Electron optics
C9940 3-Dimensional Transmission Electron Microscopy
S1007 Doing structural biology with the electron microscope
February 23, 2015
Correction/clarification from last week
http://ernst.ruska.de
First Siemens microscope, 1939
http://emu.msim.org.uk
First commercial EM, 1937
Metropolitan-Vickers EM1
(EM2 shown)
The first commercial
electron microscope
was actually by the
British company
Metropolitan-Vickers
in 1937. However,
the magnification was
worse than for the
light microscope, so
the Siemens is
considered “first.”
Correction/clarification
Metropolitan Vickers
eventually became
AEI, which built a 1.2
million volt EM-7.
http://www.wadsworth.org
Contrast transfer function
Why do we defocus?
1.0
0.1
Typical amplitude contrast is estimated a 0.08-0.12
(minus noise)
water
macromolecule
Instead of amplitude contrast,
we'll use phase contrast.
Phase contrast in light microscopy
Bright-field image Phase-contrast image
http://www.microbehunter.com
In EM, even with defocus, the contrast is poor.
Signal-to-noise ratio for cryoEM typically given to be between 0.07 and 0.10.
E. coli 70S ribosomes, field width ~1440Å.
unfiltered filtered
http://www.microscopy.ethz.ch
http://electron6.phys.utk.edu
Relationship between imaging and diffraction
Optical path
Specimen
Back focal plane
Image plane
At focus, all we would see is amplitude contrast.
Specimen
Back focal plane
Image plane
Optical path with defocus
Perfect focus
Image plane
Focal plane
O
A B
OA path of unscattered beam
OB path of scattered beam
The length OA is
also the amount of defocus Δf
Optical path with defocus
What is the path difference between the scattered and unscattered beams?
Path difference as a function of Δf
OB = OA/cos(a)
Expressed in the number of wavelengths λ
Phase difference is the sine
O
A B
a
Some typical values
OA = Δf = 10,000 Å
λ = 0.02 Å
a < 0.01
A more precise formulation of the CTF can be found in
Erickson & Klug A (1970). Philosophical Transactions of the Royal Society B. 261:105.
Proper form the CTF
where:
Cs: spherical aberration
k: spatial frequency (resolution)
What do we mean by spatial frequency?
origin
spatial frequency
From Wikipedia
PowerspectrumProfile
How does the CTF affect an image?
original
original
combined
Still a zero present