Post on 21-Jun-2020
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What happened thus far
• 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
• Example: STED microscopy
• Example: Localization microscopy
• Example: Scanning probe microscopy
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Microscopy
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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 …
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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?
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What happened thus far
• 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
• Example: STED microscopy
• Example: Localization microscopy
• Example: Scanning probe microscopy
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Fluorescent molecules – Jablonski diagram
• Stokes shift of fluorescence allows to spectrally separate (intense) pump light from (weak) fluorescence
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Excitation rate ~ | m .E(x,y;zo)| 2
µ: transition dipole moment
Rhodamine 6G
Fluorescent molecules – Jablonski diagram
• Stokes shift of fluorescence allows to spectrally separate (intense) pump light from (weak) fluorescence
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Excitation rate ~ | m .E(x,y;zo)| 2
µ: transition dipole moment
Fluorescent molecules – Jablonski diagram
• Stokes shift of fluorescence allows to spectrally separate (intense) pump light from (weak) fluorescence
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Excitation rate ~ | m .E(x,y;zo)| 2
µ: transition dipole moment
Fluorescent molecules – Jablonski diagram
• Stokes shift of fluorescence allows to spectrally separate (intense) pump light from (weak) fluorescence
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Excitation rate ~ | m .E(x,y;zo)| 2
µ: transition dipole moment
• 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
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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
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“bucket” detector Sample position
Fluorescence microscopy
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What happened thus far
• 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
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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
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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)
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Conventional µscopy vs. STED
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Willig et al., Nat. Meth. 4, 915(2007)
500 nm
Conventional µscopy vs. STED
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Willig et al., Nat. Meth. 4, 915(2007)
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
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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
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STED – how it works
• Set up overlapping excitation and depletion lasers (both can naturally only be focused to the diffraction limit!)
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STED – how it works
• Apply a weak/short pump pulse (linear regime of charging curve)
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STED – how it works
• Apply a weak/short pump pulse (linear regime of charging curve)
• Apply a strong depletion pulse
• Register fluorescence photons arriving after depletion pulse
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See HW problem!
STED – how it works
• FWHM of area of remaining pumped fluorophores after STED pulse
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Characteristic saturation intensity:
STED – how it works
• FWHM of area of remaining pumped fluorophores after STED pulse
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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
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Excitation beam profile
Depletion beam profile
Willig et al., Nat. Meth. 4, 915(2007)
What happened thus far
• 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
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STORM/PALM – localization microscopy
Different names for (in principle) the same technique:
• Photoactivated localization microscopy (PALM)
• Stochastic optical reconstruction microcopy (STORM)
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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)
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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
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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”
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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
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Nobel prize in chemistry 2014
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Eric Betzig, Stefan W. Hell and William E. Moerner "for the development of super-resolved fluorescence microscopy".
What happened thus far
• 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
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Wait a minute …
• Did the microscopy techniques discussed so far make use of any evanescent fields?
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Near-field microscopy
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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)
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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
• …
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NSOM – localized detection
• Field distribution in photonic crystal waveguide
• Interferometric technique allows phase sensitive mapping of field
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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?
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