OM by doublet lens by doublet lens
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In EM we can combine an electromagnetic (converging) lens with an electrostatic (diverging) lens to create an achromatic lens
Correction of CA in EMCorrection of CA in EMby achromatic lens by achromatic lens
LEO Gemini Lens
Electromagnetic lens
Electrostatic lens
Sample
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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 electron velocity is stable, the illumination source is monochromatic .
Correction of CA by usingCorrection of CA by usingmonochromatic wave source monochromatic wave source
Mo
no
chro
mat
ic
sou
rce
The problem arises when electrons are differentially scattered within the specimen, slowing some more than others, and thus producing polychromatic illumination from a primary monochromatic beam. So aberration is unavoidable.
Scattering causes polychromatic waveScattering causes polychromatic wave
Primary monochromatic electrons
Scattered polychromatic electrons
Sample
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The chromatic aberration are most profound at the edges of the lens.
By placing an aperture immediately after the specimen, chromatic aberration is reduced along with increasing contrast.
CA correction by CA correction by aperture (at lens edges)aperture (at lens edges)
Edges beam
Narrow aperture
Many focal planes
One focal plane
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Spherical aberrationSpherical aberration
When wavelengths enter and leave the lens field at different angles, it results in a defect known as spherical aberration (SA).
The result is similar to that of chromatic aberration in that wavelengths are brought to different focal points.
Spherical aberration
Mo
no
ch
rom
atic
so
urc
e
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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.
SA correction by aperture SA correction by aperture
Edges beam
Narrow apertureOne focal plane
Many focal planes
Astigmatism - distorted image, caused by:
Lens unsymmetrical, objects will be focussed to different focal planes, resulting in an astigmatic image
Dirt on aperture
Astigmatism Astigmatism Lens
Focal point F1
Y-planeFocal point F1
Z-planeFocal point F2
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Astigmatism Astigmatism
Lens
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In OM astigmatism 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 - a ring of electromagnets positioned around the beam to “push” and “pull” the beam to make it more perfectly circular.
Correction by stigmator Correction by stigmator
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