1. Basic Optics - uni-heidelberg.de · 1. Basic Optics Simon Hubertus, ... • Fiber Optics ... 700...

24.10.2017

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1. Basic OpticsSimon Hubertus, M.Sc.

Computer Assisted Clinical MedicineMedical Faculty Mannheim Heidelberg University

Theodor-Kutzer-Ufer 1-3D-68167 Mannheim, Germany

[email protected]/inst/cbtm/ckm

Biomedical Optics – „Basic Optics“

Simon HubertusI Slide 2/42 I 10/24/2017

My Academic Background…

B.Sc. in Physics at RWTH Aachen University (2011-2014)

Saarland

M.Sc. in Biomedical Engineering at Imperial College London (2014-2015)

PhD Thesis at the Institute of Computer AssistedClinical Medicine in Mannheim (2016-present)

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My Academic Background…

PhD student in „Tissue Structure and Function“ at the Institute of Computer Assisted Clinical Medicine in Mannheim

[pp

m]

OE

F

CM

RO

2 [µ

mol

/100

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in]



Further Topics at CKM…

• Functional MRI• Medical Imaging and Image Analysis• Multinuclear NMR• RF Methods and Imaging• MRI Sequence Development

Interested in Bachelor's or Master's Thesis? visit: http://www.umm.uni-heidelberg.de/inst/cbtm/ckm/groups/

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Outline: Biomedical Optics

1. Lecture – Basic Optics

• Invention of the LASER

• Properties of Light

• Geometrical Optics

• Yet even more Properties of Light..

2. Lecture – LASER Physics and Systems

3. Lecture – LASER Resonators

4. Lecture – Tissue Interactions I

5. Lecture – Tissue Interactions II

6. Lecture – Biomedical Applications

Wednesday, 20.12.207, 1-3pmHouse 1, Level 0, Lecture Hall 09



Literature

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LASER

A few Laser applications • Laser cutting in industry• Laser Printers• Optical Disc Drives• Barcode Scanners• Laser Pointer• Laser Surgery• Fiber Optics• Free-Space Communication• Distance measurements (LUNAR LASER Ranging Experiment: precision < 4cm!!)• Two-photon excitation microscopy• Alignment check (MRI, radiotherapy) • many more…

LASER

Light Amplification by Stimulated Emission of Radiation

A LASER is a device that emits light through a processof optical amplification based on the stimulated emission ofelectromagnetic radiation



Invention of the LASER

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Discovery of Stimulated Emission in 1917

Einstein coefficients:Bki AbsorptionBik stimulated EmissionAik spontaneous Emission

Albert Einstein

* 14.3.1879, Ulm, Germany† 18.4.1955, Princeton, USA



1953 First MASER Constructed

Charles Hard Townes

* 28.7.1915, Greenville, USA† 27.1.2015, Oakland, USA

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1960 First LASER Constructed

Theodore Harold Maiman

* 11.7.1927, Los Angeles, USA† 5.5.2007, Vancouver, Canada

Pulsed solid-state LASER



1960 First LASER Constructed

Ali Javan

William Bennett, Jr.

Donald Herriott

at Bell Telephone Laboratories

Continuous gas LASER

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Nobel Prize in Physics in 1964

„…for fundamental work in the field of quantum electronics, which has led to the

construction of oscillators and amplifiers based on the maser-laser principle“

Aleksandr Mikhailovich Prokhorov

* 11.7.1916, Atherton, Australia† 8.1.2002, Moscow, Russia

Nicolay Gennadiyevich Basov

* 14.12.1922, Usman, Russia† 1.7.2001, Moscow, Russia

Charles Hard Townes

* 28.7.1915, Greenville, USA

† 27.1.2015, Oakland, USA



Properties of Light

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Wave – Particle Duality




Matter Light

Particle Wave

Einstein (1905)

Photoelectric effect (Nobel Prize 1921)

Quantum optics

De Broglie (1924)

Wave-like behaviour of all matter

Geometric optics

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E = h·ν = p·cp = h/λ

E: energyp: linear momentumh: Planck's constant = 4.1·10-15 eVs

Light Quantum

Photons (γ)

dispersion in vacuum λ · ν = c

λ: wavelengthν: frequencyc: speed of light = 299 792 458 m/s

Electromagnetic Wave

ψ(t)=I0⋅eiωt

t

λ

I0

Question:What's the energy difference ∆E between violet (λ=400nm) and red light (λ=700nm)?

Solution: ∆E = 1.3 eV



Electromagnetic Spectrum

visible spectrum: λ = 400 – 700 nm, ν = 4.3 – 7.5 ⋅ 1014 Hz

Geometric optics

(wave character)

Quantum optics

(particle character)

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Electromagnetic (EM) Waves

Electromagnetic waves are defined by

• Electric field: , • Magnetic field: , • Wave vector: , with ⁄

, ,



Electromagnetic Fields in Dielectric Media

electric field

Electric displacement field:

polarisation

magnetic field

Magnetic induction:

magnetisation

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Maxwell's Equations for Static Fields1. Charges are the sources of electric fields

Divergence of electric field is created by charges

2. Magnetic monopoles do not exist

In the absence of magnetic monopoles, divergence of the magnetic field lines is always zero

∙

! ∙ "# $%

&'

∙ 0

! ∙ "# 0

&'



Maxwell's Equations for Dynamic Fields3. A changing magnetic field creates an electric field

4. An electric current and a changing electric field creates a magnetic field

⨯ *++

⨯ ,- ++

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Geometrical Optics



Geometrical Optics

Simplified model of optics:

1. Light propagates as rays in homogeneous media2. At the border of two homogeneous and isotropic media,

light obeys the Law of Reflection and Refraction3. The direction of light propagation is arbitrary4. Crossing light rays do not interfere

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Fermat‘s Principle

• Refractive index n: cmedium = c/n

• vacuum: 1

• air: 1.0003

• water: 1.333

• lenses: 1.5

• Optical path length: . / nd234

The optical length of the path followed by light between the points A and B is an extremum.

