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Microscopy
Femius Koenderink
Center for NanophotonicsFOM Institute AMOLFAmsterdam
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2
Ernst Abbe
Cofounder of Zeiss: Zeiss, Abbe, Schott
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1. Microscopy at the diffraction limit
- What is the diffraction limit
- Spatial frequencies and Fourier transforms
- High NA imaging
2. Microscopy beyond the diffraction limit
- Localization microscopy – powerful cheat of Abbe
requires photochemistry
- Scanning probe microscopy l/100
- Vector, amplitude, and phase images
- Tedious, prone to artefacts
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What is a microscope
11
Object
planeTube lens
f=200 mmImage
plane
objective
Objectives:
Typically f = 2 mm
Opening angle = 75o
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Arbitrary source distribution
i
2
1, ; , , e d d
4
x yk x k y
x yk k z x y z x y
E E
Describe field as superposition of plane waves (Fourier transform):
iˆ, , , ; e d dx yk x k y
x y x yx y z k k z k k
E E
E
This representation is called
‘Angular spectrum representation’
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Arbitrary source distribution
i
2
1, ; , , e d d
4
x yk x k y
x yk k z x y z x y
E E
Describe field as superposition of plane waves (Fourier transform):
iˆ, , , ; e d dx yk x k y
x y x yx y z k k z k k
E E
Field at z=0 (object) propagates in free space as
iˆ ˆ, ; , ;0 e zk z
x y x yk k z k k E E
2 2 2
0z x yk nk k k
E
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Arbitrary source distribution
Field at z=0 (object) propagates in free space as
iˆ ˆ, ; , ;0 e zk z
x y x yk k z k k E E
2 2 2
0z x yk nk k k
The propagator is oscillating for
and exponentially decaying for
22 2
0x yk k nk
22 2
0x yk k nk
Near field = Exponentially confined fast spatial fluctuations
Far field = Propagating fields = bound by diffraction limit
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Example – Gaussian beam
Suppose we have a Gaussian object
It’s spectral representation is Gaussian
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Now find the field along the beam
Insert the Gaussian into
Paraxial approximation
If only small angles contribute
Again we are transforming a Gaussian
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Gaussian beam optics
A gaussian object results in a gaussian beam as far field
Diffraction: the beam widens away from the waist
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Gaussian beam optics
Diffraction: the beam widens away from the waist
The narrower the waist, the more the divergence
Note how the law
Relates spot size and numerical aperture NA=n sinq
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Diffraction optics intuition
1) Narrow beams lead to larger angular divergence
2) Larger beams can hence be more tightly focused
3) Angular far field profile to first order is just the Fourier
transform of the source distribution
- Gaussian beam
- Also: diffraction by pinholes, and slits.
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Arbitrary source distribution
Field at z=0 (object) propagates in free space as
iˆ ˆ, ; , ;0 e zk z
x y x yk k z k k E E
2 2 2
0z x yk nk k k
The propagator H is oscillating for
and exponentially decaying for
22 2
0x yk k nk
22 2
0x yk k nk
Near field = Exponentially confined fast spatial fluctuations
Far field = Propagating fields = bound by diffraction limit
Small objects <> wide beams and high NA’s
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The diffraction limitImage of a point source in a microscope, collecting part of the
angular spectrum of the source:
Rayleigh criterion: two point sources
distinguishable if spaced by the distance
between the maximum and the first
minimum of the Airy pattern
+
q sinNA n q
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What’s in a rigorous calculation
Abbe sine condition `aplanatic lens’
High NA: 1. hemispherical reference surface
2. constant power in rays upon crossing reference
3. Upon refraction, polarization vector refracts too
Strategy works for illumination and collection geometry
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What’s in a rigorous calculation
Compare normal ray optics: lenses approximated as planes
Abbe sine condition is `holy design rule’ for microscopes
Abbe sine condition
High NA: hemispherical reference surface
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Important consequences
Polarized as incident
Polarized along the beam
Best focus is l/2NA in size
Strong focusing adds polarization out-of-plane
Focus is not quite cylindrical in shape due to polarization
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High NA imaging
The ultimate smallest object is a molecule
Z-dipole In-plane Tilted 45 deg
NA=1.4
In focus
NA=0.4
In focus
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Confocal microscope
Highest resolution imaging
with lenses
1. Overfill high NA objective
with a parallel beam
2. Color separate output at
dichroic element
3. Tube lens to focus on point
detector
Resolution from confocality: (1) small laser spot
(2) detection pinhole
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Why NA really helps
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
Objective opening angle (degrees)90756030 450
NA=0.4 4%
NA=0.95 35%
NA=0.9 28%
Captu
red f
raction o
f 4
s
r
Objective NA
NA=0.7 15%
15
NA means
1. Resolution
2. Detectionefficiency
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Seeing single molecules
Single quantum dot emitters, blinking, spectra, lifetime
- Photochemistry/photophysics on individual quantum systems- Performance of single photon sources [cavities, photonic crystals..]
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Enabling equipment tricks
For room temperature experiments the universal tricks are:Dilution- l/2 detection or excitation volume- Diluted samples to < 1 molecule per 1 mm2
-Filtering- 108 laser line rejection filters
Efficient photon collection- Very high NA objective
Shot noise level detection- Silicon CCDs and APDs 60% q.efficiency
low read out & dark noise
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Fourier microscopy
Direct evidence of
k|| + G conservation
objective(NA=0.95)
back apertureSupercontinuum light source(Fianium)+ AOTF
l=600 nm
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Single scatterer radiation patterns
24
Cts/p
xl (0.1
s)
In phase-excited plasmon rods radiate like a line of dipoles: donut x sinc function
Potential: visualize radiation pattern of any SINGLE antenna
0
1200
ky
kx
(l=600 nm)
1um x 100 nm Au
0
500
ky
kx
(l=600 nm)
2um x 100 nm Au
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1. Microscopy at the diffraction limit
- What is the diffraction limit
- Spatial frequencies and Fourier transforms
- High NA imaging
2. Microscopy beyond the diffraction limit
- Scanning probe to beat the diffraction limit
- Example imaging molecules
- Example imaing photonic structure
- Artefacts
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Microscopy
Why is there a
barrier in optical
microscopy
resolution?
