Biomedical Optics Basic Optics

Transcription

1 1. Basic Optics Simon Hubertus, M.Sc. Computer Assisted Clinical Medicine Medical Faculty Mannheim Heidelberg University Theodor-Kutzer-Ufer 1-3 D Mannheim, Germany My Academic Background Saarland B.Sc. in Physics at RWTH Aachen University ( ) M.Sc. in Biomedical Engineering at Imperial College London ( ) PhD Thesis at the Institute of Computer Assisted Clinical Medicine in Mannheim (2016-present) Simon HubertusI Slide 2/42 I 10/24/2017 1

2 My Academic Background PhD student in Tissue Structure and Function at the Institute of Computer Assisted Clinical Medicine in Mannheim [ppm] OEF CMRO2 [µmol/100g/min] Simon HubertusI Slide 3/42 I 10/24/2017 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: Simon HubertusI Slide 4/42 I 10/24/2017 2

3 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, , 1-3pm House 1, Level 0, Lecture Hall 09 Simon HubertusI Slide 5/42 I 10/24/2017 Literature Simon HubertusI Slide 6/42 I 10/24/2017 3

4 LASER A LASER is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation LASER Light Amplification by Stimulated Emission of Radiation 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 Simon HubertusI Slide 7/42 I 10/24/2017 Invention of the LASER Simon HubertusI Slide 8/42 I 10/24/2017 4

5 Discovery of Stimulated Emission in 1917 Albert Einstein * , Ulm, Germany , Princeton, USA Einstein coefficients: B ki Absorption B ik stimulated Emission spontaneous Emission A ik Simon HubertusI Slide 9/42 I 10/24/ First MASER Constructed Charles Hard Townes * , Greenville, USA , Oakland, USA Simon HubertusI Slide 10/42 I 10/24/2017 5

6 1960 First LASER Constructed Theodore Harold Maiman * , Los Angeles, USA , Vancouver, Canada Pulsed solid-state LASER Simon HubertusI Slide 11/42 I 10/24/ First LASER Constructed Ali Javan William Bennett, Jr. Donald Herriott at Bell Telephone Laboratories Continuous gas LASER Simon HubertusI Slide 12/42 I 10/24/2017 6

7 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 Charles Hard Townes * , Greenville, USA , Oakland, USA Nicolay Gennadiyevich Basov * , Usman, Russia , Moscow, Russia Aleksandr Mikhailovich Prokhorov * , Atherton, Australia , Moscow, Russia Simon HubertusI Slide 13/42 I 10/24/2017 Properties of Light Simon HubertusI Slide 14/42 I 10/24/2017 7

8 Wave Particle Duality Simon HubertusI Slide 15/42 I 10/24/2017 Wave Particle Duality Matter Light De Broglie (1924) Wave-like behaviour of all matter Einstein (1905) Photoelectric effect (Nobel Prize 1921) Quantum optics Geometric optics Particle Wave Simon HubertusI Slide 16/42 I 10/24/2017 8

9 Wave Particle Duality Electromagnetic Wave λ ψ(t)=i 0 e iωt Light Quantum Photons (γ) I 0 t dispersion in vacuum λ ν = c λ: wavelength ν: frequency c: speed of light = m/s E = h ν = p c p = h/λ E: energy p: linear momentum h: Planck's constant = evs Question: What's the energy difference E between violet (λ=400nm) and red light (λ=700nm)? Solution: E = 1.3 ev Simon HubertusI Slide 17/42 I 10/24/2017 Electromagnetic Spectrum Geometric optics (wave character) Quantum optics (particle character) visible spectrum: λ = nm, ν = Hz Simon HubertusI Slide 18/42 I 10/24/2017 9

10 Electromagnetic (EM) Waves Electromagnetic waves are defined by Electric field:, Magnetic field:, Wave vector:, with,, Simon HubertusI Slide 19/42 I 10/24/2017 Electromagnetic Fields in Dielectric Media Electric displacement field: electric field polarisation Magnetic induction: magnetic field magnetisation Simon HubertusI Slide 20/42 I 10/24/

11 Maxwell's Equations for Static Fields 1. Charges are the sources of electric fields! "#$% &' Divergence of electric field is created by charges 2. Magnetic monopoles do not exist 0! "# 0 &' In the absence of magnetic monopoles, divergence of the magnetic field lines is always zero Simon HubertusI Slide 21/42 I 10/24/2017 Maxwell's Equations for Dynamic Fields 3. A changing magnetic field creates an electric field * An electric current and a changing electric field creates a magnetic field, Simon HubertusI Slide 22/42 I 10/24/

