SLIDE 1
Correcting the Image
- N. Grigorieff
What is “Wrong” with the Image?
Xing Zhang 2007
Correcting the Image N. Grigorieff What is Wrong with the Image? - - PowerPoint PPT Presentation
Correcting the Image N. Grigorieff What is Wrong with the Image? - - PowerPoint PPT Presentation
Correcting the Image N. Grigorieff What is Wrong with the Image? Xing Zhang 2007 Electron Diffraction 4 3.4 Baldwin & Henderson 1984 Image Contrast [ ] ( ) ( ( ) ( ) ) ( ) ( ) ( ) 2 MTF = + 2 k k k k k k P
SLIDE 2
SLIDE 3
4 Å
Electron Diffraction
Baldwin & Henderson 1984
3.4 Å
SLIDE 4
Image Contrast
( ) ( ) ( ) ( ) ( ) ( )
[ ]
( )
k k k k k k
2 2MTF
CTF ENV B S P
i i
+ =
( ) ( )
2 2 2 e s
B MTF B + + k k
S = signal Bi = imaged background ENVi = CTF envelope MTF = Detector MTF Bs = shot noise Be = detector noise
Zeng et al. 2007
SLIDE 5
Things to Worry About
- Quality
– Resolution, contrast
- Contrast transfer function
– Defocus, astigmatism, beam tilt, envelope
- Magnification
– Variations from image to image/within images
- Ewald sphere (for large objects)
- Contrast normalization
- Inelastic and multiple scattering
– Energy filter, diffraction theory
SLIDE 6
Rotavirus Double-Layer Particles
1000 Å
SLIDE 7
Side Chains
Xing Zhang Ethan Settembre 2007
Rotavirus double-layer particles 8400 particles
SLIDE 8
Image Quality - Grids
SLIDE 9
Image Quality – Location on Grid
SLIDE 10
Image Quality - Defocus
SLIDE 11
Thin Rings
6.5 Å 3.8 Å
SLIDE 12
Determining the CTF
E = 120 kV, ∆f = 21000 Å, Cs = 2 mm, A = 0.15 Model Experiment Image power spectrum
Mindell & Grigorieff 2003
CTFFIND3
SLIDE 13
Defocus Gradient
van Heel et al. 2000
Defocus [Å] y x [μm]
Mindell & Grigorieff 2003
CTFTILT
SLIDE 14
Θ
Δf Δr = ΔfΘ
Displaced Information
SLIDE 15
Margins
160 Å
Å 130 5.3mrad Å 25000 = × = Θ Δ = Δ f r
SLIDE 16
Ewald Sphere
Phase error = 60° for 700 Å particle at 300 kV
B A B* A * O k0 B' kL kR FL FR A'
SLIDE 17
Normalization
( ) ( ) ( ) ( ) ( ) ( ) ( )
[ ]
( )
[ ]
I I y x I y x I I I y x I y x I bg var bg avg , , ˆ var avg , , ˆ − = − =
Sorzano et al. 2004
SLIDE 18
( )
( )
( )
∑ ∫ ∫
= +
φ Θ φ φ Θ φ φ =
N i n i n i i n
p p X N A
1 ) ( ) ( ) 1 (
d , d , 1
( ) ( ) ( )
Θ φ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ σ − φ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ σ π = Θ φ | 2 exp 2 1 ,
2 2
f A X p
i M i
Structure for n+1 iteration Probability function Xi: ith image N: # of images φ: alignment parameters Θ: model parameters σ: noise in images : positional probab.
f
Maximum Likelihood
Sigworth 1998
SLIDE 19
Noise Model
Zeng et al. 2007
SLIDE 20
ML processing of 2D crystals
Crystallography Alignment of individual unit cells using ML approach
SLIDE 21
Systematic Error
10 20 30 40 50 60 70 10 20 30 40 50 60 70 Model phase error [deg] Data phase error [deg]
Refined 3D structure
- f bacteriorhodopsin
Grigorieff et al. 1996
SLIDE 22
Inelastic Image
Unfiltered 0 eV 25 eV
300 kV, 6 μm underfocus, 15 eV energy window
Chen Xu 2007
SLIDE 23
Things to Worry About ?
- Quality
– Resolution, contrast
- Contrast transfer function
– Defocus, astigmatism, beam tilt, envelope
- Magnification
– Variations from image to image/within images
- Ewald sphere (for large objects)
- Contrast normalization
- Inelastic and multiple scattering
– Energy filter, diffraction theory
SLIDE 24
Acknowledgements
- Rotavirus DLP
Xing Zhang, Ethan Settembre
(Harrison lab)
- Purple membrane
Fritz Zemlin, Erich Beckmann
- ML of 2D crystals
Xiangyan Zeng (Stahlberg lab)
- CTFFIND3/TILT
Joe Mindell
- Ewald sphere
Matthias Wolf, David DeRosier
- Inelastic scattering
Chen Xu
- Financial Support: