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The electron microscope: the contrast transfer function (CTF)
Javier Vargas
Centro Nacional de Biotecnología-CSIC
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What is an electron microscope?
Why electron microscopes?
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What is an electron microscope?
An electron microscope is a tool for obtaining projection images of very small biological objects
Evolution
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Important characteristics of cryoEM images
1) Projection images
2) Phase contrast and WPA
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Projection images
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Images are formed by phase contrast
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projection images
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3DEM as an inverse problem3DEM as an inverse problem
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Limitations of cryo-electron microscopy
1) Radiation damage.
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.3) The samples are very small.
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.3) The samples are very small.
4) Presence of ice.
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.3) The samples are very small.
4) Presence of ice.5) Charging: non conductive samples charge up and act like lenses.
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.3) The samples are very small.4) Presence of ice.5) Charging: non conductive samples charge up and act like lenses.6) Expensive. Titan Krios around 1000€/day (NeCEN)
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.3) The samples are very small.4) Presence of ice.5) Charging: non conductive samples charge up and act like lenses.6) Expensive. Titan Krios around 1000€/day (NeCEN)
We obtain very noisy images
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Limitations of cryo-electron microscopy
1) Radiation damage.2) Electron lenses.3) The samples are very small.4) Presence of ice.5) Charging: non conductive samples charge up and act like lenses.6) Expensive. Titan Krios around 1000€/day (NeCEN)
We require a lot of images
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Why use electrons?:
Advantages Disadvantages
Visible light
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Why use electrons?:
Advantages Disadvantages
Visible light Not very damaging
Easily focused
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Why use electrons?:
Advantages Disadvantages
Visible light Not very damaging
Easily focused
Long wavelengths (~400 nm)
Poor Penetration
X rays
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Why use electrons?:
Advantages Disadvantages
Visible light Not very damaging
Easily focused
Long wavelengths (~400 nm)
Poor Penetration
X rays Small wavelength (Angstromgs)
Good penetration
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Why use electrons?:
Advantages Disadvantages
Visible light Not very damaging
Easily focused
Long wavelengths (~400 nm)
Poor Penetration
X rays Small wavelength (Angstromgs)
Good penetration
Hard to focus
Damage Samples
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Why use electrons?:
Advantages Disadvantages
Visible light Not very damaging
Easily focused
Long wavelengths (~400 nm)
Poor Penetration
X rays Small wavelength (Angstromgs)
Good penetration
Hard to focus
Damage Samples
Electrons Small wavelength (pm)
Can be focused
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Why use electrons?:
Advantages Disadvantages
Visible light Not very damaging
Easily focused
Long wavelengths (~400 nm)
Poor Penetration
X rays Small wavelength (Angstromgs)
Good penetration
Hard to focus
Damage Samples
Electrons Small wavelength (pm)
Can be focused
Damage Samples
Poor Penetration
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Electrons energy
Electrons wavelength
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Why electron microscopes?
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electron microscopy
light microscopy
Why electron microscopes?
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electron microscopes
Electrons energy
Electrons wavelength
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The contrast transfer function (CTF)
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Main idea
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Perfect system: the image of a point is a point
Real system: the image of a point is a spot
Hubble telescope was myopic !!!
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Perfect system: the image of a point is a point
Real system: the image of a point is a spot
Hubble telescope was myopic !!!
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Perfect system: the image of a point is a point
Real system: the image of a point is a spot
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IntroductionIntroduction
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There is no any perfect real system!!
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Transfer functions
Frequency increase
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Transfer functions
bass treble
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Transfer functions
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Transfer functions
CTF
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Transfer functions
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Transfer functions
8 Ǻ
With phase-plate
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RRRRRR sin1cos 2AAECTF
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RRR
R
RRRRRR
sin
0
sin1cos 2
ECTF
A
AAECTF
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RRR
R
RRRRRR
sin
0
sin1cos 2
ECTF
A
AAECTF
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Spherical m,Astigmatis Defocus,F
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Matlab Script to simulate the CTF
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How a real microscope distort the ideal projections?
Assuming a LTI system
PSFII ir
CTFIFTIFT ir ·
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Defocus = 0 A.
Astigmatism = 0 A.
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Defocus = 0 A.
Astigmatism = 0 A.
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Defocus = 0 A.
Astigmatism = 0 A.
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Defocus = 1000 A (0.1 um).
Astigmatism = 0
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Defocus = 10000 A (1um)
Astigmatism = 0
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Defocus = 5500 A (0.55 um)
Astigmatism = 4500 A (0.45 um)
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How a real microscope distort the ideal projections?
Assuming a LTI system
PSFII ir
CTFIFTIFT ir ·
CTFIFTFTI ir ·1
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A little bit of theory…
CTF is important because:
1. Image restoration (deconvolution)
2. Micrograph screening
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1. Image restoration (deconvolution)
Problem: CTF have zeros
1CTF Is not well defined at some points
CTFIFTFTI ir ·1 11 · CTFIFTFTI ri
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11 · CTFIFTFTI ri
Wiener filter
22
2
1 1·
KCTF
CTF
CTFIFTFTI ri
No problems in frequencies 0, yxCTF
1. Image restoration (deconvolution)
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CTF is important because:
2. Micrograph screening
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CTF is important because:
2. Micrograph screening
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Questions?