Martin Frimmer ([email protected]) Photonics Laboratory ......Welcome! 3 Martin Frimmer ([email protected]) Photonics Laboratory (Prof. Lukas Novotny) HPP M24 This lecture is about learning

Welcome!

www.photonics.ethz.ch 1

Martin Frimmer ([email protected])Photonics Laboratory (Prof. Lukas Novotny)HPP, floor M

Welcome!


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


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

What is this lecture about?


• 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


The Helmholtz equation and plane waves


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







• Gaussian beams







How does focusing by a lens work?


x

Intensity

Boundless.com



x

k

q1 = 0°

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

Intensity



x

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

q1 = 20°

k

Intensity



x

q1 = ± 20°

k k

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

Intensity



x

q1 = ± 45°

kk k

Intensity



x

q1 = ± 80°

k k

Intensity



x

q1 = 0°, ±45°

kkk

k

Intensity



x

q1 = 0°, ±15°, ±30°, ±45°,

±60°, ±75°

Intensity



x

q1 = 0°, ±15°, ±30°, ±45°,

±60°, ±75°+apodization

Intensity



Angular spectrum


MATH :

Angular spectrum


MATH :

PHYS :

Angular spectrum


MATH :

PHYS :

Together:

Angular spectrum


PHYS :

Together:

Paraxial approximation


mit

Fields propagate predominantly in z-direction !

On the menu today







• Gaussian beams







Gaussian beams


Gaussian Beams


Waist Radius

Wavefront Radius

Phase Correction

Rayleigh Range

Gaussian Beams


A better description of focused fields


Far-field


?

Method of stationary phase :

Far-field


Angular spectrum in terms of far-field


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


So what does a lens do?


Ray Continuity

(energy conservation)

Angular spectrum representation


Change coordinates

Coordinates on reference sphereCoordinates in focal region NA

Strongly focused Gaussian beam


Strongly focused Gaussian beam


Weakly focused beam

• Assume strongly overfilled back-aperture

• Assume small NA


Focal plane (z=0):

Not Gaussian !

:

Why is this a jinc?

On the menu today







• Gaussian beams







Imaging of point sources: Single molecule detection


Fluorescent molecules – Jablonski diagram


Single molecule detection


fluorescence rate ~ excitation rate

x

y

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

Single molecule detection


What does the image of a point-source look like


Source Plane Image Plane

Point-spread function


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







• Gaussian beams







Documents

Martin Frimmer ([email protected]) Photonics Laboratory ......Welcome! 3 Martin Frimmer ([email protected]) Photonics Laboratory (Prof. Lukas Novotny) HPP M24 This lecture is about learning