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Electron microscopy
InnoCore project
Jiri Novacek

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Sylabus



n Lecture 1: Applications of electron microscopy in life-   science research
n Lecture 2: Transmission electron microscope, cryo-electron   microscopy, principles of image
formation
n Lecture 3: Fourier transform, techniques for 3D model   determination in cryo-EM

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Sylabus



n Lecture 1: Applications of electron microscopy in life-   science research
n Lecture 2: Transmission electron microscope, cryo-electron   microscopy, principles of image
formation
n Lecture 3: Fourier transform, techniques for 3D model   determination in cryo-EM

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Content



n Fourier transform
nContrast transfer function
n Single particle analysis
n Cryo-electron tomography

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Fourier transform



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Fourier series is an expansion of a function f(x) in terms of an infinite sum of sines and cosines
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The higher the spatial frequencies
(i.e. higher resolution) are included,
the more faithful the representation
of the original signal will be.

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Fourier transform

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Fourier transform

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Digitization

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Discrete Fourier transform

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Discrete Fourier transform - sampling



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Sufficient sampling                            Insufficient sampling
 - the period of the finest oscillation is 2 pixels
 - the spatial frequency of this oscillation is 0.5px-1
 - the finest detectabble oscicillation is what is
 known as “Nyquist frequency”
 - the edge of the Fourier transform corresponds
to Nyquist frequency

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Nyquist frequency

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Image formation



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          FT   IFT                            FT    IFT                                       FT
IFT
OBJECT
FT(object)
 MICROSCOPE
POINT SPREAD
FUNCTION
IMAGE IN THE
MICROSCOPE
FT(image)
CONTRAST
TRANSFER
FUNCTION
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Image formation

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Contrast transfer function



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A – amplitude contrast
s – spatial frequency
Cs – spherical abberation
λ – electron wavelength
z – defocus

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Image formation



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Low defocus                                High defocus

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Parameters required for 3D reconstruction

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Single particle analysis

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Single particle analysis

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Electron tomography

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Electron tomography

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Electron tomography

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Thank you for attention
jiri.novacek@ceitec.muni.cz