martin frimmer ([email protected]) photonics laboratory ......welcome! 3 martin frimmer...
TRANSCRIPT
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Welcome!
www.photonics.ethz.ch 1
Martin Frimmer ([email protected])Photonics Laboratory (Prof. Lukas Novotny)HPP, floor M
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Welcome!
www.photonics.ethz.ch 3
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!
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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
www.photonics.ethz.ch 4
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What is this lecture about?
www.photonics.ethz.ch 10
• 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”.
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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
www.photonics.ethz.ch 11
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The Helmholtz equation and plane waves
www.photonics.ethz.ch 12
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
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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
www.photonics.ethz.ch 13
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How does focusing by a lens work?
www.photonics.ethz.ch 14
x
Intensity
Boundless.com
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How does focusing by a lens work?
www.photonics.ethz.ch 15
x
k
q1 = 0°
I(x) = E(x) E*(x) = ?
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 16
x
I(x) = E(x) E*(x) = ?
q1 = 20°
k
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 17
x
q1 = ± 20°
k k
I(x) = E(x) E*(x) = ?
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 18
x
q1 = ± 45°
kk k
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 19
x
q1 = ± 80°
k k
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 20
x
q1 = 0°, ±45°
kkk
k
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 21
x
q1 = 0°, ±15°, ±30°, ±45°,
±60°, ±75°
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 22
x
q1 = 0°, ±15°, ±30°, ±45°,
±60°, ±75°+apodization
Intensity
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How does focusing by a lens work?
www.photonics.ethz.ch 23
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Angular spectrum
www.photonics.ethz.ch 24
MATH :
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Angular spectrum
www.photonics.ethz.ch 25
MATH :
PHYS :
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Angular spectrum
www.photonics.ethz.ch 26
MATH :
PHYS :
Together:
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Angular spectrum
www.photonics.ethz.ch 27
PHYS :
Together:
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Paraxial approximation
www.photonics.ethz.ch 28
mit
Fields propagate predominantly in z-direction !
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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
www.photonics.ethz.ch 29
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Gaussian beams
www.photonics.ethz.ch 30
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Gaussian Beams
www.photonics.ethz.ch 31
Waist Radius
Wavefront Radius
Phase Correction
Rayleigh Range
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Gaussian Beams
www.photonics.ethz.ch 32
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A better description of focused fields
www.photonics.ethz.ch 33
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Far-field
www.photonics.ethz.ch 34
?
Method of stationary phase :
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Far-field
www.photonics.ethz.ch 35
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Angular spectrum in terms of far-field
www.photonics.ethz.ch 37
For kz ~ k: Fourier Optics !
From method of stationary phase:
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Boundless.com
Back to the lens
• We can calculate the field near a focus if we just know the far-field
www.photonics.ethz.ch 38
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So what does a lens do?
www.photonics.ethz.ch 39
Ray Continuity
(energy conservation)
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Angular spectrum representation
www.photonics.ethz.ch 45
Change coordinates
Coordinates on reference sphereCoordinates in focal region NA
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Strongly focused Gaussian beam
www.photonics.ethz.ch 49
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Strongly focused Gaussian beam
www.photonics.ethz.ch 50
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Weakly focused beam
• Assume strongly overfilled back-aperture
• Assume small NA
www.photonics.ethz.ch 51
Focal plane (z=0):
Not Gaussian !
:
Why is this a jinc?
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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
www.photonics.ethz.ch 52
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Imaging of point sources: Single molecule detection
www.photonics.ethz.ch 53
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Fluorescent molecules – Jablonski diagram
www.photonics.ethz.ch 54
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Single molecule detection
www.photonics.ethz.ch 55
fluorescence rate ~ excitation rate
x
y
contrast ~ | m .E(x,y;zo)| 2
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Single molecule detection
www.photonics.ethz.ch 56
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What does the image of a point-source look like
www.photonics.ethz.ch 57
Source Plane Image Plane
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Point-spread function
www.photonics.ethz.ch 62
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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
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Abbe’s Resolution Limit
www.photonics.ethz.ch 64E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).
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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
www.photonics.ethz.ch 65