4. Detection of Photons
4.1 Advanced Optical Microscopy
4.1.1 wide field microscopy
4.1.2 confocal microscopy
4.1.3 photothermal microscopy
4.1.4 STED microscopy below the diffraction limit
4.1.5 PALM/STORM detection techniques for super-resolution
optical microscopy
direct imaging
bright field microscopy
dark field microscopy
differential interference contrast micr.
phase contrast microscopy
fluorescence microscopy
+++
advantages
illumination of the whole sample
highly parallel
very fast imaging
drawbacks
illumination of the whole sample
no sectioning capabilities (usually)
background fluorescence
raster scanning
confocal microscopy
near field microscopy
STED microscopy
spinning disc microscopy
+++
advantages
illumination of a small sample volume
detection from a small sample volume
sectioning capability
lower background
drawbacks
slow imaging
first microscope
poor mans microscope
luxory microscope
http://www.microscopyu.com/articles/formulas/conjugatemicroscope.html
raster scanning microscopy
microscope objective
typical microscope objectives are so called “infinity-corrected”
image is created at infinite distance from the objective
very useful, because we then have infinite space to place optical elements
complex optical system
replaced by simple lens
microscope objective
immersion objective lens
no immersion medium
immersion medium
immersion medium
ray path through microscope
simplified wide field microscope
intermediate
image plane
microscope
objective
object
image
eye piece
tube lens
magnification
tube lens focal distance (mm)
• tube lens focal distance is typically fixed for
each microscope objective manufacturer
• varying tube lens focal distance leads to new
magnification
Olympus
180
Nikon
200
Zeiss
165
imaging small objects
single PS particle with 600 nm emission
Bildgröße [µm]
2.0
1.5
1.0
0.5
0.0
0.0
diffraction limit
0.5
1.0
1.5
Partikelgröße [µm]
microscopy image works down to 380 nm
2.0
diffraction limit
resolution = two or one object?
the point spread function (psf) = intensity pattern in the focal area of a lens
this is equivalent to the image of a point source (light path is reversible)
light is diffracted on the aperture of the microscope objective
pattern is square magnitude of complex amplitude
lens
aperture
p(ξ, ρ) = |a(ξ, ρ)|2
a(ξ, ρ) is Fourier transform of the aperture
(Fraunhofer diffraction)
dimensionless variables
ξ(z) =
2π
N A2 z
nλ
ρ(r) =
2π
N A2 r
λ
the integrated intensity in every transverse plane is the same
diffraction limit
ρresel
0.6
Intensity distribution in the focal plane
0.5
• only true for paraxial optics, but similar for high NA
intensity
0.4
0.3
• usually termed resel (resolution element)
0.2
ρresel
0.1
0.0
-10
is the radius of the so called Airy disc
ρresel = 1.22π
-5
0
5
10
distance in focal plane
rresel
1.2
λ
= 0.61
NA
intensity
0.8
Intensity distribution along the optical axis
0.4
0.0
-40
-20
0
20
distance along optical axis
40
the point spread function in 3d
the psf is a complicated pattern in 3d space
often psf refers to the radial distribution
in the focal plane
opt
ical
axi
s
diffraction changes with wavelength
therefore psf too!!!
focal p
lan
radius e
R. H. Webb, Rep. Prog. Phys. 59 (1996) 427.
optical resolution
optical resolution
two psf separated by one resel in plane
ρresel
0.6
• dip between the maxima is resolved
• dip is 26 % = Rayleigh criterion
26 %
0.4
intensity
Rayleigh: two objects can be resolved if
rresel = 0.61
0.2
0.0
-10
λ
NA
338 nm for wavelength 500 nm, NA=0.9
406 nm for wavelength 600 nm, NA=0.9
-5
0
5
10
15
distance in focal plane
• same can be done along the optical axis
first minimum at
zaxis =
2nλ
N A2
this is the axial resolution
about 1.2 µm for 500 nm, NA=0.9
about 1.5 µm for 600 nm, NA=0.9
Beugungsbild
-1000
-500
0
x,y [nm]
500
1000
Mikroskopie - zwei Partikel
490 nm PS Kugeln
Beugungsminimum
-1000
-500
0
x,y [nm]
22 %
-500
0
x [nm]
500
500
1000
Auflösung - Abbe
die Information, dass es zwei Quellen sind wird nicht aufgesammelt
Auflösung - beugungsbegrenzt
Abbe
Rayleigh
Ein 1 nm kleines Objekt, dass Licht mit 600 nm
emittiert sieht so aus, als wäre er 300 nm groß!
