Download Principles of TEM image formation Principles of TEM image

Lecture 3
Principles of
TEM image formation
Light microscope - Electron microscope
Elastic and inelastic scattering
Amplitude and phase objects
Phase contrast microscope, Zernike plate
Aberrations
Contrast transfer function - Point spread function
Filters, Correction of CTF, problems
E. Orlova
November 2004
Image processing for cryo EM, 2004
What is common in all these instruments?
Eyepiece
Light microscope
Electron microscope
Using a lens to magnify the image of a small object
F – focal length of the lens
A1 - size of the object
A2 - size of the image
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Eyepiece
Light microscopy
Electron microscopy
Light
source
Condenser
Objective
Object
lens
lens
The first optical microscope
was created in 1611 by Kepler
Image
Electron
Lens
V
Object
windings
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Image
In a magnetic field the electron has a curved trajectory.
The force generated by magnetic field B is normal to both
the velocity V of the electron and to magnetic field B.
A lens for electrons was constructed in 1926 by H. Busch.
In 1930 the first electron microscope was developed.
Ernst Ruska (1906-1988),
Nobel prize 1986
(www.nobel.se)
First electron microscope
Elastic and inelastic scattering of electrons
In an elastic collision of the electron with the atom the
electron will be scattered through an angle Q. The kinetic
energy of the incident electron is not changed significantly.
In an inelastic collision a part of the kinetic energy is
transferred to the atom and transformed into another kind of
energy.
Interaction of the electron beam with the sample
Some electrons go through the sample without any interaction, some of
them will be deflected from the original direction, some will interact with
atoms.
Biological objects consist of C, O, P, N
Heavy metal stain
Cu grid
Continuous carbon film
Contrast in the EM depends on the atomic number of the
atoms in the specimen: the higher the atomic number, the
more electrons are scattered, and the greater is the
contrast. Hence, to make biomacromolecules - that are
composed mainly of carbon, oxygen, nitrogen, and
hydrogen - visible, they are usually impregnated - or
stained - with heavy metal salts containing osmium,
uranium, or lead
A very thin film of metal salt covers the support film
everywhere except where it has been excluded by the
presence of an adsorbed macromolecule or supramolecular
structure. Because the macromolecule allows the electrons
to pass much more readily than does the surrounding heavy
metal film, a reversed or negative image of the molecule is
created, hence the name 'negative staining'.
Biological sample
Vitreous ice
Cu grid
Holy carbon film
Amplitude object
Object
Plane light wave falls
on the specimen
Section of the object
Image
Some parts of
the specimen
are not
transparent.
The amplitude
of the emerged
wave is
changed.
Image
Phase object
Object
Plane light
wave falls
on the
transparent
specimen
Section of the object
Image
The specimen
has variations
in thickness.
The amplitude
of the emerged
wave is not
changed, but
its surface is
curved.
Image
Phase-contrast microscope
Phase contrast microscopy, first described in
1934 by Dutch physicist Fritz Zernike, is a
contrast-enhancing optical technique that can be
utilized to produce high-contrast images of
transparent specimens, such as living cells
(usually in culture), microorganisms, thin tissue
slices, lithographic patterns, fibers, latex
dispersions, glass fragments, and subcellular
particles (including nuclei and other organelles).
A transparent object varies in refractive index or thickness.
If no energy is transferred from the beam to the specimen,
then a plane light wave of uniform amplitude falls on the
specimen and emerges with uniform amplitude A0 but with
phase variations over the plane surface.
T(x,y) = A0exp[iφ(x,y)], for simplicity : A0 = 1
Assuming that the object is thin and phase shift φ is small
The approximation of the emerged wave might be
described as
exp [iφ] ≈ 1+ iφ
- the weak phase object
then T(x,y) ≈ 1+ iφ
We are able to observe only intensities, therefore the
object will be barely visible. I(x,y) is not changed in
practice.
I2 (x,y) =T2(x,y) = (1+ i φ)2 ≈ 1 + φ2
Fritz Zernike (1934) invented a method of converting the
phase variations into amplitude variations:
The phase plate adds an additional phase shift of 900 to
beams diverging from the axis, therefore
I2 (x,y) =T2(x,y) = (1 - φ)2 ≈ 1 – 2φ
1.5
1.5
1.5
emerg
ed
incident
wave
emerg
ed wave
wave
incident
wave
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11
0.15
0.1
0.5
0.5
0.5
0.05
00 00
1
11
-0.051
scattered
wave
scattered wave
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811
901
991
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181 271
271 361
361 451
451 541
541 631
631 721
721 811
811 901
901 991
181
-0.5
-0.5
-0.5
-0.1
-0.15
-1
-1-1
emerg
emerged
ed wave
wave
-1.5
-1.5
-1.5
scattered
wave
scattered wave
iφ
result of influence
of the phase plate
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wave
Phase-contrast microscope
Wavefronts passing through the annulus
illuminate the specimen and either pass through
undeviated or are diffracted and retarded in
phase by structures and phase gradients present
in the specimen. Undeviated and diffracted light
collected by the objective is segregated at the
rear focal plane by a phase plate that transforms
differences in phase into amplitude differences.
Then light is focused at the intermediate image
plane to form the final phase contrast image
observed in the eyepieces.