„Light minimises the time to travel from point A to point B.“

Help

Beach

Sea



Reflection

θθ’

angle of incidence = angle of reflection

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Refraction

Snell's Law

n

n’

Normal

θ

θ’

A

B



Total Reflection

Fiber optic cable: Total reflection important for signal transmission!

Water tank: Reflected and refracted light components!

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Total Reflection

critical angle

n

n’

Normal

n’ > n

θc

sin(θ) =1

Question:What is the critical angle for a light beam travelling from water to air?

Solution: ϴc = 49°

refractive index n

vacuum: 1air: 1.0003water: 1.333lenses: 1.5



Lenses

Ray tracing diagram for converging lense

16

17 1

8

Ray tracing diagram for a Galilean telescope and an object with finite distance

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Yet even more Properties ofLight..



Dispersion

Refractive index depends on wavelengthof incoming light:

n = n(λ)

λ ∙ 8 :;

⇔ 8 :∙;

⇔ = >∙:;>

with = 2@8 and 2@/λ

Normal dispersion: dn/dλ B 0 stronger refraction of blue light

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Dispersion – Group and Phase Velocity

Gaussian wave packageWave package: Ψ D, ∑ FGeIJKLM>KNG

Group velocity = ,velocity of wave package‘

OPQRST d=d F ∙ d/Ud

Phase velocity = ‚velocity of the phase‘

OTVWXY = F

nIf U U ⇒ OTVWXY [ OPQRST⇒ Dispersion

OTVWXYOPQRST

https://de.wikipedia.org/wiki/Gruppengeschwindigkeit#/media/File:Wave_group.gif



Interference..

Taken fromhttp://www.eso.org/public/archives/images/screen/potw1404a.jpg

..is the superposition of waves.

constructive

destructive

Just a french astronaut creating interference..

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Coherence

Coherence time: ∆] ^∆_

Coherence length: ∆2] F ∙ ∆]

Time in which phase differencedoes not exceed 2@

Distance that light travels in ∆]

I

ννa 5·1014 Hz

LASER: ∆τ = 10 ms ⇒ ∆s = 3000 km

Sun: ∆τ = 10 fs ⇒ ∆s = 3 µm

source: P.W. Milonni, J.H. Elberly. Lasers. Wiley 1988



Michelson-Interferometer

• Splitting LASER in two rays

• Detection of interference

• Michelson-Morley experiment (1887):⇒Aether hypothesis

• LIGO⇒Detection of gravitational waves;∆2 10Mm

Schematic diagram of Michelson-Interferometer

Interference pattern for diverging rays

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Diffraction

• Change of light path when passingrestricted space

• Fresnel diffraction: " ≪ de

• Fraunhofer diffraction: " ≫ deg

• Diffraction limit for telescope:

hiIj ^.∙d

Intensity distribution for diffraction at a slit with different widths b



Directionality

∆θ

A

λ Question:What's the opening angle in steradians, givenλ = 500 nm, A = 25 mm² ?

∆Ω m λ# m ∆n

Light bulb:Strongly divergentLow irradiance(intensity)

LASER:Slightly divergentHigh irradiance(intensity)

*steradians (sr): dimensionless variable for the solid angle related to the area „A“ it cuts out of a sphere: Ω=A/r2 [sr]

Solution:

∆Ω = 10-8 steradians*

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Spectral Radiance

“A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body). This is true for radiation of all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.” Siegel, Robert; Howell, John R. (2002). Thermal Radiation Heat Transfer; Volume 1 (4th ed.). Taylor & Francis. p. 7.

_ 8@νFp

qνer_/>s * 1

t_ F _ _# ∙ ∆ν

u_ t_∆Ω

Spectral energy density

Spectral irradiance

Spectral radiance



Spectral Radiance

“A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body). This is true for radiation of all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.” Siegel, Robert; Howell, John R. (2002). Thermal Radiation Heat Transfer; Volume 1 (4th ed.). Taylor & Francis. p. 7.

_ 8@νFp

qνer_/>s * 1

t_ F _ _# ∙ ∆ν

u_ t_∆Ω

Spectral energy density

Spectral irradiance

Spectral radiance

Sun:u_ 1.5 ∙ 10M^ W/(cm2 Hz sr)

HeNe-LASER:u_ 25 W/(cm2 Hz sr)

NdGlas-LASER:u_ 2 ∙ 10w W/(cm2 Hz sr)

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Repetition

• Einstein: Explenation of stimulatedemission 1917

• First pulsed ruby LASER by Maiman in 1960

• Nobel prizes for Townes, Basow andProkhorov in 1964: fundamental work in quantum electronicsfacilitatingLASERs/MASERs

• Light has both wave and particle character• Electromagnetic wave: oscillating B- and

E fields• Maxwell's Equation: foundation of

electrodynamics

• Fermat‘s principle: (total) relfection, refraction

• Lens equation• Dispersion: Group and phase velocity• Interference and coherence• Diffraction

Properties of LASER Light• High Directionality: small ∆Ω=λ2/A• High Spectral Radiance β=I/∆Ω

• Small bandwidth ∆ω

• High spatial and temporal coherence (Michelson Interferometer)



Next Lecture

2. LASER Physics and Systems

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