reality is different
same psf but different noise level
0.5
0.4
0.2
intensity
intensity
0.3
0.3
0.2
0.1
0.1
0.0
-10
0
10
distance in focal plane
0.0
-10
0
10
distance in focal plane
the resolution criterion is arbitrary, but can be at least exactly
determined
always hunt for the best signal to noise ratio!
special techniques
special techniques - dark field microscopy
dark field image of a silicified cell
special techniques - phase contrast microscopy
Related Laureate:
The Nobel Prize in
Physics, 1953
- Frits (Frederik) Zernike »
double 1/4 wavelength retardation of the source and the diffracted
wave leads to destructive interference in the image plane
special techniques - DIC microscopy
DIC - differential interference contrast
special techniques - DIC microscopy
special techniques - DIC microscopy
special techniques - DIC microscopy
special techniques - DIC microscopy
special techniques - field fluorescence microscope
prism
lens
I-CCD
intensified frame transfer
CCD (Pentamax)
filter
microscope
objective
Ar+ laser
514 nm
sample
cryostat
wide field microscope in the POM Lab
measurement of the airy disc
15 µm
Michael Barth. Molecule in Photonic Crystal, POM Lab
R. H. Webb, Rep. Prog. Phys. 59 (1996) 427.
single molecule defocused imaging
typically defocusing is unwanted, but it contains information
single DiI molecules in a wide field fluorescence microscope
defocused imaging (orientational imaging)
Michael Barth, POM Lab
wide field dynamic imaging
single CdSe quantum dots
F. Cichos, POM Lab
Brownian motion of single dye molecules
F. Cichos, POM Lab
this lecture
• raster scanning microscopy
- confocal microscopy - principle
- optical resolution
- point spread function
- role of the pinhole
- beyond the Abbe limit of resolution
- point spread function engineering
- stimulated emission depletion
raster scanning microscopy - confocal microscopy
• raster scanning microscopy = optical properties are evaluated point wise
• smaple or the laser beam has to be moved (this makes the hole thing slow)
moving the sample
moving the beam
sample scanning confocal microscopy
laser scanning confocal microscopy
optical near field microscopy
100 µm x 100 µm x 20 µm
scanner as used in the POM lab (Physik Instrumente)
confocal microscopy - idea
wide field microscopy
• image is sharp in depth of field
• other areas unsharp but contribute
to background
• pinhole blocks light from unsharp regions
(this is a spatial filter)
• light from small sample volume is detected
confocal microscopy
• combine this with local illumination
better contrast, slightly higher resolution
but at the cost of imaging a point only
Marvin Minsky,1955
patented 1957
first page of the patent (Marvin Minsky)
photo of the confocal microscope prototype
their centers are further apart than the first minimum of the Airy
function (see figure 2.12, the minimum is at 1.22 ). Following this
typical
confocal
definition, the resolution can be defined
as in equation
2.63.setup
The
height of the intensity dip in the middle of the structure amounts to
26.5%.
confocal microscope
Dichroic
Mirror
filter
Excitation
Pinhole
Sample
pro
• small excitation volume
ø 300 nm
Δz 500 nm
Microscope
Objective
• small detection volume
• spatial filtering due to pinhole
(sectioning capabilities)
Detection
Pinhole
con
• small excitation volume
no parallel data acquisition
Detector/APD
Figure 2.14: In this figure the principle setup of a confocal microscope is shown. One major component is the pinhole in the detection
arm, which allows a higher resolution in the depth of the sample.
