lecture lecture 33 principles of tem image...

Principles of TEM image formation

Principles of TEM image formation

Lecture 3Lecture Lecture 33

Light microscope Light microscope -- Electron microscope Electron microscope Elastic and inelastic scattering Elastic and inelastic scattering Amplitude and phase objectsAmplitude and phase objectsPhase contrast microscope, Zernike platePhase contrast microscope, Zernike plateAberrations Aberrations Contrast transfer function Contrast transfer function -- Point spread function Point spread function Filters, Correction of CTF, problemsFilters, Correction of CTF, problems

E. OrlovaE. Orlova

Image processing for cryo EM, 2004Image processing forImage processing for cryocryo EM, 2004EM, 2004

November 2004November 2004

What is common in all these instruments?What is common in all these instruments?

EyepieceEyepiece

Light microscopeLight microscope

Electron microscopeElectron microscope

Using a lens to magnify the image of a small object

F – focal length of the lens A1 - size of the object A2 - size of the imageF – focal length of the lens A1 - size of the object A2 - size of the image

Bacterium

Animal cell

Ribosome

Virus Globular

proteinPlant cell

AtomSmall

molecules

The first optical microscope was created in 1611 by KeplerThe first optical microscope

was created in 1611 by Kepler

Object

Image

Objective lens

Condenserlens

Lightsource

Electron microscopyElectron microscopyLight microscopyLight microscopy

EyepieceEyepiece

Ob ject

Image

Obj ective le nsCo ndens erlens

Li ghtsou rce

Object

Image

LensElectron

X

windingsV

F

B

In a magnetic field the electron has a curved trajectory. The force generated by magnetic field B is normal to both the velocity V of the electron and to magnetic field B.

A lens for electrons was constructed in 1926 by H. Busch.In 1930 the first electron microscope was developed.

In a magnetic field the electron has a curved trajectory. The force generated by magnetic field B is normal to both the velocity V of the electron and to magnetic field B.

A lens for electrons was constructed in 1926 by H. Busch.In 1930 the first electron microscope was developed.

Ernst Ernst RuskaRuska (1906(1906--1988), 1988), Nobel prize 1986 Nobel prize 1986 (www.(www.nobelnobel.se).se)

First electron microscope First electron microscope

Elastic and inelastic scattering of electronsElastic and inelastic scattering of electrons

In an elastic collision of the electron with the atom the electron will be scattered through an angle Q. The kinetic energy of the incident electron is not changed significantly.In an inelastic collision a part of the kinetic energy is transferred to the atom and transformed into another kind of energy.

In an elastic collision of the electron with the atom the electron will be scattered through an angle Q. The kinetic energy of the incident electron is not changed significantly.In an inelastic collision a part of the kinetic energy is transferred to the atom and transformed into another kind of energy.

Interaction of the electron beam with the sampleInteraction of the electron beam with the sample

Some electrons go through the sample without any interaction, some of them will be deflected from the original direction, some will interact with atoms.

Heavy metal stainHeavy metal stain

Biological objects consist of C, O, P, NBiological objects consist of C, O, P, N

Cu gridCu grid

Continuous carbon filmContinuous carbon film

Contrast in the EM depends on the atomic number of the Contrast in the EM depends on the atomic number of the atoms in the specimen: the higher the atomic number, the atoms in the specimen: the higher the atomic number, the more electrons are scattered, and the greater is the more electrons are scattered, and the greater is the contrast. Hence, to makecontrast. Hence, to make biomacromoleculesbiomacromolecules -- that are that are composed mainly of carbon, oxygen, nitrogen, and composed mainly of carbon, oxygen, nitrogen, and hydrogenhydrogen -- visible, they are usually impregnated visible, they are usually impregnated -- or or stained stained -- with heavy metal salts containing osmium, with heavy metal salts containing osmium, uranium, or leaduranium, or lead

A very thin film of metal salt covers the support film A very thin film of metal salt covers the support film everywhere except where it has been excluded by the everywhere except where it has been excluded by the presence of an adsorbed macromolecule or presence of an adsorbed macromolecule or supramolecularsupramolecularstructure. Because the macromolecule allows the electrons structure. Because the macromolecule allows the electrons to pass much more readily than does the surrounding heavy to pass much more readily than does the surrounding heavy metal film, a reversed or negative image of the molecule is metal film, a reversed or negative image of the molecule is created, hence the name 'negative staining'.created, hence the name 'negative staining'.

Vitreous iceVitreous ice

Biological sampleBiological sampleBiological sample

Cu gridCu grid

Holy carbon filmHoly carbon film

Amplitude objectAmplitude object

Plane light wave falls on the specimen

Some parts of the specimen are not transparent. The amplitude of the emerged wave is changed.

Object

Section of the object

Image

Image

Phase objectPhase object

Plane light wave falls on the transparent specimen

The specimen has variations in thickness. The amplitude of the emerged wave is not changed, but its surface is curved.

