The electron microscope:
Image Formation, The contrast transfer function (CTF),
Direct Electron Detectors
José María Carazo
Centro Nacional de Biotecnología-CSIC
Instruct Image Processing Center
[email protected]
What is an electron microscope?
Why electron microscopes?
What is an electron microscope?
An electron microscope is a tool for obtaining
projection images of very small biological objects
Evolution
Why use electrons?:
Advantages
Visible light
Disadvantage
s
Why use electrons?:
Advantages
Visible light
Not very
damaging
Easily focused
Disadvantage
s
Why use electrons?:
Visible light
Advantages
Disadvantage
s
Not very
damaging
Long
wavelengths
(~400 nm)
Easily focused
X rays
Poor
Penetration
Why use electrons?:
Visible light
Advantages
Disadvantage
s
Not very
damaging
Long
wavelengths
(~400 nm)
Easily focused
X rays
Small
wavelength
(Angstromgs)
Good
penetration
Poor
Penetration
Why use electrons?:
Visible light
Advantages
Disadvantage
s
Not very
damaging
Long
wavelengths
(~400 nm)
Easily focused
X rays
Small
wavelength
(Angstromgs)
Good
penetration
Poor
Penetration
Hard to focus
Damage
Samples
Why use electrons?:
Visible light
Advantages
Disadvantage
s
Not very
damaging
Long
wavelengths
(~400 nm)
Easily focused
X rays
Small
wavelength
(Angstromgs)
Good
penetration
Electrons
Small
wavelength
Poor
Penetration
Hard to focus
Damage
Samples
Why use electrons?:
Visible light
Advantages
Disadvantage
s
Not very
damaging
Long
wavelengths
(~400 nm)
Easily focused
X rays
Small
wavelength
(Angstromgs)
Good
penetration
Electrons
Small
wavelength
(pm)
Poor
Penetration
Hard to focus
Damage
Samples
Damage
Samples
Poor
Electron microscopes
Electrons energy
Electrons wavelength
Not so easy…. The EM visualizes
the “invisible”!
-Difference between what you see with
your iPhone and what you see at the EM.
-How does my object interfere with
radiation?. Remember Klingons “cloaking
device”!
Think in Fourier Space
Changing the “amplitude”
(attenuation)
Changing the “wavelength” (“color)
Changing “the phase origin”
Think in Fourier Space: Waves!
In short: Overcoming a “cloaking
device”
-Changing the amplitude:
Biological specimens do not absorb
They are transparent to your iPhone!
-Changing the Wavelength (“color like”)
Biological specimens do not inelastically interact with electrons.
Electrons do not change “color”
-Changing the phase origin
Very subtle change: Phase objects!
Images are formed by phase
contrast
The contrast transfer function
(CTF)
Main idea
Introduction
Perfect system: the image of a point is a
point
Real system: the image of a point is a spot
Hubble telescope was myopic !!!
Perfect system: the image of a point is a
point
Real system: the image of a point is a spot
Hubble telescope was myopic !!!
There is no any perfect real system!!
Perfect system: the image of a point is a
point
Real system: the image of a point is a spot
Transfer functions
Frequency
increase
Transfer functions
Transfer functions
bass
treble
Transfer functions
CTF
Transfer functions
CTF  R   E  R  sin    R  
CTF  R   E  R  sin    R  
 F Defocus, Astigmatis m, Spherical 
How a real microscope distort the
ideal projections?
Assuming a LTI system
I r I i  PSF
FT  I r  FT  I i  ·CTF
Matlab Script to simulate the CTF
Defocus = 0 A.
Astigmatism = 0 A.
Defocus = 1000 A (0.1 um).
Astigmatism = 0
Defocus = 10000 A (1um)
Astigmatism = 0
Defocus = 5500 A (0.55 um)
Astigmatism = 4500 A (0.45 um)
How a real microscope distort the
ideal projections?
Assuming a LTI system
I r I i  PSF
FT  I r  FT  I i  ·CTF
I r FT  1  FT  I i  ·CTF 
3DEM as an inverse problem
• Projection images
Projection images
But, remember…… estimate and restore the CTF!
Reconstruction as a
linear set of equations
J
f (r )  x j b j (r )
j 1
J
yi  li , j x j
li , j 1,0
j 1
y1 6
y 2 4
x1 4
x 2 3
x3 2
x 4 1
y 3 7
y 4 3
 x1  x3 6 


 x2  x4 4

x

x

7

1
2


 x3  x4 3
Direct-electron Detector
Devices (DDDs)
Directly detects electrons.
Suitable for automation.
Better signal-to-noise ratio than
film.
Direct-electron Detector
Devices (DDDs)
Directly detects electrons.
Suitable for automation.
Better signal-to-noise ratio than
film.
Very fast acquisition
(17-100s frames/second)
Direct-electron Detector Devices (DDDs)
Directly detects electrons.
Suitable for automation.
Better signal-to-noise ratio than
film.
Very fast acquisition
(17-100s frames/second)
We can “see” how the particles
behaves as a function of the
dose!
Direct-electron Detector
Devices (DDDs)
Directly detects electrons.
Suitable for automation.
Better signal-to-noise ratio than
film.
Very fast acquisition
(17-100s frames/second)
We can “see” how the particles
behaves as a function of the
dose!
The particles move !!!
Beam Induced Movement
A little bit of theory…
CTF is important because:
1. Image restoration (deconvolution)
2. Micrograph screening
1. Image restoration (deconvolution)
I r FT  1  FT  I i  ·CTF 

I i FT  1 FT  I r  ·CTF  1
Problem: CTF have zeros
 CTF   1
Is not well defined at some
points

1. Image restoration (deconvolution)
Wiener filter

I i FT  1 FT  I r ·CTF  1

2



CTF
1
1
I i  FT  FT  I r  ·

2
2

 CTF CTF  K  

No problems in frequenciesCTF
 ,    0
x
y
CTF is important because:
2. Micrograph screening
CTF is important because:
2. Micrograph screening
In the nutshell
• An electron microscope is not
perfect, and it has a “CTF”
– Estimate and restore the CTF!
• EM Images are “projection
images”, you have to “invert”
them to go to 3D
• New EM videos allow for much
higher sensitivity and BIM
Questions?