12 Geometrical Optics Simon HubertusI Slide 23/42 I 10/24/2017 Geometrical Optics Simplified model of optics: 1. Light propagates as rays in homogeneous media 2. At the border of two homogeneous and isotropic media, light obeys the Law of Reflection and Refraction 3. The direction of light propagation is arbitrary 4. Crossing light rays do not interfere Simon HubertusI Slide 24/42 I 10/24/

13 Fermat s Principle Refractive index n: c medium = c/n vacuum: 1 air: water: lenses: 1.5 Beach Help 3 Optical path length:. / n d2 4 Sea 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. Simon HubertusI Slide 25/42 I 10/24/2017 Reflection angle of incidence = angle of reflection θ θ Simon HubertusI Slide 26/42 I 10/24/

14 Refraction Snell's Law A Normal n θ n θ B Simon HubertusI Slide 27/42 I 10/24/2017 Total Reflection Water tank: Reflected and refracted light components! Fiber optic cable: Total reflection important for signal transmission! Simon HubertusI Slide 28/42 I 10/24/

15 Total Reflection Normal refractive index n vacuum: 1 air: water: lenses: 1.5 n n θ c n > n sin(θ) =1 critical angle Question: What is the critical angle for a light beam travelling from water to air? Solution: ϴ c = 49 Simon HubertusI Slide 29/42 I 10/24/2017 Lenses Ray tracing diagram for converging lense Ray tracing diagram for a Galilean telescope and an object with finite distance Simon HubertusI Slide 30/42 I 10/24/

16 Yet even more Properties of Light.. Simon HubertusI Slide 31/42 I 10/24/2017 Dispersion Refractive index depends on wavelength of 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 Simon HubertusI Slide 32/42 I 10/24/

17 Dispersion Group and Phase Velocity Gaussian wave package Wave package: Ψ D, F G e IJ KLM> K N G Group velocity =,velocity of wave package O PQRST d= d F d/u d Phase velocity = velocity of the phase If U U O TVWXY [O PQRST Dispersion O TVWXY = F n O TVWXY O PQRST Simon HubertusI Slide 33/42 I 10/24/2017 Interference....is the superposition of waves. constructive Just a french astronaut creating interference.. Taken from destructive Simon HubertusI Slide 34/42 I 10/24/

18 Coherence Coherence time: ] ^ _ Time in which phase difference does not exceed 2@ Coherence length: 2 ] F ] Distance that light travels in ] I LASER: τ = 10 ms s = 3000 km Sun: τ = 10 fs s = 3µm ν a Hz ν source: P.W. Milonni, J.H. Elberly. Lasers. Wiley 1988 Simon HubertusI Slide 35/42 I 10/24/2017 Michelson-Interferometer Splitting LASER in two rays Detection of interference Michelson-Morley experiment (1887): Aether hypothesis Schematic diagram of Michelson-Interferometer LIGO Detection of gravitational waves; 2 10 M m Interference pattern for diverging rays Simon HubertusI Slide 36/42 I 10/24/

19 Diffraction Change of light path when passing restricted space Fresnel diffraction: " de Fraunhofer diffraction: " de Diffraction limit for telescope: h iij ^. d g Intensity distribution for diffraction at a slit with different widths b Simon HubertusI Slide 37/42 I 10/24/2017 Directionality Light bulb: Strongly divergent Low irradiance (intensity) LASER: Slightly divergent High irradiance (intensity) λ A θ Ω m λ # m n Simon HubertusI Slide 38/42 I 10/24/2017 Question: What's the opening angle in steradians, given λ = 500 nm, A = 25 mm²? Solution: Ω = 10-8 steradians* *steradians (sr): dimensionless variable for the solid angle related to the area A it cuts out of a sphere: Ω=A/r2 [sr] 19

20 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. Spectral energy density _ 8@ν F p qν e r_/>s *1 Spectral irradiance t _ F # ν Spectral radiance u _ t _ Ω Simon HubertusI Slide 39/42 I 10/24/2017 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. Sun: u _ M^ W/(cm 2 Hz sr) Spectral energy density _ 8@ν F p qν e r_/>s *1 HeNe-LASER: u _ 25 W/(cm 2 Hz sr) NdGlas-LASER: u _ 2 10 w W/(cm 2 Hz sr) Spectral irradiance t _ F # ν Spectral radiance u _ t _ Ω Simon HubertusI Slide 40/42 I 10/24/

21 Repetition Einstein: Explenation of stimulated emission 1917 First pulsed ruby LASER by Maiman in 1960 Nobel prizes for Townes, Basow and Prokhorov in 1964: fundamental work in quantum electronics facilitating LASERs/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) Simon HubertusI Slide 41/42 I 10/24/2017 Next Lecture 2. LASER Physics and Systems Simon HubertusI Slide 42/42 I 10/24/