Mc mullan imageformation
- 2. Russo 2010 Only use direct beam, elasticall scattered and inelastically scattered contributions
- 3. Wavelengths Green light 5600.000 Å 100 keV 0.037 Å 200 keV 0.025 Å 300 keV 0.020 Å Green light/300 keV ~2.8 x 106
- 4. Electron lens Electron lens behaves just like an optical lens. Electrons spiral in the magnetic field
- 5. Electron lens Quality of electron lens is equivalent to using a sphere for an optical lens.
- 6. Apertures θ=λ/d 4Å at 300 keV Θ=0.02/4 = 5 mrad = 0.3 degθ is the scattering angle
- 7. θ=λ/d 4Å at 300 keV Θ=0.02/4 = 5 mrad = 0.3 deg Focal length, f, ~3 mm Distance to diffraction plane is approximately the focal length and so ~3 mm. 4Å spot at distance: fθ = 15 μm in diffraction plane – distances from optical axis are very small
- 8. Transmission Electron microscope (bright field phase contrast) Source Condenser lens 1 Condenser lens 2 Objective lens Sample Objecive aperture Intermediate lens Projector lens Detector ● Condenser lens combination sets virtual source position. ● Condenser aperture set illumination angle ● Objective aperture provides a high frequency cut-off. ● Objective aperture provides a source of secondary electrons to help neutralise charge. build up on sample.
- 10. Russo 2010
- 12. How many electrons interact with the sample at once?
- 13. Dim Beam is Extremely Coherent (extreme case Falcon3 counting) ● 0.5 e/pixel/s ● 4096x4096 => 16 million pixels => 10 million electrons per second ● 300 keV electrons travel at 0.78 speed of light => 2x10e8 m/s ● Average distance between electrons: 2x10e8 m/s /(1x10e7/s) = 20 m ● Cannot use microprobe because Fresnel rings cover the image
- 14. Phase object Ψ ~ 1 + iσ V |Ψ|2 ~ 1 + (σV)2 ~ 1 To first order there is no contrast!
- 15. How do you see something? Aperture contrast (objective aperture) Defocus Phase plate
- 16. Phase Plate Ψ ~ 1 + Φiσ V |Ψ|2 ~ 1 + 2 σV Ideally Φ ~ i So Ψ ~ 1 - σ V
- 17. Weak phase approximation (simplified) -i s f/2i s f/2 Y ~ 1 – isf exp( -i c)/2 + isf exp( -i c)/2-i s f/2 exp(-ic )i s f/2 exp(-ic ) c(q) = 2p ( Df q2 /2 – Cs q4 /4)/l |Y|2 ~ 1 – 2sf sin( c) Sample Lens Image Focusing wavefunction back to image plane introduces a phase shift of exp(-ic) where: in which Df is the defocus, Cs the spherical aberration, l the wavelength and q the scattering angle (q= l/d). Scattered component of wavefunction is small and given by isf in which f is the projected potential and s=2pmel/h2 . Wavefunction at image plane is so image i.e, probability of an electron arrival, is
- 18. Image FormationImage Formation Bright field phase contrastBright field phase contrast (gives most signal per unit of(gives most signal per unit of radiation damage)radiation damage) In focusIn focus 3 um3 um1 um1 um
- 19. Pt/Ir Falcon III, 128 e/pixel Noise whitened power spectra
- 20. Falcon II, 28 e/pixel Noise whitened power spectra
- 21. Daily use of Thon RingsDaily use of Thon Rings FEI Falcon III Detector (carbon film) Alignment: Pivot points Astigmatism Beam tilt
- 23. 1 electron every pixel – image information just visible. Image are always noisy – due to finite number of electrons that can be used
- 24. High resolution signal is below the noise.
- 25. Drift corrected image Motion of selected particles
- 26. Bright field phase contrast of weakly scattering object.