The electron microscope: the contrast transfer function (CTF)

Javier Vargas

Centro Nacional de Biotecnología-CSIC

jvargas@cnb.csic.es

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

Important characteristics of cryoEM images

1) Projection images

2) Phase contrast and WPA

Projection images

Images are formed by phase contrast

projection images

3DEM as an inverse problem3DEM as an inverse problem

Limitations of cryo-electron microscopy

1) Radiation damage.

Limitations of cryo-electron microscopy

1) Radiation damage.2) Electron lenses.

Limitations of cryo-electron microscopy

1) Radiation damage.2) Electron lenses.3) The samples are very small.

Limitations of cryo-electron microscopy

1) Radiation damage.2) Electron lenses.3) The samples are very small.

4) Presence of ice.

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.

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)

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

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

Why use electrons?:

Advantages Disadvantages

Visible light

Why use electrons?:

Advantages Disadvantages

Visible light Not very damaging

Easily focused

Why use electrons?:

Advantages Disadvantages

Visible light Not very damaging

Easily focused

Long wavelengths (~400 nm)

Poor Penetration

X rays

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

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

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

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

Electrons energy

Electrons wavelength

Why electron microscopes?

electron microscopy

light microscopy

Why electron microscopes?

electron microscopes

Electrons energy

Electrons wavelength

The contrast transfer function (CTF)

Main idea

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 !!!

Perfect system: the image of a point is a point

Real system: the image of a point is a spot

IntroductionIntroduction

There is no any perfect real system!!

Transfer functions

Frequency increase

Transfer functions

bass treble

Transfer functions

Transfer functions

CTF

Transfer functions

Transfer functions

8 Ǻ

With phase-plate

RRRRRR sin1cos 2AAECTF

RRR

R

RRRRRR

sin

0

sin1cos 2

ECTF

A

AAECTF

RRR

R

RRRRRR

sin

0

sin1cos 2

ECTF

A

AAECTF

Spherical m,Astigmatis Defocus,F

Matlab Script to simulate the CTF

How a real microscope distort the ideal projections?

Assuming a LTI system

PSFII ir

CTFIFTIFT ir ·

Defocus = 0 A.

Astigmatism = 0 A.

Defocus = 0 A.

Astigmatism = 0 A.

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

PSFII ir

CTFIFTIFT ir ·

CTFIFTFTI ir ·1

A little bit of theory…

CTF is important because:

1. Image restoration (deconvolution)

2. Micrograph screening

1. Image restoration (deconvolution)

Problem: CTF have zeros

1CTF Is not well defined at some points

CTFIFTFTI ir ·1 11 · CTFIFTFTI ri

11 · CTFIFTFTI ri

Wiener filter

22

2

1 1·

KCTF

CTF

CTFIFTFTI ri

No problems in frequencies 0, yxCTF

1. Image restoration (deconvolution)

CTF is important because:

2. Micrograph screening

CTF is important because:

2. Micrograph screening

Questions?