Today’s Topic: Lec 3
Prep for Labs 1 & 2
3-D imaging—how to get a nice 2D Image when
your samples are 3D. (Deconvolution, with
point scanning or with Wide-field Imaging.)
Getting distances out with FRET– donor
quenching, sensitized acceptor emission; and
orientation effects.
You should have read the book chapter on microscopy
AND either Lab 1 or Lab 2 Handout
Paul Selvin
(Last time) Convolution (pinhole) microscopy
Way to improve the z-resolution by collecting less out-of-focus fluorescence,
via a pinhole and scanning excitation with focused light.
Great especially for thick samples, but takes time, complicated optics and requires
fluorophores that are very stable. (why?)
Focused Light creates
fluorescence which
Light mostly
gets to detector
gets rejected
Confocal microscopy prevents out-of-focus
blur from being detected by placing a pinhole
aperture between the objective and the
detector, through which only in-focus light rays
can pass.
http://micro.magnet.fsu.edu/primer/digitalimaging/deconv
olution/deconintro.html
Fluorescence
(dark-field)
Point-Spread Deconvolution Imaging
http://www.microscopyu.com/articles/confoca
l/confocalintrobasics.html
What if you let light go in (no pinhole)
and don’t scan—i.e. use wide-field excitation.
Can you mathematically discriminate against out-of-focus light?
Deconvolution
For each focal plane in the specimen,
a corresponding image plane is
recorded by the detector and
subsequently stored in a data analysis
computer. During deconvolution
analysis, the entire series of optical
sections is analyzed to create a threedimensional montage.
By knowing the (mathematical)
transfer function, can you do better?
Called deconvolution techniques.
Common technique: take a series of
z-axis and then unscramble them.
http://micro.magnet.fsu.edu/primer/digitalimaging/deconv
olution/deconintro.html
Wide-field deconvolution imaging
There are many ways of doing this
You will use this
Nikon: http://www.meyerinst.com/imagingsoftware/autoquant/index.htm
How to figure out what out-of-focus
light gets through?
Simplest way: make a 2D sample, scan through it in z and then back-calculate
Deconvolution: 2 Techniques
Deblurring and image restoration
Deblurring Algorithms are fundamentally two-dimensiona: they subtract away the
average of the nearest neighbors in a 3D stack. For example, the nearest-neighbor
algorithm operates on the plane z by blurring the neighboring planes (z + 1 and z - 1,
using a digital blurring filter), then subtracting the blurred planes from the z plane.
In contrast, image restoration algorithms are properly termed "three-dimensional"
because they operate simultaneously on every pixel in a three-dimensional image
stack. Instead of subtracting blur, they attempt to reassign blurred light to the proper
in-focus location.
+ Computationally simple.
-
Add noise, reduce signal
Sometimes distort image
http://micro.magnet.fsu.edu/primer/digitalimaging/deconv
olution/deconalgorithms.html
Deconvolution Image Restoration
Instead of subtracting blur (as deblurring methods do), Image Restoration
Algorithms attempt to reassign blurred light to the proper in-focus location. This is
performed by reversing the convolution operation inherent in the imaging system.
If the imaging system is modeled as a convolution of the object with the point
spread function, then a deconvolution of the raw image should restore the object.
However, never know PSF perfectly. Varies
from point-to-point, especially as a
function of z and by color. You guess or
take some average.
(De-)Convolution
Get crisp images
(De-)Convolution
Blind Deconvolution
an image reconstruction technique:
object and PSF are estimated
The algorithm was developed by altering the maximum likelihood estimation
procedure so that not only the object, but also the point spread function is
estimated.
Another family of iterative algorithms uses probabilistic error criteria borrowed
from statistical theory. Likelihood, a reverse variation of probability, is
employed in the maximum likelihood estimation (MLE)
Using this approach, an initial estimate of the object is made and the estimate
is then convolved with a theoretical point spread function calculated from
optical parameters of the imaging system. The resulting blurred estimate is
compared with the raw image, a correction is computed, and this correction is
employed to generate a new estimate, as described above. This same
correction is also applied to the point spread function, generating a new point
spread function estimate. In further iterations, the point spread function
estimate and the object estimate are updated together.
