What happened thus far · 2019-08-03 · What happened thus far •Optical imaging: •Focusing by a lens •Angular spectrum •Paraxial approximation •Gaussian beams •Focusing

What happened thus far

• Optical imaging:

• Focusing by a lens

• Angular spectrum

• Paraxial approximation

• Gaussian beams


• The diffraction limit: How well can we focus light?

• The resolution limit: How well can we discriminate two points?

• Optical microscopy

• Optical imaging systems

• Real-world (dipolar) sources: Fluorophores and scatterers

• Example: Fluorescence microscopy

• Example: STED microscopy

• Example: Localization microscopy

• Example: Scanning probe microscopy

www.photonics.ethz.ch 1

Microscopy


Point-spread function (PSF)

• The PSF is a characteristic of an imaging system

• The PSF is the image of a (mathematical) point source

• The PSF is not a point (but spread) to a width … because …


Source Plane Image Plane

Imaging system

Classical resolution limit

www.photonics.ethz.ch 4E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).

Source Plane Image Plane

Two point sources

Performance of optical imaging systems

• Which element determines resolution of this imaging system?

• What is the magnification of this imaging system?



• Optical imaging:


• Angular spectrum

• Paraxial approximation

• Gaussian beams


• The diffraction limit: How well can we focus light?

• The resolution limit: How well can we discriminate two points?

• Optical microscopy

• Optical imaging systems

• Real-world (dipolar) sources: Fluorophores and scatterers

• Example: Fluorescence microscopy

• Example: STED microscopy

• Example: Localization microscopy

• Example: Scanning probe microscopy


Fluorescent molecules – Jablonski diagram

• Stokes shift of fluorescence allows to spectrally separate (intense) pump light from (weak) fluorescence


Excitation rate ~ | m .E(x,y;zo)| 2

µ: transition dipole moment

Rhodamine 6G
















• In practice, we often quantify the interaction rate between a fluorophore and a light field via a cross section s

Fluorescence microscopy: Epi-illumination

• Illuminate entire sample homogeneously

• Image sample plane onto pixelated detector

• Each fluorophore generates a signal according to the PSF

• Resolution is


Position on detector

Scanning fluorescence microscopy

• Create a pump-focus on a sample covered with fluorophores

• Move sample transversally to optical axis

• Record fluorescence photons on detector

• You can spatially separate two emitters when their distance exceeds


“bucket” detector Sample position

Fluorescence microscopy



• Optical imaging:• Focusing by a lens

• Angular spectrum• Paraxial approximation• Gaussian beams• Focusing by a lens

• The diffraction limit: How well can we focus light?• The resolution limit: How well can we discriminate two points? • Optical microscopy

• Optical imaging systems• Real-world (dipolar) sources: Fluorophores and scatterers• Example: Fluorescence microscopy

• Superresolution microscopy• Example: STED microscopy• Example: Localization microscopy• Example: Scanning probe microscopy


STED microscopy

• STED = stimulated emission depletion

• Allows fluorescence microscopy beyond the diffraction limit

• Ingredients:

• (at least) 4-level system

• conventional fluorescence microscope

• Pump laser

• Depletion laser

• We need to understand

• The diffraction limit

• A four-level system in the presence of light fields


Westphal and Hell, Phys. Rev. Lett. 94, 143903 (2005)

Once again: The diffraction limit

• Intensity pattern of two interfering plane waves in a medium with refractive index n is a sine-squared with period d=l/(2n sinq)

• Abbe’s diffraction limit (originally derived for a focused beam)


Conventional µscopy vs. STED


Willig et al., Nat. Meth. 4, 915(2007)

500 nm

Conventional µscopy vs. STED



500 nm

Population of excited state in absence of STED beam

• 4-level system created by two electronic states (of a fluorophore) and vibrational excitation

• Vibrational relaxation infinitely fast

• Start in ground state, turn on pump


Population of excited state in absence of STED beam

• Start in excited state (with certain probability), turn on depletion laser

• Exponential decrease of population as function of time

• Depletion field “helps” spontaneous emission


STED – how it works

• Set up overlapping excitation and depletion lasers (both can naturally only be focused to the diffraction limit!)



• Apply a weak/short pump pulse (linear regime of charging curve)



• Apply a weak/short pump pulse (linear regime of charging curve)

• Apply a strong depletion pulse

• Register fluorescence photons arriving after depletion pulse


See HW problem!


• FWHM of area of remaining pumped fluorophores after STED pulse


Characteristic saturation intensity:


• FWHM of area of remaining pumped fluorophores after STED pulse


Characteristic saturation intensity:

So what is the secret here?The pump beam is focused to the diffraction limit.The STED beam is focused to the diffraction limit. Why is the resolution beyond the diffraction limit?

STED – how it really works


Excitation beam profile

Depletion beam profile









STORM/PALM – localization microscopy

Different names for (in principle) the same technique:

• Photoactivated localization microscopy (PALM)

• Stochastic optical reconstruction microcopy (STORM)


STORM – localization microscopy

• Abbe tells me how closely spaced two sources can be for them to be discernible

• But how well can I localize a single emitter? (given that I know it is a single one)


STORM – localization microscopy

• Emitter 1 on, emitter 2 off localize emitter 1 better than diffraction limit

• Emitter 2 on, emitter 1 off localize emitter 2 better than diffraction limit

For this technique we need fluorophores which can be switched on and off


detector

Source plane

Imaging system

Jablonski diagram

• When continuously exciting a molecule, the fluorescence intensity switches on and off

• Some fluorophores are also “photoswitchable”, such that light of a specific wavelength turns the emitter “on” or “off”


Long-lived states (fluorescence is “off”)Molecules “blink”

www3.nd.edu Most molecules stochastically switch between a “bright” and a “dark” state.Furthermore, there are “photoswitchable” emitters.

STORM

• https://www.microscopyu.com/tutorials/stochastic-optical-reconstruction-microscopy-storm-imaging


Nobel prize in chemistry 2014


Eric Betzig, Stefan W. Hell and William E. Moerner "for the development of super-resolved fluorescence microscopy".








Wait a minute …

• Did the microscopy techniques discussed so far make use of any evanescent fields?


Near-field microscopy


Confocal:

Near-field:

• So far we played some tricks to enhance the resolution of an image in the far-field (what were these tricks?)

• But how can we image the evanescent near-fields, which never propagate to our lens?

Near-field scanning optical microscopy (NSOM)


Hecht et al., J Chem. Phys. 112, 7761

NSOM – operation modes

Localized excitation

• Create subdiffraction-sized illumination spot with aperture probe

• Collect scattered field/fluorescence with conventional far-field optics

Localized detection

• Excite with conventional far-field optics

• Collect scattered field/fluorescence with aperture probe

Localized excitation and detection

• …


NSOM – localized detection

• Field distribution in photonic crystal waveguide

• Interferometric technique allows phase sensitive mapping of field


Gersen et al., Phys. Rev. Lett. 94, 123901Rothenberg and Kuipers, Nat. Phot. 8, 919

Summary

• What is the angular spectrum?

• How well can I focus a beam of light with a lens?

• Which functional form does the focus of a lens have?

• What is the focal depth of a focused beam?

• What is the point-spread function?

• How well can I localize a single emitter?

• What is the resolution limit of STED/PALM/NSOM?


Documents

What happened thus far · 2019-08-03 · What happened thus far •Optical imaging: •Focusing by a lens •Angular spectrum •Paraxial approximation •Gaussian beams •Focusing