7. θ=λ/d
4Å at 300 keV
Θ=0.02/4
= 5 mrad
= 0.3 deg
Focal length, f, ~3 mm
Distance to diffraction plane is approximately
the focal length and so ~3 mm.
4Å spot at distance: fθ = 15 μm in diffraction
plane – distances from optical axis are very
small
8. Transmission Electron microscope
(bright field phase contrast)
Source
Condenser lens 1
Condenser lens 2
Objective lens
Sample
Objecive aperture
Intermediate lens
Projector lens
Detector
●
Condenser lens combination sets virtual
source position.
●
Condenser aperture set illumination angle
●
Objective aperture provides a high frequency
cut-off.
●
Objective aperture provides a source of
secondary electrons to help neutralise charge.
build up on sample.
13. Dim Beam is Extremely Coherent
(extreme case Falcon3 counting)
●
0.5 e/pixel/s
●
4096x4096 => 16 million pixels => 10 million electrons
per second
●
300 keV electrons travel at 0.78 speed of light =>
2x10e8 m/s
●
Average distance between electrons:
2x10e8 m/s /(1x10e7/s) = 20 m
●
Cannot use microprobe because Fresnel rings cover
the image
14. Phase object
Ψ ~ 1 + iσ V
|Ψ|2
~ 1 + (σV)2
~ 1
To first order there is no contrast!
15. How do you see something?
Aperture contrast (objective
aperture)
Defocus
Phase plate
16. Phase Plate
Ψ ~ 1 + Φiσ V
|Ψ|2
~ 1 + 2 σV
Ideally Φ ~ i
So Ψ ~ 1 - σ V
17. Weak phase approximation (simplified)
-i s f/2i s f/2
Y ~ 1 – isf exp( -i c)/2 + isf exp( -i c)/2-i s f/2 exp(-ic )i s f/2 exp(-ic )
c(q) = 2p ( Df
q2
/2 – Cs
q4
/4)/l
|Y|2
~ 1 – 2sf sin( c)
Sample
Lens
Image
Focusing wavefunction back to image plane introduces
a phase shift of exp(-ic) where:
in which Df
is the defocus, Cs
the spherical aberration, l the
wavelength and q the scattering angle (q= l/d).
Scattered component of wavefunction is small and given by isf
in which f is the projected potential and s=2pmel/h2
.
Wavefunction at image plane is
so image i.e, probability of an electron arrival, is
18. Image FormationImage Formation
Bright field phase contrastBright field phase contrast
(gives most signal per unit of(gives most signal per unit of
radiation damage)radiation damage)
In focusIn focus 3 um3 um1 um1 um