The angular deviation causes differences in
optical path between two trajectories of rays
scattered by different parts of lens.
Contrast can be created in electron microscope if:
1. Some of electrons scattered by the specimen may
be removed by aperture
2. Spherical aberration is present
3. The viewing plane is not conjugate to the specimen
plane, i.e., the image is not exactly in focus
The imaging properties of an objective lens are
described by a contrast-transfer function,
independent of any particular specimen structure. That
has been described for electron microscope by Scherzer
in 1949 (J.Appl.Phys., 20, 20-29)
Aberrations in lenses
y
Ideal lens
Astigmatic
aberration
x
Spherical aberration
Chromatic
aberration
The phase structure of the specimen image is
described by:
PhCF = sin[π/2(Csλ3q4-2∆zλq2)]
The amplitude structure of the specimen image is
described by:
AmCF = cos[π/2(Csλ3q4-2∆zλq2)]
Cs – spherical aberration coefficient
∆Z – defocus
q – spatial frequency
λ – wave length of electrons
Phase CTF formula from
the weak phase approximation
Phase CTF = -2 sin [π(∆zλq2 - Csλ3q4/2)]
Cs – spherical aberration coefficient
∆Z – defocus
q – spatial frequency
λ – electron wavelength
Convolution of two functions
?
Convolution of two functions represents a distribution of the
one function determined by the second one.
Convolution can be calculated in the real space (space of
the image) or using reciprocal space ( Fourier space =
Fourier transforms)
Function
Fourier transform
Function
Fourier transform
Product
of Fourier transforms
Convolution of two functions
Reversed Fourier transformation
Low pass filter
High pass filter
Low pass filter
High pass filter
Gaussian filter
Half width R = 0.4
Band pass filter
R1=0.1, R2=0.5
Low pass filter
High pass filter
Low pass filter
High pass filter
CTF 1
CTF 2
Point spread function
Voltage 200 kV
Defocus 1.5 µ
Voltage 200 kV
Defocus 3.5 µ
Contrast transfer function
Convolution of objects (functions) is equivalent
to filtering.
An unwanted example of filtering, which must be
corrected, is given by the effect of the point
spread function on the image. The Fourier
transform of the point spread function is the
contrast transfer function, which multiplies the
FT of the image.
The phase structure of the specimen image is
described by:
PhCF = sin[π/2(Csλ3q4-2∆zλq2)]
The amplitude structure of the specimen image is
described by:
AmCF = cos[π/2(Csλ3q4-2∆zλq2)]
Cs – spherical aberration coefficient
∆Z – defocus
q – spatial frequency
λ – wave length of electrons
∆:
∆:
1 Scherzer
original
∆:
1 Scherzer
10 Scherzer
∆:
10 Scherzer
∆Z = -4.8 µm
−4.0 µm
-3.2 µm
-2.4 µm
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-1.6 µm
1.6 µm
−0.8 µm
2.4 µm
~0. µm
3.2 µm
0.8 µm
4.0 µm
Defocus
series of
ferritin
molecules
on a 5nm
carbon
supporting
film,
V=100keV
Defocus
Defocus
Causes of CTF decay
• Loss of spatial coherence - source size
Tungsten
FEG
• Image drift
• Thick ice
• Specimen charging
• Chromatic aberration - variation in voltage
• Variation of lens current
FEG images of carbon film
0.5 µm
1 µm
Astigmatism
Drift
References
Frank, J. (1996) Three-dimensional electron microscopy of
macromolecular assemblies. Academic Press, San Diego.
Reimer, L. (1989) Transmission electron microscopy.
Springer-Verlag, Berlin
Hawkes & Valdrè (1990) Biophysical electron microscopy.
Academic Press, London.
Hawkes, P. W. in Electron tomography: three-dimensional
imaging with the transmission electron microscope (ed.
Frank, J.) (Plenum Press, New York and London, 1992).
Erickson, H. P. & Klug, A. The Fourier transform of an
electron micrograph: effects of defocusing and
aberrations, and implications for the use of underfocus
contrast enhancement. Phil. Trans. Roy. Soc. Lond. B
261, 105-118 (1970).
Erickson, H. P. and A. Klug (1971) Measurement and
compensation of defocusing and aberrations by fourier
processing of electron micrographs. Phil. Trans. R. Soc.
Lond. B. 261, 105-118.
Dubochet, J., M. Adrian, J.-J. Chang, J.-C. Homo, Lepault,
J., A. W. McDowall and P. Schultz (1988) Cryo-electron
microscopy of vitrified specimens. Quart. Rev. Biophys.
21, 129-228.
Toyoshima, C. and N. Unwin (1988) Contrast transfer for
frozen-hydrated specimens: determination from pairs
of defocused images. Ultramicroscopy. 25, 279-292.
Zemlin, F. (1994) Expected contribution of the fieldemission gun to high-resolution transmission electron
microscopy. Micron 25, 223-226.
Zemlin, F. (1992) Desired features of cryoelectron
microscope for the electron crystallography of
biological material. Ultramicroscopy. 46, 25-32.
4-14 September 2005,
Birkbeck College, London
EMBO Course on
Image processing in Cryomicroscopy
Single particle analysis
Fitting