Transcript (2/11/08) "Resolutions"

Lecture 9 Announcements
Next Wed.
Quiz covering reading–
Kinosita & Cross (2 articles) on ATPase
Homework due
Today
Techniques for measuring distances
(where physicists have made a big impact on bio.)
X-ray diffraction (atomic resolution)
Electron (Imaging) Microscopy (nm-scale)
Visible (Imaging) Microscopy (nm - µm)
Bacteria on head of a pin
at different magnifications
Microscopes
Cells discovered with invention of microscope.
MBC, Fig. 4-
Or with CCD
1000x, 0.2um
106x, 2 nm
20,000, 10 nm (3-d)
Resolution: The Rayleigh criteria
How well can you resolve two point objects?
A single spot will be smeared out, no matter
how small the spot is, because of the
wavelength of light to ~ l/2.
Point-Spread Function (PSF)
What determines (ultimate, i.e. best) resolution of
technique… microscope, eye, etc.?
[2 parts]
1. Primarily λ (wavelength).
Why? Uncertainty principle (Will show).
2. Collection Angle/focal length/ Numerical Aperture
Resolution ≈ # λ/N.A.
# = a factor = ½ (details not important)
Resolution ≈ λ/2N.A.
What is uncertainty principle, applied here?
Photon 1
Δpx Δx ≥ h/2π Δx = resolution; how small spot
Remember: Applies to each direction!
Photon 1: p = p ŷ
Photon 2: px = p sin θ
: py = p cos θ
Δpx = p sin θ – (- p sin θ)
= 2p sin θ
Δx = resolution
Calculating resolution
DpDx = h/2p
2psinq Dx = h/2p
p = h/l
Wavelength at screen
… need n.
Where does n come in?
n in resolution
Coverslip (glass)
(thin, n= 1.33)
object
Fill with oil (n ~ 1.5)
where air = 1
(Homework)
Wavelength & Resolution
lvisible=≈ 400-700 nm
l/2 N.A.: air= l/2: oil= l/(2)(1.4)
l = 500 nm: Best resolution 200-250 nm
400 nm
514 532
633
750
red
green
blue
purple
Short l
488
Long l
Modern day optical microscopes are highly optimized–
perfect diffraction limited. (Electron microscopes are 1000’s
of times worse.)
l of electrons
(Who was famous guy who got
Nobel prize in 1929 for the
“wave nature of electrons”?
What relationship between
wavelength and E, p, does
this correspond to?
Debroglie
E= hn = hc/l; p = h/l
Where does Planck’s constant come from?
Relationship
between radiation
of an object and its
temperature
The Planck constant came from law of black body
radiation: that the electromagnetic radiation emitted by a
black body could be modeled as a set of harmonic
oscillators with quantized energy of the form: E = hn
http://en.wikipedia.org/wiki/Black-body
Resolution of Electron Microscope
Given electron 100 KeV,
(typical upper-value for electron microscope)
what is l?
h =6.63 × 10-34 J-sec = 4.1 × 10-15 eV-sec
E100kV = 0.004 nm (really short!)
In reality, because not perfect electron lenses,
resolution is ~1 nm.
Far from ideal.
Accuracy vs. Resolution
What’s the difference?
Point-object:
Accuracy is how well you can tell where it is.
Resolution is how well you can tell two identical objects apart
Unlimited accuracy
Crater Lake
W.E. Moerner
lin
Enough photons
(w/photons1/2)
Center Prism-type
determined
to ~ 1.3 nm
TIR 0.2 sec integration
center
lout
280
Photons
N ~10,000 photons
w ~ 250 nm
D ~  1.25 nm
What limits, in practice,
accuracy?
Ans: drift of the stage
240
200
160
120
width
250 nm
80
40
0
(other things will be discussed later)
5
10
15
Y ax
15
10
20
is
Z-Data from Columns 1-21
20
25
25
5
ta
X Da
1-500 msec
0
Class evaluation
1. What was the most interesting thing you
learned in class today?
2. What are you confused about?
3. Related to today’s subject, what would you like
to know more about?
4. Any helpful comments.
Answer, and turn in at the end of class.