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!

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 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

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:

(E, H, k) are mutually orthogonal for

wavelength

period

Phase velocity

follows

from follows

real valued

On the menu today

• Gaussian beams

How does focusing by a lens work?

Intensity

Boundless.com

q1 = 0°

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

Intensity

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

q1 = 20°

Intensity

q1 = ± 20°

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

Intensity

q1 = ± 45°

Intensity

q1 = ± 80°

Intensity

q1 = 0°, ±45°

Intensity

q1 = 0°, ±15°, ±30°, ±45°,

±60°, ±75°

Intensity

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

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

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

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

Abbe’s Resolution Limit

www.photonics.ethz.ch 64E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).

On the menu today

• Gaussian beams

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

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