Images: AutoQuant
Not-deconvoluted
Blind Deconvolution
Briggs, Biophotonics2004
Different Deconvolution Algorithms
The original (raw) image is illustrated in Figure 3(a). The results of deblurring by a nearest
neighbor algorithm appear in Figure 3(b), with processing parameters set for 95 percent haze
removal. The same image slice is illustrated after deconvolution by an inverse (Wiener) filter
(Figure 3(c)), and by iterative blind deconvolution (Figure 3(d)), incorporating an adaptive point
spread function method.
http://micro.magnet.fsu.edu/primer/digitalimaging/deconv
olution/deconalgorithms.html
Fluorescence Resonance Energy Transfer (FRET)
Spectroscopic Ruler for measuring nm-scale distances, binding
1.0
E
0.8
Energy
Transfer
Donor
Acceptor
E
0.6
1
1  ( R / R0 ) 6
0.4
Ro  50 Å
0.2
0.0
0
25
50
75
100
R (Å)
D
A
Time
Dipole-dipole Distant-dependent
Energy transfer
Look at relative amounts
of green & red
R0
D
D
A
A
Time
FRET Works
First shown in 1967 (Haugland and Stryer, PNAS)
How to measure Energy Transfer
1. Donor intensity decrease; 2. Donor lifetime decrease;
3. Acceptor increase.
E.T. by changes in donor.
E.T. by increase in acceptor
Need to compare two samples,
D-only, and D-A.
fluorescence and compare it to
residual donor emission.
Need to compare one sample at two l and
also measure their quantum yields.
Where
are the
donor’s intensity, and
excited state lifetime in the
presence of acceptor, and
________ are the same but
without the acceptor.
D
A
Time
R0
D
D
A
A
Time
With a measureable E.T. signal
E.T. leads to
decrease in
Donor
Emission &
Increase in
Acceptor
Emission
http://mekentosj.com/science/fret/
Example of FRET
Fluorescein
Rhodamine
Fluorescein: Donor
Rhodamine Acceptor
Example of FRET via acceptor-emission
Exc = 488 nm
Fluorescein
Rhodamine
From “extracted acceptor
emission”
You can determine how much
direct fluorescence there is by
shining a second wavelength
at acceptor where donor
doesn’t absorb. (For Fl-Rh
pair, go to the red, about 550
nm.) Then multiply this by the
relative absorbance of Rh at
488/550 nm!
Terms in Ro
1
E
1  ( R / R0 ) 6
Ro = 0.21( JqD n k
-4
2
)
1
6
in Angstroms
• J is the normalized spectral overlap of the donor emission (fD) and
acceptor absorption (eA) . Does donor emit where acceptor absorbs?
• qD is the quantum efficiency (or quantum yield) for donor emission
in the absence of acceptor (qD = number of photons emitted divided
by number of photons absorbed).
• n is the index of refraction (1.33 for water; 1.29 for many organic
molecules).
• k2 is a geometric factor related to the relative orientation of the
transition dipoles of the donor and acceptor and their relative
orientation in space. Very important; often set = 2/3.
Terms in Ro
J: Does donor emit where acceptor absorbs?

Ro  0.21 Jq D n k
4
2

1
6
in Angstroms
where J is the normalized spectral overlap of the donor emission
(fD) and acceptor absorption (eA)
Spectral Overlap
between Donor
(CFP) & Acceptor
(YFP) Emission
Ro≈ 49-52Å.
k2 : Orientation Factor
The spatial relationship between the DONOR emission dipole moment and the
ACCEPTOR absorption dipole moment
y
qD
D
R
z
qDA q
A
A
(0< k2 >4)
k2 often = 2/3
x
where qDA is the angle between the donor and acceptor transition dipole
moments, qD (qA) is the angle between the donor (acceptor) transition dipole
moment and the R vector joining the two dyes.
k2 ranges from 0 if all angles are 90°, to 4 if all angles are 0°, and equals 2/3 if the
donor and acceptor rapidly and completely rotate during the donor excited state
lifetime.
 k 2 is usually not known and is assumed to have a value of 2/3
(Randomized distribution)
 This assumption assumes D and A probes exhibit a high degree of rotational motion
Can measure whether donor & acceptor randomize by looking at polarization.
The End