Microscopy

Femius Koenderink

Center for NanophotonicsFOM Institute AMOLFAmsterdam

2

Ernst Abbe

Cofounder of Zeiss: Zeiss, Abbe, Schott

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

What is a microscope

11

Object

planeTube lens

f=200 mmImage

plane

objective

Objectives:

Typically f = 2 mm

Opening angle = 75o

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’

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

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

Example – Gaussian beam

Suppose we have a Gaussian object

It’s spectral representation is Gaussian

Now find the field along the beam

Insert the Gaussian into

Paraxial approximation

If only small angles contribute

Again we are transforming a Gaussian

Gaussian beam optics

A gaussian object results in a gaussian beam as far field

Diffraction: the beam widens away from the waist

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

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.

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

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

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

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

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

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

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

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

Seeing single molecules

Single quantum dot emitters, blinking, spectra, lifetime

- Photochemistry/photophysics on individual quantum systems- Performance of single photon sources [cavities, photonic crystals..]

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

Fourier microscopy

Direct evidence of

k|| + G conservation

objective(NA=0.95)

back apertureSupercontinuum light source(Fianium)+ AOTF

l=600 nm

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

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

Microscopy

Why is there a

barrier in optical

microscopy

resolution?

And how can it be

broken?

Nobel prize 2015

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

Imaging sequence

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)

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

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.

Aperture probefibre type

Aperture probemicrolever type

Metallic particleSingle emitter

Probing beyond the diffraction limit

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

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

Mapping the near field of the probe

90o0o 1 mm

100 nm

Perylene orange in PMMA

Two arms of the

interferometer

equal in length gives

temporal overlap on the

detector

Time-resolved near-field scanning tunneling microscopy

Measurement of guiding & bending

38

Sample: AIST JapanMeas: AMOLF

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

Topographic artefacts

Topography: convolution of sample and tip

Optical: weighted by exponential factor

Tricky: topography and optical pick up are shifted sideways

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

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

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