The science of light P. Ewart Oxford Physics: Second Year, Optics - PowerPoint PPT Presentation

The science of light P. Ewart

Oxford Physics: Second Year, Optics • Lecture notes: On web site NB outline notes! • Textbooks: Hecht, Optics Klein and Furtak, Optics Lipson, Lipson and Lipson , Optical Physics Brooker, Modern Classical Optics • Problems: Material for four tutorials plus past Finals papers A2 • Practical Course: Manuscripts and Experience

Oxford Physics: Second Year, Optics Structure of the Course 1. Geometrical Optics 2. Physical Optics ( Interference ) Diffraction Theory (Scalar) Fourier Theory 3. Analysis of light ( Interferometers ) Diffraction Gratings Michelson (Fourier Transform) Fabry-Perot 4. Polarization of light (Vector)

Electronics Electromagnetism Optics Quantum Electronics 10 -7 < T < 10 7 K; e - > 10 9 eV; superconductor Quantum Optics Photonics

Oxford Physics: Second Year, Optics Astronomical observatory, Hawaii, 4200m above sea level.

Oxford Physics: Second Year, Optics Multi-segment Objective mirror, Keck Obsevatory

Oxford Physics: Second Year, Optics Hubble Space Telescope, HST, In orbit

Oxford Physics: Second Year, Optics HST Deep Field Oldest objects in the Universe: 13 billion years

Oxford Physics: Second Year, Optics HST Image: Gravitational lensing

Oxford Physics: Second Year, Optics SEM Image: Insect head

Oxford Physics: Second Year, Optics Coherent Light: Laser physics: Holography, Telecommunications Quantum optics Quantum computing Ultra-cold atoms Laser nuclear ignition Medical applications Engineering Chemistry Environmental sensing Metrology ……etc.!

Oxford Physics: Second Year, Optics CD/DVD Player: optical tracking assembly

Oxford Physics: Second Year, Optics Optics in Physics • Astronomy and Cosmology • Microscopy • Spectroscopy and Atomic Theory • Quantum Theory • Relativity Theory • Lasers

Oxford Physics: Second Year, Optics Geometrical Optics • Ignores wave nature of light • Basic technology for optical instruments • Fermat’s principle: “Light propagating between two points follows a path, or paths, for which the time taken is an extremum”

Oxford Physics: Second Year, Optics Ray tracing - revision Focal point axis Focal point

Oxford Physics: Second Year, Optics Simple magnifier a Magnifier: Object angular magnification at near point = b/a Eyepiece of Telescopes, Microscopes etc. b Virtual image at near point Short focal length lens

Oxford Physics: Second Year, Optics P 1 Thick lens or compound lens Back First Focal Principal Plane Plane Location of equivalent thin lens

Oxford Physics: Second Year, Optics Thick lens or P 2 compound lens Front Second Focal Principal Plane Plane

Oxford Physics: Second Year, Optics Telephoto lens Focal Principal Plane Plane f T Equivalent thin lens

Oxford Physics: Second Year, Optics Wide angle lens Principal Focal Plane Plane f W

Oxford Physics: Second Year, Optics Astronomical Telescope f O f E b = b/a = f o /f E angular magnification

Oxford Physics: Second Year, Optics Galilean Telescope angular magnification = b/a = f o /f E

Oxford Physics: Second Year, Optics Newtonian Telescope f o angular magnification f E = b/a b = f o /f E

Oxford Physics: Second Year, Optics The compound microscope Objective magnification = v/u Eyepiece magnifies real image of object

Oxford Physics: Second Year, Optics What size to make the lenses? Aperture stop Image of objective in eyepiece Eye piece ~ pupil size Objective: Image in eye-piece ~ pupil size

Oxford Physics: Second Year, Optics (a) (b) Field stop

Oxford Physics: Second Year, Optics ILLUMINATION OF OPTICAL INSTRUMENTS f / no. : focal length diameter

Oxford Physics: Second Year, Optics Lecture 2: Waves and Diffraction • Interference • Analytical method • Phasor method • Diffraction at 2-D apertures

Oxford Physics: Second Year, Optics T  u u t, x Time t,z or distance axis Phase change of 2 p

Oxford Physics: Second Year, Optics P r 1 r 2 q d dsin q D

Oxford Physics: Second Year, Optics Phasor diagram Imaginary u  Real

Oxford Physics: Second Year, Optics Phasor diagram for 2-slit interference u p u /r u o o r /  u /r u o o r