Objects which are not in the image plane are virtually cut out by
• imaging by scanning (slow)
confocal microscopy - lateral resolution
illumination and imaging is done with the same lens
psf is a the product of illumination and detection psf !
pconf (ξ, ρ) = p(ξ, ρ) × p(ξ, ρ) confocal
detection with an infinitely small detector (pinhole)
ρresel
0.6
0.6
0.5
0.4
intensity
intensity
0.4
0.3
0.2
0.2
0.1
0.0
-10
-5
0
5
10
distance in focal plane
0.0
-10
-5
0
5
10
15
distance in focal plane
to obtain a 26 % dip two psf ’s are separate by
• the psf is narrower than in wide field
• fringes are deacreased in intensity
the squared psf makes the resolution!
∆rconf = 0.44
λ
NA
lateral resolution is 72% of wide field microscopy
500 nm, NA=0.9 gives 244 nm resolution
intensity
0.4
0.3
confocal microscopy
- axial resolution
0.2
0.1
0.0
-10
∆zaxis = 1.5
nλ
N A2
5
10
1.2
0.8
intensity
Iaxis ∝
! " ! ""4
ξ
ξ
/
sin
4
4
0
distance in focal plane
was only square for wide field microscopy
!
-5
0.4
about 0.9 µm for 500 nm, NA=0.9
axial resolution is 75% of wide field microscopy
0.0
-40
-20
0
20
distance along optical axis
but goes with
the squared psf makes the resolution of the confocal microscope!
40
the effect of squared psf
Confocal optical microscopy
436
R H Webb
wide field psf
Figure 8. p(⇤, ⌥) for the
parallel to it: in (a) this
diffraction pattern, and in (
case.
Figure 7. The point-spread function in through-focus series. Each sub-picture is from a plane
parallel to the focal plane. These are actual photographs as a microscope is stepped through
the confocal psf in 3d
confocal psf
wide field psf
main difference in the lobes
gives better contrast
integrated intensity over each
plane is constant
integrated intensity over each
plane is not constant
R. H. Webb, Rep. Prog. Phys. 59 (1996) 427.
getting contrast
444
R H Webb
the surpression of the diffraction pattern
increases contrast, since dim objects are not obscured
by the diffraction fringes
Figure 16. Two points of very different (200:1)
remission intensity, are well resolved (4.5 resels). In
(a) the conventional view leaves the dimmer point
obscured, but in (b) the confocal contrast enhancement
allows its display.
Arrows indicate the weaker
remitter.
So a bright object near a dim one is less likely to contribute background light—to spoil
the contrast. In turn, that means that the resolved dim object can be seen as resolved.
As an example, figure 16 shows two point objects in the focal plane that are separated
the pinhole resolution and contrast
• the pinhole does not change the psf
• the psf is a property of the objective (NA)
but
the pinhole corresponds to a certain area in the object plane
the bigger the pinhole, the more photons will go through it
example:
1 mm pinhole corresponds to 10 µm in the object plane for a 100x objective
each point light source in the object plane
gives rise to a psf in the image plane
(pinhole)
the detection intensity is a convolution of psf and pinhole
large pinhole blurs the psf
this has o be multiplied by the excitation psf
10 µm
a pinhole smaller than 1 resel will not improve resolution
it will only reduce detected light
effect of the pinhole
despite the large pinhole
confocality preserved
R. H. Webb, Rep. Prog. Phys. 59 (1996) 427.
the truth
so far the psf was only for paraxial approximation
for objective lenses the paraxial approximation is not valid
true electric field
I0 (ξ, ρ) =
!θ
√
2
J0 (ρ sin α/ sin θ) cos α sin α(1 + cos α)eiξ cos α/ sin θ dα
!θ
√
2
J1 (ρ sin α/ sin θ) cos α sin2 α eiξ cos α/ sin θ dα
0
I1 (ξ, ρ) =
0
I2 (ξ, ρ) =
!θ
√
iξ cos α/ sin2 θ
J2 (ρ sin α/ sin θ) cos α sin α(1 + cos α)e
dα
0
J0 , J1 , J2
are Bessel function of first kind
the real point spread function
three Bessel functions
J0 , J1 , J2
point spread function for a high NA lens
1.0
J0,J1,J2
p(ξ, ρ) = {|I0 |2 + 2|I1 |2 + |I2 |2 }
(unpolarized light)
0.5
confocal psf for a high NA lens
0.0
-0.5
0
pconf (ξ, ρ) = {|I0 |2 + 2|I1 |2 + |I2 |2 }2
10
20
30
40
distance
I1 (ξ, ρ = 0) = I2 (ξ, ρ = 0) = 0
50
example confocal image
silicon quantum dots
10 µm
J. Martin, POM/OSMP Lab
Disk Microscopy
59
special techniques - spinning disc confocal microscopy
B
How to improve the resolution?