And how can it be
broken?
Nobel prize 2015
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Localization of a molecule
Idea: if you know you have a single object, you can find its localization to much better than the diffraction limit
Single molecule CCD imagesDifferent exposure times
Least square fitting of GaussianError diminishes with photon count N
Beam waist Pixel size Background noise
Biophysical Journal 82(5) 2775–2783
Note: not true diffraction barrier breaking
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Imaging sequence
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Cheating the diffraction limit
PALM, STORM: beat Abbe limit by seeing a single molecule at a time
Using a stochastic on/off switch to keep most molecules dark
Resolution: how discernible are two objects ?If you have a single object, you can fit the center of a Gaussian with arbitrary precision (depends on noise)
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Arbitrary source distribution
Field at z=0 (object) propagates in free space as
iˆ ˆ, ; , ;0 e zk z
x y x yk k z k k E E
2 2 2
0z x yk nk k k
The propagator H is oscillating for
and exponentially decaying for
22 2
0x yk k nk
22 2
0x yk k nk
Near field = Exponentially confined fast spatial fluctuations
Far field = Propagating fields = bound by diffraction limit
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Breaking the diffraction limit in near-field microscopy
A small aperture in the near field of the source can scatter also the
evanescent field of the source to a detector in the far field.
Image obtained by scanning the aperture
Alternatively, the aperture can be used to
illuminate only a very small spot.
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Aperture probefibre type
Aperture probemicrolever type
Metallic particleSingle emitter
Probing beyond the diffraction limit
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glass
aluminum
500 nm
100 nm
100 nm
l
35 nm
aperture
– well defined aperture
– flat endface
– isotropic polarisation
– high brightness up 1 mW
Ex Ey Ez
With excitation Ex , kz, :
Focussed ion beam (FIB) etched NSOM probe
Veerman, Otter, Kuipers, van Hulst, Appl. Phys. Lett. 74, 3115 (1998)
x
y
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Shear force feedback: molecular scale topography
Feedback on phase
Tip -sample < 5 nm
RMS ~ 0.1 nm
Feedback loop:
sample
Lateral
movement,
A0 ~ 0.1 nm
Tuning fork
32 kHz
Q ~ 500
Df
w0
A0
piezo
1.7 x 1.7 mm
3 x 3 mm
Steps on graphite (HOPG)
~ 0.8 nm step
~ 3 mono-atomic steps
DNAwidth 14 nm
height 1.4 nm
DNA on
mica
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Mapping the near field of the probe
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90o0o 1 mm
100 nm
Perylene orange in PMMA
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Two arms of the
interferometer
equal in length gives
temporal overlap on the
detector
Time-resolved near-field scanning tunneling microscopy
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Measurement of guiding & bending
38
Sample: AIST JapanMeas: AMOLF
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1. Microscopy at the diffraction limit
- What is the diffraction limit
- Spatial frequencies and Fourier transforms
- High NA imaging
2. Microscopy beyond the diffraction limit
- Localization microscopy – powerful cheat of Abbe
requires photochemistry
- Scanning probe microscopy l/100
- Vector, amplitude, and phase images
- Tedious, prone to artefacts
![Page 40: Microscopy - amolf.nl · PDF file(Fianium) + AOTF l=600 nm. Single scatterer radiation patterns 24 s) In phase-excited plasmon rods radiate like a line of dipoles: donut x sinc function](https://reader031.vdocuments.us/reader031/viewer/2022022503/5ab00c467f8b9a22118dfe8e/html5/thumbnails/40.jpg)
Topographic artefacts
Topography: convolution of sample and tip
Optical: weighted by exponential factor
Tricky: topography and optical pick up are shifted sideways
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41
Narrow cavity resonance
Laser: grating tunable diode laser
20 MHz linewidth around 1565 nm
Detection: InGaAs APD (IdQuantique)
1565.0 1565.2 1565.40
25
50
75
100
125
Co
unts
Wavelength (nm)
Picked up by tip
Few mm above cavity Q =(10.5) 105
Lorentz Q =88000
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November
2006
42
Resonance shift
1565.0 1565.2 1565.40
25
50
75
100
125
Co
unts
Wavelength (nm)
Few mm above cavity
~10 nm above cavity
Line shifts by 1 linewidth
Glass tip: Dw/w ~ 1.2 104
(Dl of 20 pm)
Consistent with
2 /
0
2
mode 0
| ( ) |
max( ( ) | ( ) | )
z dE r e
V E
w
w
D
r r
Inserting a polarizability
comparable to the
mode volume shifts w
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43
Tuning vs mode intensity
0 1 2 3 4 5-8 -6 -4 -2
1565.20
1565.25
1565.30
1565.35
1565.40
1565.45
Transverse to W1Along W1
l o
f m
ax.
sig
nal (n
m)
Position (mm)
-2 -1 0 1 2-4 -2 0 2 40.0
0.5
1.0
Transverse to W1Along W1
|E|2
(n
orm
.) i
n t
he
sla
b
Position (mm)
Experiment
FDTD
In this case the Dw/w and not
Intensity maps |E|2