Electron Optics
Basic Introduction
Bob Ashley
6-14-2013
Overview
• Why electrons?
• Wavelength and visible light
• Effects of diffraction and resolution
• Lens design
• Defects and distortions
• Magnification
Electron Duality
• Electrons have a particle and wave nature
• Wave and particle nature
• Source
Why Electrons?
•
Wavelength (λ)
• Measurement of sinusoidal
wave distance peak to peak
• Visible light small segment
• Electrons wavelength dependent
on velocity
• 200kV scope 1.2 x 10-3 nm
http://reich-chemistry.wikispaces.com/Fall.2008.MMA.Boyle.Timeline
The Wave
• Radiate from source in widening circles
• Diffraction phenomenon
• Wave strike edge and bend
• Interference of waves
http://images.tutorvista.com
Phase
•
Difference between two waves having the same electrical degrees or time and having
the same frequency are in phase.
Illustration of phase shift. The horizontal axis
• Can interfere with other waves.
• Constructive interference
• Additive property of two waves
• Destructive interference
• Cancelling waves
• Scattering
• Wave deviation from trajectory
with resultant wave phase difference
•
•
Coherent
• Constant phase difference
• Not necessary to be in phase
Incoherent
• Multiple phases combine and cancel
represents an angle (phase) that is increasing with
time.
Wikipedia
=
Waves combine (constructive,
coherent)
=
Waves combine 180° out of
phase (destructive, coherent)
=
Waves that combine with
varying phases nearly cancel
out (incoherent addition)
www.scribd.com/doc/27753743/Coherence-Incoherence-And-LightScattering
Diffraction
• Waves interfere with the initial wave front
• Appear to have a series of bright parallel bands or fringes
• Fresnel Fringes freh-nell
• Resolution is degraded
• Edges fuzzy rather than distinct
Airy Discs
• The airy discs are the ringed patterns of Fresnel
fringes
• When they overlap more difficult to discern two points
as independent and thus resolution is poorer
• Airy disc radius is the measurement of resolution
• Point Spread Function
Figure: Bizzola Electron Microscopy 1999
http://greenfluorescentblog.files.wordpress.com/
Some Math
• The math behind resolution (radius of airy disc)
• λ= wavelength, n= refractive index (what medium the
wave is passing through glass etc.), α= aperture angle
of lens
r=
0.612λ
______________
n (sinα)
Resolving Power
• Light microscope
• r = 172 nm
• Electron Microscope
• r = .003 nm theoretical
• r = .27 nm point to point in JEOL 2100 scope
• Why?
The Holy Trinity
• Resolution, Magnification, and Contrast
• Tradeoffs
• None can be fully actualized
The Holy Trinity
Resolution, Magnification, and Contrast
• Resolution
• The ability to distinguish two closely placed entities
that otherwise might appear as one
Adobe.com
The Holy Trinity
Resolution, Magnification, and Contrast
• Magnification
• The measure of the increase in diameter of a structure
from it’s original size
Holy Trinity
Resolution, Magnification, and Contrast
• Contrast
• The ability to distinguish differences in intensity values
between bright and dark areas.
Contrast
• Two types in electron microscopy
• Amplitude contrast (scattering contrast)
• Subtractive effect where various shades are evident by loss of
electrons
• Main source of most electron microscope contrast (except
cryo)
• Phase Contrast (interference contrast)
• Interference of diffracted waves cause intensity differences
due to loss of energy and the corresponding shorter focal
points
• Appear as bright ring or halo around the edge of an object
• Fresnel ‘freh-nell’ fringe
Lenses and Magnification
• Double convex converging lens
• Same optical properties of light
microscopes and electron
microscopes
• Image formation in a lens
• Same optical properties of light
microscopes and electron
microscopes
• Refraction
www.passmyexams.co.uk
Bizzola Electron Microscopy 1999
Electromagnetic Lenses
•
Electrons move in helical pattern
• Very influenced by magnetic fields
• Mass is small and require “mean free path”- high vacuum
Bizzola Electron Microscopy 1999
Resolution Limiting
Phenomena
• Electromagnetic lens defects
• Spherical aberration
• Chromatic aberration
• Astigmatism
• Beam coherence
• Source of electron beam
Wikipedia
Spherical Aberration
•
Due to geometry of electromagnetic lenses such that rays passing through
the periphery of the lens are refracted more that rays passing along the axis
• Circle of minimum confusion
http://electron6.phys.utk.edu/
• Corrected in EM with apertures
to eliminate some of the peripheral rays
but results in decrease aperture angle and
therefore resolution
This is Cs programs for image processing
2.0 mm in 2100, constant
Bizzola Electron Microscopy 1999
Chromatic Aberration
•
Distortion in lens in which there is a failure to focus different wavelength rays to
converge on same point.
• In light it’s the different color wavelengths
• In electrons shorter wavelength electrons are more energetic and have a longer
focal length than longer wavelength electrons.
• Results in enlargement of focal point similar to Airy disc
• Minimized by ensuring stable voltage of source
• Good vacuum
• Thinner specimens
• Electrons transmitted through specimen will
change their energy and wavelength
Astigmatism
•
Radial blur results when a lens field is not
symmetrical in strength but stronger in one
plane and weaker in another
• Only part of image will be in focus at a
given time
• Point would appear elliptical rather than
spherical
•
Corrected by
• Properly centered apertures
• Stigmators of condenser and objective lens
Nature Protocols 3, - 977 - 990 (2008)
Magnification in the Transmission
Electron Microscope
•
Three magnify lenses in the electron microscope
• Objective
• Intermediate
• Projector
image distance
•
Mag =
___________________
object distance
•
Magnification is product of the individual magnifying powers of each lens MT =
MO x MI x MP
• Light microscope 1,000x
• EM 1,000,000x
• Useful magnification = resolution of eye (CCD) / resolution of lens system
The TEM…To Be Continued
Bizzola Electron Microscopy 1999
Susan Hafenstein
Pixel size
Calculating your Pixel size
Knowing the size of each pixel in the digital image
Used to produce a magnification bar and Measure objects
For 3D cryoEM is is needed when determining the CTF
and calculating the reconstruction
Information is imbedded in the ccd
(in DM3 format – accessible by Digital
Micrograph program)
OR
available in posted table on “Microscope
magnifications and pixel sizes”
OR
You can calculate from the known
magnification used to record the image
Film
• There are 25,400 microns/inch.
• 25,400 microns/inch divided by dpi = scan step size
• The Nikon Super Coolscan 8000ED scans at 4000dpi
• 25,400 microns/inch divided by 8000 = 6.35 micron
• 6.35 microns = 63,500 angstrom
• Divide 63,500 by the Magnification of microscope to get the
pixel size
63,500
---------- =
59,000
1.08 Angstrom / pixel
Calculation of Pixel Size From a CCD Image You have to
know the actual pixel size of the CCD cameras and the
magnification of your image.
As an example: 15 microns = 150,000 Å..
camera pixel size (in Å)
------------------------------ = the pixel size at the specimen
magnification
level
How big a box?
Diameter
Of object
20 %
Note: Or + 50%, or X2, or X3
Box size
(don’t forget to ‘feather’)
Example:
Picornavirus = 300Å
+ 60 Å
box = 360Å
if your pixel size is 2.14Å/pixel
you should select 168 pixel diameter for your
box size
• Workshop:
• Same data --- different programs
• Same program --- different data
• Beginners + intermediate + experienced