Oxford Physics: Second Year, Optics Diffraction from a single slit P q n i s y +a/2 + r r y dy q y sin q -a/2 D

Oxford Physics: Second Year, Optics Intensity pattern from diffraction at single slit 1.0 0.8 0.6 2 ( b ) sinc 0.4 0.2 0.0 -10 -5 0 5 10 p p p p p p b

Oxford Physics: Second Year, Optics P +a/2 r q a sin q -a/2 D

Oxford Physics: Second Year, Optics Phasors and resultant at different angles q q0 R = R O P q0 / R P 

Oxford Physics: Second Year, Optics  /  R P R R  R sin  / 2 

Oxford Physics: Second Year, Optics Phasor arc to first minimum Phasor arc to second minimum

Oxford Physics: Second Year, Optics y x q  z

Diffraction from a rectangular aperture

Oxford Physics: Second Year, Optics Diffraction pattern from circular aperture Intensity y x Point Spread Function

Diffraction from a circular aperture

Diffraction from circular apertures

Oxford Physics: Second Year, Optics Dust pattern Diffraction pattern Basis of particle sizing instruments

Oxford Physics: Second Year, Optics Lecture 3: Diffraction theory and wave propagation • Fraunhofer diffraction • Huygens-Fresnel theory of wave propagation • Fresnel-Kirchoff diffraction integral

Oxford Physics: Second Year, Optics y x q  z

Diffraction from a circular aperture

Oxford Physics: Second Year, Optics Fraunhofer Diffraction A diffraction pattern for which the phase of the light at the observation point is a linear function of the position for all points in the diffracting aperture is Fraunhofer diffraction How linear is linear?

Oxford Physics: Second Year, Optics r < /0 r r R a R a observing source R R point diffracting aperture

Oxford Physics: Second Year, Optics Fraunhofer Diffraction A diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction

Oxford Physics: Second Year, Optics P A O C B f

Oxford Physics: Second Year, Optics u v Diffracted waves Equivalent lens imaged system Fraunhofer diffraction: in image plane of system

Oxford Physics: Second Year, Optics (a) P O (b) P O Equivalent lens system: Fraunhofer diffraction is independent of aperture position

Oxford Physics: Second Year, Optics Fresnel’s Theory of wave propagation

Oxford Physics: Second Year, Optics d S n r P z -z 0 Plane wave surface unobstructed Huygens secondary sources on wavefront at -z radiate to point P on new wavefront at z = 0

Oxford Physics: Second Year, Optics r n r n r n r n P q q Construction of elements of equal area on wavefront

Oxford Physics: Second Year, Optics r p r p (q+  /2)  (q+ /2) R p R p q q First Half Period Zone Resultant, R p , represents amplitude from 1 st HPZ

Oxford Physics: Second Year, Optics Phase difference of  /2  /2 at edge of 1st HPZ q r p P O q

Oxford Physics: Second Year, Optics R p As n a infinity resultant a ½ diameter of 1 st HPZ

Oxford Physics: Second Year, Optics Fresnel-Kirchoff diffraction integral  d  i u S     ikr o u ( n, r ) e p r

Oxford Physics: Second Year, Optics Babinet’s Principle

Oxford Physics: Second Year, Optics Lectures 1 - 3: The story so far • Geometrical optics No wave effects • Scalar diffraction theory: Analytical methods Phasor methods • Fresnel-Kirchoff diffraction integral: propagation of plane waves

Oxford Physics: Second Year, Optics Joseph Fraunhofer Augustin Fresnel Gustav Robert Kirchhoff (1824 – 1887) (1787 - 1826) (1788 - 1827) d   Phase at observation is i u S     ikr o u ( n, r ) e linear function of position p r in aperture:  = k sin q y Fresnel-Kirchoff Diffraction Integral

Oxford Physics: Second Year, Optics Lecture 4: Fourier methods • Fraunhofer diffraction as a Fourier transform • Convolution theorem – solving difficult diffraction problems • Useful Fourier transforms and convolutions

Oxford Physics: Second Year, Optics Fresnel-Kirchoff diffraction integral: i u dS      ikr o u ( n . r ) e p r Simplifies to:   b  b  a i x u A ( ) u ( x ) e d x p   where b = ksin q Note: A ( b ) is the Fourier transform of u ( x ) The Fraunhofer diffraction pattern is the Fourier transform of the amplitude function in the diffracting aperture