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Electron Microscopy Lecture 2: 1. The optical microscopy and its
limitations;
2. Properties of electrons
Boquan Li
Office: WB239
Phone: x6025
TEM Column
TEM Column
Why Optical Microscopy?
The principle of geometric optics and image formation based on optical lens
properties are the same in TEM;
The concepts of resolution, magnification, depth of field and lens aberration are the
same;
Refreshing for those who use optical microscopes.
Nature of Light
Laws of Reflection and Refraction
Definition of the half-angle
Numerical Aperture
Single Lens and Ray Diagrams
lens
object
Image plane Front focal plane
Back focal plane
A
B
B
A
O F
F
Let BO=u, OB=v, FO=OF=f
fvu111
Lens formula Magnification
uv
ABBAM ''
Optical axis
Single Lens and Ray Diagrams
Image is real, inverted and
magnifed.
fuf 2
fu Image is virtual, erect
and magnified.
fu 2
Image is real, inverted
and demagnified.
Back Focal Plane
Diffraction pattern
Two-Lens System and Ray
Diagrams
Resolution: Diffraction Limit and
Rayleighs Criterion
Aperture
75 m pinhole 100 m pinhole
Airy rings from diffraction of a laser beam:
When light passes
though an aperture,
diffraction occurs so
that a parallel beam
of light is transformed
into a series of
cones.
Light Intensity Distribution
Rayleigh Criterion
sin61.0
211 d
r
Resolution-Influence of NA
Resolution-Influence of NA
Resolution-Influence of Wavelength
Resolution-Influence of Wavelength
Resolution-Influence of Wavelength
Resolution-Influence of Wavelength
Diffraction Limit of Optical
Microscopes
Here r1 is the smallest distance that can be
resolved, is the wavelength of the visible light, is the refractive index, and is the semi-angle of collection of the magnifying
lens.
For the shortest wavelength of the visible
spectrum, 400 nm, and the biggest
possible numerical aperture sin is 1.6, so the resolution of a good light
microscope is about 150 nm.
Depth of field
The range of positions for the object that appears sharp in the image
2
tansin
61.0h
Decreasing the convergence angle will increase the DOF, but
decrease the resolution.
Depth of Focus
Range of positions at which the image can be viewed
without appearing out of focus, for a fixed position of
the object.
2
2
2
Mu
v
du
dv
The higher the magnification, the higher the DOF.
For constant focal length, if we differentiate the lens
formula, then,
Electrons
Charged particles
Can be accelerated by an electric field
Can be bent by either electric or magnetic fields
Can be easily generated by heating a filament
Can be detected using phosphor plates or films
The Wave Nature of Electrons
de Broglie equation (1924):
ph
Here is the wavelength of a particle, h is the Planck constant, and p is the momentum of the particle.
I believe it is a first feeble ray of light on this
worst of our physics enigmas".
A. Einstein
Wavelength of Electrons
mpmveE 2/2/ 22
An electron accelerated by an electric
potential has energy:
emh 02/
So
Wavelength of Electrons
Considering relativistic effects:
200 2/12/ cmeemh
Electron Wavelengths as a
Function of Accelerating Voltage
Accelerating
voltage (kV)
Nonrelativistic
wavelength(nm)
Relativistic
wavelength(nm)
100 0.00386 0.00370
120 0.00352 0.00335
200 0.00273 0.00251
300 0.00223 0.00197
400 0.00193 0.00164
1000 0.00122 0.00087
Relative wavelengths
Cu = 1.5406
100 = 0.037
120 = 0.0335
200 = 0.0251
300 = 0.0197
Electron
wavelengths are
about 50X
smaller than X-
ray.
XRD
Brief history of the TEM development 1924 - Louis de Broglie theorized that the electron
had wave-like characteristics;
1927 - Davisson and Germer carried out electron diffraction experiments (wave nature);
1931 - Max Knoll and Ernst Ruska developed electromagnetic lenses and constructed the first electron microscope most crucial step, for which Ruska received the Nobel Prize in 1986;
1933 - Ruskas EM exceeded the resolution of the light microscope. It had an accelerating voltage of 75 kV;
1939 - Siemens supplied the first commercially available electron microscope;
Today - JEOL and FEI build thousands of EM.
Evolution of TEM Instrumentation
First TEM, 1931
JEM-ARM200F, 2009
JEM-100, 1980s