lateral resolution of 244 nm is not bad (SNR is important)
but axial resolution (0.9 µm) is bad!
axial resolution scales with NA-2
∆zaxis = 1.5
nλ
N A2
currently NA=1.6 is the current microscope objective limit, but for n=1.5
simple idea:
use a larger solid angle with two microscope objectives
4pi psf:
p(ξ, ρ, φ)4P i = |a(ξ, ρ)|2 = |a1 (ξ, ρ, φ) + a2 (ξ, ρ, φ)|2
S. Hell and E. H. K. Stelzer, ‘‘Properties of a 4Pi confocal fluorescence microscope,’ ’ J. Opt. Soc. Am. A 9, 2159–2166 1992.
axial resolution - 4pi point spread function
illumination
two objective illumination
interference of the two
optical fields
sharper main maximum in the middle
but two strong side lobes
det
exc
p(ξ, ρ)conf
4P i = p(ξ, ρ)4P i p(ξ, ρ)
image from M. Martinez-Corral, G.I.T. Imaging & Microscopy 2/2002
4pi confocal setup
4pi excitation - 4pi detection
image from M. Martinez-Corral, G.I.T. Imaging & Microscopy 2/2002
increasing lateral resolution
fluorescence of organic molecules
Rhodamine 6G
emission spectrum of a single R6G molecule
emission intensity
fluorescence
excitation
S1
S0
50
vibrational levels
electronic level
vibrational levels
electronic level
40
30
20
10
0
500
600
emission wavelength [nm]
vibrational relaxation ~10-13 s
spontaneous emission ~10-9 s
700
stimulated emission
incident photon flux stimulates emission at frequency of
incident light if molecule is in the excited state (and if it can emit/absorb at this frequency)
for monochromatic light
probability density for
stimulated emission
excited organic molecules
incident photon flux
S1
absorption cross section
stimulated
photon
photon
S0
for polymchromatic light
(but narrower than linewidth)
mean incident photon flux
stimulated emission and absorption have the same probability
point spread function engineering
modify the shape and phase of the exciting beam to manipulate the shape of the
point spread function
phase plate
objective lens
phase shift
depending on the phase shift and the form of the
the wave plate, different focal intensity patterns are obtained
no phase shift
point spread function engineering
different point spread functions for different phase plates
Type I
Type II
π
π
π
Phasefilter
y
y
x
76
x
36
x
0.5 µm
0.5 µm
0
0.5 µm
0
y
0
y
z
5 in xy
4
z
Axial
Section
z
76
75
0.5 µm
0.5 µm
0
π
y
25
Lateral
Section
Type III
36
0.5 µm
0
http://www.ub.uni-heidelberg.de/archiv/4902
0
stimulated depletion microscopy
objective lens
tube lens
detector
stimulated depletion microscopy combines
confocal microscopy and emission depletion
with an engineered psf to increase resolution
bandpass filter
phase plate
STED laser
40
typically pulsed
fs-ps
typically pulsed
10-100 ps
30
20
STED
exciting laser
excitation
50
10
time
0
500
600
700
Examples - Stimulated Depletion Microscopy
Examples - Single Molecule STED
Excitation
STED
y
y
0.5 µm
x
x
Phasefilter:
π
y
0.4 µm
Conventional
Lars Kastrup, phd thesis, Heidelberg
x
STED
http://www.ub.uni-heidelberg.de/archiv/5033