Martin Frimmer (mfrimmer@ethz.ch) Photonics Laboratory ... ... Welcome! 3 Martin Frimmer...

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Transcript of Martin Frimmer (mfrimmer@ethz.ch) Photonics Laboratory ... ... Welcome! 3 Martin Frimmer...

  • Welcome!

    www.photonics.ethz.ch 1

    Martin Frimmer (mfrimmer@ethz.ch) Photonics Laboratory (Prof. Lukas Novotny) HPP, floor M

  • Welcome!

    www.photonics.ethz.ch 3

    Martin Frimmer (mfrimmer@ethz.ch) 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 information www.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

    http://www.photonics.ethz.ch/

  • 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”.

  • 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

  • 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

  • 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

  • How does focusing by a lens work?

    www.photonics.ethz.ch 14

    x

    Intensity

    Boundless.com

  • How does focusing by a lens work?

    www.photonics.ethz.ch 15

    x

    k

    q1 = 0°

    I(x) = E(x) E*(x) = ?

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 16

    x

    I(x) = E(x) E*(x) = ?

    q1 = 20°

    k

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 17

    x

    q1 = ± 20°

    k k

    I(x) = E(x) E*(x) = ?

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 18

    x

    q1 = ± 45°

    kk k

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 19

    x

    q1 = ± 80°

    k k

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 20

    x

    q1 = 0°, ±45°

    kk k

    k

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 21

    x

    q1 = 0°, ±15°, ±30°, ±45°, ±60°, ±75°

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 22

    x

    q1 = 0°, ±15°, ±30°, ±45°, ±60°, ±75°

    +apodization

    Intensity

  • How does focusing by a lens work?

    www.photonics.ethz.ch 23

  • Angular spectrum

    www.photonics.ethz.ch 24

    MATH :

  • Angular spectrum

    www.photonics.ethz.ch 25

    MATH :

    PHYS :

  • Angular spectrum

    www.photonics.ethz.ch 26

    MATH :

    PHYS :

    Together:

  • Angular spectrum

    www.photonics.ethz.ch 27

    PHYS :

    Together:

  • Paraxial approximation

    www.photonics.ethz.ch 28

    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

    www.photonics.ethz.ch 29

  • Gaussian beams

    www.photonics.ethz.ch 30

  • Gaussian Beams

    www.photonics.ethz.ch 31

    Waist Radius

    Wavefront Radius

    Phase Correction

    Rayleigh Range

  • Gaussian Beams

    www.photonics.ethz.ch 32

  • A better description of focused fields

    www.photonics.ethz.ch 33

  • Far-field

    www.photonics.ethz.ch 34

    ?

    Method of stationary phase :

  • Far-field

    www.photonics.ethz.ch 35

  • Angular spectrum in terms of far-field

    www.photonics.ethz.ch 37

    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

    www.photonics.ethz.ch 38

  • So what does a lens do?

    www.photonics.ethz.ch 39

    Ray Continuity

    (energy conservation)

  • Angular spectrum representation

    www.photonics.ethz.ch 45

    Change coordinates

    Coordinates on reference sphereCoordinates in focal region NA

  • Strongly focused Gaussian beam

    www.photonics.ethz.ch 49

  • Strongly focused Gaussian beam

    www.photonics.ethz.ch 50

  • 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?

  • 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

  • Imaging of point sources: Single molecule detection

    www.photonics.ethz.ch 53

  • Fluorescent molecules – Jablonski diagram

    www.photonics.ethz.ch 54

  • Single molecule detection

    www.photonics.ethz.ch 55

    fluorescence rate ~ excitation rate

    x

    y

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

  • Single molecule detection

    www.photonics.ethz.ch 56

  • What does the image of a point-source look like

    www.photonics.ethz.ch 57

    Source Plane Image Plane

  • Point-spread function

    www.photonics.ethz.ch 62

  • Classical resolution limit

    www.photonics.ethz.ch 63 E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).

    Source Plane Image Plane

    4 4

  • Abbe’s Resolution Limit

    www.photonics.ethz.ch 64 E. 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

    www.photonics.ethz.ch 65