Object

Section of the object

Image

Image

Phase-contrast microscopePhase-contrast microscope

Phase contrast microscopy, first described in Phase contrast microscopy, first described in 1934 by Dutch physicist 1934 by Dutch physicist FritFritzz ZernikeZernike, is a, is acontrastcontrast--enhancing optical techniqueenhancing optical technique that can be that can be utilized to utilized to produce highproduce high--contrast imagescontrast images of of transparent specimenstransparent specimens, such as living cells , such as living cells (usually in culture), microorganisms, thin(usually in culture), microorganisms, thin tissue tissue slices, lithographic patterns, fibers, latex slices, lithographic patterns, fibers, latex dispersions, glass fragments, and dispersions, glass fragments, and subcellularsubcellularparticles (including nuclei and other organelles).particles (including nuclei and other organelles).

A transparent object varies in refractive index or thickness.If no energy is transferred from the beam to the specimen, then a plane light wave of uniform amplitude falls on the specimen and emerges with uniform amplitude A0 but with phase variations over the plane surface.

T(x,y) = A0exp[iφ(x,y)], for simplicity : A0 = 1

Assuming that the object is thin and phase shift φ is smallThe approximation of the emerged wave might be described as

exp [iφ] ≈ 1+ iφ - the weak phase object

then T(x,y) ≈ 1+ iφ

A transparent object varies in refractive index or thickness.If no energy is transferred from the beam to the specimen, then a plane light wave of uniform amplitude falls on the specimen and emerges with uniform amplitude A0 but with phase variations over the plane surface.

T(x,y) = A0exp[iφ(x,y)], for simplicity : A0 = 1

Assuming that the object is thin and phase shift φ is smallThe approximation of the emerged wave might be described as

exp [iφ] ≈ 1+ iφ - the weak phase object

then T(x,y) ≈ 1+ iφ

We are able to observe only intensities, therefore the object will be barely visible. I(x,y) is not changed in practice.

I2 (x,y) =T2(x,y) = (1+ i φ)2 ≈ 1 + φ2

Fritz Zernike (1934) invented a method of converting the phase variations into amplitude variations: The phase plate adds an additional phase shift of 900 to beams diverging from the axis, therefore

I2 (x,y) =T2(x,y) = (1 - φ)2 ≈ 1 – 2φ

We are able to observe only intensities, therefore the object will be barely visible. I(x,y) is not changed in practice.

I2 (x,y) =T2(x,y) = (1+ i φ)2 ≈ 1 + φ2

Fritz Zernike (1934) invented a method of converting the phase variations into amplitude variations: The phase plate adds an additional phase shift of 900 to beams diverging from the axis, therefore

I2 (x,y) =T2(x,y) = (1 - φ)2 ≈ 1 – 2φ

-1.5

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scattered wavescattered wave

incident waveincident wave

scattered wavescattered waveiφiφ 900900

incident waveincident wave

emerged waveemerged wave

result of influence of the phase plateresult of influence of the phase plate

-1.5

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1.5

1 91 181 271 361 451 541 631 721 811 901 991

emerged waveemerged wave

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

1 91 181 271 361 451 541 631 721 811 901 991

-1.5

-1

-0.5

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1.5

1 91 181 271 361 451 541 631 721 811 901 991

emerged waveemerged wave

Phase-contrast microscopePhase-contrast microscope

WavefrontsWavefronts passing through the annulus passing through the annulus illuminate the specimen and either pass through illuminate the specimen and either pass through undeviatedundeviated or are diffracted and retarded in or are diffracted and retarded in phase by structures and phase gradients present phase by structures and phase gradients present in the specimen. in the specimen. UndeviatedUndeviated and diffracted light and diffracted light collected by the objective is segregated at the collected by the objective is segregated at the rear focal plane by a phase platerear focal plane by a phase plate that transforms that transforms differences in phase into amplitude differences. differences in phase into amplitude differences. Then light isThen light is focused at the intermediate image focused at the intermediate image plane to form the final phase contrast image plane to form the final phase contrast image observed in the eyepieces.observed in the eyepieces.

The angular deviation causes differences in The angular deviation causes differences in optical path between two trajectories of rays optical path between two trajectories of rays scattered by different parts of lens.scattered by different parts of lens.

Contrast can be created in electron microscope if:Contrast can be created in electron microscope if:1.1. Some of electronsSome of electrons scattered by the specimen may scattered by the specimen may

be be removed by apertureremoved by aperture2.2. Spherical aberration is presentSpherical aberration is present3.3. The viewing plane is not conjugate to the specimen The viewing plane is not conjugate to the specimen

plane, i.e., plane, i.e., the image is not exactly in focusthe image is not exactly in focus

The imaging properties of an objective lens are The imaging properties of an objective lens are described by a contrastdescribed by a contrast--transfer function,transfer function,independent of any particular specimen structure. That independent of any particular specimen structure. That has been described for electron microscope by has been described for electron microscope by Scherzer Scherzer in 1949 (J.in 1949 (J.ApplAppl.Phys., 20, 20.Phys., 20, 20--29)29)

