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Lecture 3 Principles of TEM image formation Light microscope - Electron microscope Elastic and inelastic scattering Amplitude and phase objects Phase contrast microscope, Zernike plate Aberrations Contrast transfer function - Point spread function Filters, Correction of CTF, problems E. Orlova November 2004 Image processing for cryo EM, 2004 What is common in all these instruments? Eyepiece Light microscope Electron 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 image l lar all l e u l e m l m iu lc ob iSnm ulesm o ce r l a s e t s G t n u ibo te lec to c im r a i o a l n r V R P B A p mo A Eyepiece Light microscopy Electron microscopy Light source Condenser Objective Object lens lens The first optical microscope was created in 1611 by Kepler Image Electron Lens V Object windings F X B i g L t h u rc o s e o n C s re e d b e O jc t O j e b vc ti e l s n e l n s Ia m e g Image 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 Ruska (1906-1988), Nobel prize 1986 (www.nobel.se) First electron microscope Elastic 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. Interaction 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. Biological objects consist of C, O, P, N Heavy metal stain Cu grid Continuous carbon film Contrast in the EM depends on the atomic number of the atoms in the specimen: the higher the atomic number, the more electrons are scattered, and the greater is the contrast. Hence, to make biomacromolecules - that are composed mainly of carbon, oxygen, nitrogen, and hydrogen - visible, they are usually impregnated - or stained - with heavy metal salts containing osmium, uranium, or lead A very thin film of metal salt covers the support film everywhere except where it has been excluded by the presence of an adsorbed macromolecule or supramolecular structure. Because the macromolecule allows the electrons to pass much more readily than does the surrounding heavy metal film, a reversed or negative image of the molecule is created, hence the name 'negative staining'. Biological sample Vitreous ice Cu grid Holy carbon film Amplitude object Object Plane light wave falls on the specimen Section of the object Image Some parts of the specimen are not transparent. The amplitude of the emerged wave is changed. Image Phase object Object Plane light wave falls on the transparent specimen Section of the object Image The specimen has variations in thickness. The amplitude of the emerged wave is not changed, but its surface is curved. Image Phase-contrast microscope Phase contrast microscopy, first described in 1934 by Dutch physicist Fritz Zernike, is a contrast-enhancing optical technique that can be utilized to produce high-contrast images of transparent specimens, such as living cells (usually in culture), microorganisms, thin tissue slices, lithographic patterns, fibers, latex dispersions, glass fragments, and subcellular 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 small The 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 1.5 1.5 1.5 emerg ed incident wave emerg ed wave wave incident wave 1 11 0.15 0.1 0.5 0.5 0.5 0.05 00 00 1 11 -0.051 scattered wave scattered wave 91 181 271 361 451 541 631 721 811 901 991 9191 181 181 271 271 361 361 451 451 541 541 631 631 721 721 811 811 901 901 991 181 -0.5 -0.5 -0.5 -0.1 -0.15 -1 -1-1 emerg emerged ed wave wave -1.5 -1.5 -1.5 scattered wave scattered wave iφ result of influence of the phase plate 90 9000 aavvee w w d e d g e r g e eem mer incident incident wave wave Phase-contrast microscope Wavefronts passing through the annulus illuminate the specimen and either pass through undeviated or are diffracted and retarded in phase by structures and phase gradients present in the specimen. Undeviated and diffracted light collected by the objective is segregated at the rear focal plane by a phase plate that transforms differences in phase into amplitude differences. Then light is focused at the intermediate image plane to form the final phase contrast image observed in the eyepieces. The angular deviation causes differences in optical path between two trajectories of rays scattered by different parts of lens. Contrast can be created in electron microscope if: 1. Some of electrons scattered by the specimen may be removed by aperture 2. Spherical aberration is present 3. The viewing plane is not conjugate to the specimen plane, i.e., the image is not exactly in focus The imaging properties of an objective lens are described by a contrast-transfer function, independent of any particular specimen structure. That has been described for electron microscope by Scherzer in 1949 (J.Appl.Phys., 20, 20-29) Aberrations in lenses y Ideal lens Astigmatic aberration x Spherical aberration Chromatic aberration 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 – defocus q – spatial frequency λ – 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 – defocus q – spatial frequency λ – electron wavelength Convolution 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 transformation Low pass filter High pass filter Low pass filter High pass filter Gaussian filter Half width R = 0.4 Band pass filter R1=0.1, R2=0.5 Low pass filter High pass filter Low pass filter High pass filter CTF 1 CTF 2 Point spread function Voltage 200 kV Defocus 1.5 µ Voltage 200 kV Defocus 3.5 µ Contrast transfer function 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 – defocus q – spatial frequency λ – wave length of electrons ∆: ∆: 1 Scherzer original ∆: 1 Scherzer 10 Scherzer ∆: 10 Scherzer ∆Z = -4.8 µm −4.0 µm -3.2 µm -2.4 µm i g L t h u rc o s e o n C s re e d b e O jc t O j e b vc ti e l s n e l n s Ia m e g -1.6 µm 1.6 µm −0.8 µm 2.4 µm ~0. µm 3.2 µm 0.8 µm 4.0 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 Tungsten FEG • Image drift • Thick ice • Specimen charging • Chromatic aberration - variation in voltage • Variation of lens current FEG images of carbon film 0.5 µm 1 µm Astigmatism Drift References Frank, J. (1996) Three-dimensional electron microscopy of macromolecular assemblies. Academic Press, San Diego. Reimer, L. (1989) Transmission electron microscopy. Springer-Verlag, Berlin Hawkes & 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. B 261, 105-118 (1970). Erickson, H. P. and A. Klug (1971) Measurement and compensation of defocusing and aberrations by fourier processing 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 fieldemission gun to high-resolution transmission electron microscopy. Micron 25, 223-226. Zemlin, F. (1992) Desired features of cryoelectron microscope for the electron crystallography of biological material. Ultramicroscopy. 46, 25-32. 4-14 September 2005, Birkbeck College, London EMBO Course on Image processing in Cryomicroscopy Single particle analysis Fitting