Welcome!
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Martin Frimmer ([email protected])Photonics Laboratory (Prof. Lukas Novotny)HPP, floor M
Welcome!
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Martin Frimmer ([email protected])Photonics Laboratory (Prof. Lukas Novotny)HPP M24
This lecture is about learning about (and controlling) the world around us using measurements based on electromagnetic radiation. At hand of examples (e.g. super-resolution microscopy, feedback-cooling of mechanical resonators), we familiarize ourselves with the concepts of measurement imprecision and measurement backaction to explore some fundamental limitations of light-based measurement and control schemes.
This is the first iteration of this course!Suggestions, corrections comments welcome!
Administrative details
• Besides lecture, website is important source of informationwww.photonics.ethz.ch Education EM Precision…
• Read Infosheet on website to find out about grading and components of course:
1. Lecture
2. Homework problems
3. Paper presentations
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What is this lecture about?
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• What do you do to find out what is inside a box?
• In this lecture, we think about “what it means, to look inside the box”.
On the menu today
• Motivation: Why precision measurements?
• Repetition: electromagnetism
• Optical imaging:
• Focusing by a lens
• Angular spectrum
• Paraxial approximation
• Gaussian beams
• The diffraction limit
• Fluorophores and fluorescence microscopy
• Super-resolution microscopy
• Example: STED microscopy
• Example: Localization microscopy
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The Helmholtz equation and plane waves
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Dispersion relation:
Plane waves: Speed of light:
Refractive index:
H
E
k
(E, H, k) are mutually orthogonal for
from
wavelength
period
Phase velocity
follows
from follows
real valued
On the menu today
• Motivation: Why precision measurements?
• Repetition: electromagnetism
• Optical imaging:
• Focusing by a lens
• Angular spectrum
• Paraxial approximation
• Gaussian beams
• The diffraction limit
• Fluorophores and fluorescence microscopy
• Super-resolution microscopy
• Example: STED microscopy
• Example: Localization microscopy
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How does focusing by a lens work?
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x
Intensity
Boundless.com
How does focusing by a lens work?
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x
k
q1 = 0°
I(x) = E(x) E*(x) = ?
Intensity
How does focusing by a lens work?
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x
I(x) = E(x) E*(x) = ?
q1 = 20°
k
Intensity
How does focusing by a lens work?
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x
q1 = ± 20°
k k
I(x) = E(x) E*(x) = ?
Intensity
How does focusing by a lens work?
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x
q1 = ± 45°
kk k
Intensity
How does focusing by a lens work?
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x
q1 = ± 80°
k k
Intensity
How does focusing by a lens work?
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x
q1 = 0°, ±45°
kkk
k
Intensity
How does focusing by a lens work?
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x
q1 = 0°, ±15°, ±30°, ±45°,
±60°, ±75°
Intensity
How does focusing by a lens work?
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x
q1 = 0°, ±15°, ±30°, ±45°,
±60°, ±75°+apodization
Intensity
How does focusing by a lens work?
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Angular spectrum
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MATH :
Angular spectrum
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MATH :
PHYS :
Angular spectrum
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MATH :
PHYS :
Together:
Angular spectrum
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PHYS :
Together:
Paraxial approximation
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mit
Fields propagate predominantly in z-direction !
On the menu today
• Motivation: Why precision measurements?
• Repetition: electromagnetism
• Optical imaging:
• Focusing by a lens
• Angular spectrum
• Paraxial approximation
• Gaussian beams
• The diffraction limit
• Fluorophores and fluorescence microscopy
• Super-resolution microscopy
• Example: STED microscopy
• Example: Localization microscopy
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Gaussian beams
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Gaussian Beams
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Waist Radius
Wavefront Radius
Phase Correction
Rayleigh Range
Gaussian Beams
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A better description of focused fields
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Far-field
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?
Method of stationary phase :
Far-field
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Angular spectrum in terms of far-field
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For kz ~ k: Fourier Optics !
From method of stationary phase:
Boundless.com
Back to the lens
• We can calculate the field near a focus if we just know the far-field
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So what does a lens do?
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Ray Continuity
(energy conservation)
Angular spectrum representation
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Change coordinates
Coordinates on reference sphereCoordinates in focal region NA
Strongly focused Gaussian beam
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Strongly focused Gaussian beam
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Weakly focused beam
• Assume strongly overfilled back-aperture
• Assume small NA
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Focal plane (z=0):
Not Gaussian !
:
Why is this a jinc?
On the menu today
• Motivation: Why precision measurements?
• Repetition: electromagnetism
• Optical imaging:
• Focusing by a lens
• Angular spectrum
• Paraxial approximation
• Gaussian beams
• The diffraction limit
• Fluorophores and fluorescence microscopy
• Super-resolution microscopy
• Example: STED microscopy
• Example: Localization microscopy
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Imaging of point sources: Single molecule detection
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Fluorescent molecules – Jablonski diagram
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Single molecule detection
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fluorescence rate ~ excitation rate
x
y
contrast ~ | m .E(x,y;zo)| 2
Single molecule detection
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What does the image of a point-source look like
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Source Plane Image Plane
Point-spread function
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Classical resolution limit
www.photonics.ethz.ch 63E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).
Source Plane Image Plane
4 4
Abbe’s Resolution Limit
www.photonics.ethz.ch 64E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).
On the menu today
• Motivation: Why precision measurements?
• Repetition: electromagnetism
• Optical imaging:
• Focusing by a lens
• Angular spectrum
• Paraxial approximation
• Gaussian beams
• The diffraction limit
• Fluorophores and fluorescence microscopy
• Super-resolution microscopy
• Example: STED microscopy
• Example: Localization microscopy
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