Ideal lensIdeal lens Astigmatic aberration

Astigmatic aberration

Spherical aberrationSpherical aberration Chromatic aberration

Chromatic aberration

Aberrations in lensesAberrations in lenses

x

y

The phase structure of the specimen image is described by:

PhCF = sin[π/2(Csλ3q4-2∆zλq2)]

The amplitude structure of the specimen image is described by:

AmCF = cos[π/2(Csλ3q4-2∆zλq2)]

Cs – spherical aberration coefficient∆Z – defocusq – spatial frequencyλ – wave length of electrons

Phase CTF formula from the weak phase approximation

Phase CTF = -2 sin [π(∆zλq2 - Csλ3q4/2)]

Cs – spherical aberration coefficient∆Z – defocusq – spatial frequencyλ – electron wavelength

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Convolution of two functionsConvolution of two functions

Convolution of two functions represents a distribution of the one function determined by the second one.Convolution can be calculated in the real space (space of the image) or using reciprocal space ( Fourier space = Fourier transforms)

Function Fourier transform

Function Fourier transform

Product of Fourier transforms

Convolution of two functions

Reversed Fourier transformationReversed Fourier transformation

Low pass filterLow pass filter High pass filterHigh pass filter

Low pass filterLow pass filter High pass filterHigh pass filter

Gaussian filterHalf width R = 0.4

Band pass filterR1=0.1, R2=0.5

Low pass filterLow pass filter High pass filterHigh pass filter

Low pass filterLow pass filter High pass filterHigh pass filter

CTF 1 CTF 2

Point spread function

Voltage 200 kVDefocus 1.5 µ

Contrast transfer function

Voltage 200 kVDefocus 3.5 µ

Convolution of objects (functions) is equivalent to filtering.

An unwanted example of filtering, which must be corrected, is given by the effect of the point spread function on the image. The Fourier transform of the point spread function is the contrast transfer function, which multiplies the FT of the image.

The phase structure of the specimen image is described by:

PhCF = sin[π/2(Csλ3q4-2∆zλq2)]

The amplitude structure of the specimen image is described by:

AmCF = cos[π/2(Csλ3q4-2∆zλq2)]

Cs – spherical aberration coefficient∆Z – defocusq – spatial frequencyλ – wave length of electrons

∆ : 10 Scherzer∆ : 1 Scherzer

original ∆: 1 Scherzer ∆ : 10 Scherzer

Ob ject

Image

Obj ective le nsCo ndens erlens

Li ghtsou rce

1.6 µm

−4.0 µm∆Z = -4.8 µm -3.2 µm

0.8 µm~0. µm−0.8 µm-1.6 µm

-2.4 µm

2.4 µm 4.0 µm3.2 µm

Defocus series of ferritin molecules on a 5nm carbon supporting film, V=100keV

Defocus

Defocus

Causes of CTF decay

• Loss of spatial coherence - source size

• Image drift• Thick ice• Specimen charging• Chromatic aberration - variation in voltage• Variation of lens current

FEGTungsten

FEG images of carbon film

0.5 µm 1 µm

Astigmatism

Drift

ReferencesFrank, J. (1996) Three-dimensional electron microscopy of

macromolecular assemblies. Academic Press, San Diego.Reimer, L. (1989) Transmission electron microscopy.

Springer-Verlag, BerlinHawkes & Valdrè (1990) Biophysical electron microscopy.

Academic Press, London.Hawkes, P. W. in Electron tomography: three-dimensional

imaging with the transmission electron microscope (ed. Frank, J.) (Plenum Press, New York and London, 1992).

Erickson, H. P. & Klug, A. The Fourier transform of an electron micrograph: effects of defocusing and aberrations, and implications for the use of underfocus contrast enhancement. Phil. Trans. Roy. Soc. Lond. B261, 105-118 (1970).

Erickson, H. P. and A. Klug (1971) Measurement and compensation of defocusing and aberrations by fourierprocessing of electron micrographs. Phil. Trans. R. Soc.Lond. B. 261, 105-118.

Dubochet, J., M. Adrian, J.-J. Chang, J.-C. Homo, Lepault, J., A. W. McDowall and P. Schultz (1988) Cryo-electron microscopy of vitrified specimens. Quart. Rev. Biophys. 21, 129-228.

Toyoshima, C. and N. Unwin (1988) Contrast transfer for frozen-hydrated specimens: determination from pairs of defocused images. Ultramicroscopy. 25, 279-292.

Zemlin, F. (1994) Expected contribution of the field-emission gun to high-resolution transmission electron microscopy. Micron 25, 223-226.

Zemlin, F. (1992) Desired features of cryoelectronmicroscope for the electron crystallography of biological material. Ultramicroscopy. 46, 25-32.

4-14 September 2005, Birkbeck College, London

EMBO Course onImage processing in Cryo-

microscopySingle particle analysis

Fitting

4-14 September 2005, Birkbeck College, London

EMBO Course onImage processing in Cryo-

microscopySingle particle analysis

Fitting