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

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

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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

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  • P. Ewart

The science of light

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  • 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

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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)

Oxford Physics: Second Year, Optics

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Electronics Optics Quantum Electronics Quantum Optics Photonics

10-7 < T < 107 K; e- > 109 eV; superconductor Electromagnetism

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Oxford Physics: Second Year, Optics

Astronomical observatory, Hawaii, 4200m above sea level.

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Oxford Physics: Second Year, Optics

Multi-segment Objective mirror, Keck Obsevatory

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Oxford Physics: Second Year, Optics

Hubble Space Telescope, HST, In orbit

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Oxford Physics: Second Year, Optics

HST Deep Field Oldest objects in the Universe: 13 billion years

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Oxford Physics: Second Year, Optics

HST Image: Gravitational lensing

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Oxford Physics: Second Year, Optics

SEM Image: Insect head

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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.!

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Oxford Physics: Second Year, Optics

CD/DVD Player: optical tracking assembly

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  • Astronomy and Cosmology
  • Microscopy
  • Spectroscopy and Atomic Theory
  • Quantum Theory
  • Relativity Theory
  • Lasers

Oxford Physics: Second Year, Optics

Optics in Physics

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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

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Ray tracing - revision

axis Focal point Focal point

Oxford Physics: Second Year, Optics

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Simple magnifier

Object at near point a Virtual image at near point b Short focal length lens

Magnifier: angular magnification = b/a Eyepiece of Telescopes, Microscopes etc.

Oxford Physics: Second Year, Optics

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Oxford Physics: Second Year, Optics

P1 First Principal Plane Back Focal Plane

Location of equivalent thin lens

Thick lens or compound lens

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Oxford Physics: Second Year, Optics

P2 Second Principal Plane Front Focal Plane

Thick lens or compound lens

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Oxford Physics: Second Year, Optics

Principal Plane Focal Plane fT

Telephoto lens Equivalent thin lens

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Oxford Physics: Second Year, Optics

Principal Plane Focal Plane fW

Wide angle lens

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Oxford Physics: Second Year, Optics

fO fE

b

angular magnification = b/a Astronomical Telescope = fo/fE

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Oxford Physics: Second Year, Optics

angular magnification = b/a Galilean Telescope = fo/fE

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Oxford Physics: Second Year, Optics

b

fo fE

angular magnification = b/a Newtonian Telescope = fo/fE

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Oxford Physics: Second Year, Optics

The compound microscope

Objective magnification = v/u Eyepiece magnifies real image of object

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Oxford Physics: Second Year, Optics

Image of objective in eyepiece

Aperture stop

What size to make the lenses? Eye piece ~ pupil size Objective: Image in eye-piece ~ pupil size

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Oxford Physics: Second Year, Optics

(a) (b)

Field stop

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Oxford Physics: Second Year, Optics

ILLUMINATION OF OPTICAL INSTRUMENTS

f/no. : focal length diameter

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Oxford Physics: Second Year, Optics

Lecture 2: Waves and Diffraction

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

u t, x T  Time

  • r distance

axis

t,z u

Phase change of 2p

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Oxford Physics: Second Year, Optics

dsinq d

q

r1 r2 P D

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Oxford Physics: Second Year, Optics

 Real Imaginary u

Phasor diagram

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Oxford Physics: Second Year, Optics

 / u /r

  • up

u /r

  • Phasor diagram for 2-slit interference

uo r uo r

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Oxford Physics: Second Year, Optics

ysinq +a/2

  • a/2

q

r r y + s i n q P D y dy

Diffraction from a single slit

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Oxford Physics: Second Year, Optics

  • 10
  • 5

5 10 0.0 0.2 0.4 0.6 0.8 1.0

p p p p p p

sinc

2(b)

b

Intensity pattern from diffraction at single slit

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Oxford Physics: Second Year, Optics

asinq +a/2

  • a/2

q

r P D

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Oxford Physics: Second Year, Optics

q0 q0

/

RO R R =

P P

Phasors and resultant at different angles q

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Oxford Physics: Second Year, Optics

R RP  /  

R sin /2 R

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Oxford Physics: Second Year, Optics

Phasor arc to first minimum Phasor arc to second minimum

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Oxford Physics: Second Year, Optics

y x z  q

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Diffraction from a rectangular aperture

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Oxford Physics: Second Year, Optics

Intensity y x

Diffraction pattern from circular aperture Point Spread Function

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Diffraction from a circular aperture

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Diffraction from circular apertures

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Oxford Physics: Second Year, Optics

Dust pattern Diffraction pattern Basis of particle sizing instruments

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Oxford Physics: Second Year, Optics

Lecture 3: Diffraction theory and wave propagation

  • Fraunhofer diffraction
  • Huygens-Fresnel theory of

wave propagation

  • Fresnel-Kirchoff diffraction

integral

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Oxford Physics: Second Year, Optics

y x z  q

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Diffraction from a circular aperture

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Oxford Physics: Second Year, Optics

Fraunhofer Diffraction How linear is linear?

A diffraction pattern for which the phase of the light at the

  • bservation point is a

linear function of the position for all points in the diffracting aperture is Fraunhofer diffraction

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Oxford Physics: Second Year, Optics

R R R R a a r r diffracting aperture source

  • bserving

point

r < /0

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Oxford Physics: Second Year, Optics

Fraunhofer Diffraction A diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction

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Oxford Physics: Second Year, Optics

O P A B C

f

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Oxford Physics: Second Year, Optics

u v

Equivalent lens system

Fraunhofer diffraction: in image plane of system

Diffracted waves imaged

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Oxford Physics: Second Year, Optics

(a) (b) O O P P

Equivalent lens system: Fraunhofer diffraction is independent of aperture position

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Oxford Physics: Second Year, Optics

Fresnel’s Theory of wave propagation

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Oxford Physics: Second Year, Optics

dS n r P z

  • z

Plane wave surface

Huygens secondary sources on wavefront at -z radiate to point P on new wavefront at z = 0

unobstructed

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Oxford Physics: Second Year, Optics

rn q rn P

Construction of elements of equal area on wavefront

rn q rn

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Oxford Physics: Second Year, Optics

(q+ /2)  q rp Rp

First Half Period Zone

(q+/2) q rp Rp

Resultant, Rp, represents amplitude from 1st HPZ

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Oxford Physics: Second Year, Optics

rp /2 q q P O

Phase difference of /2 at edge of 1st HPZ

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Oxford Physics: Second Year, Optics

As n a infinity resultant a ½ diameter of 1st HPZ Rp

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Oxford Physics: Second Year, Optics

Fresnel-Kirchoff diffraction integral

ikr

  • p

e r S u i u ) r n, ( d     

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Oxford Physics: Second Year, Optics

Babinet’s Principle

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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

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Oxford Physics: Second Year, Optics

Gustav Robert Kirchhoff (1824 –1887) Joseph Fraunhofer (1787 - 1826) Augustin Fresnel (1788 - 1827) Fresnel-Kirchoff Diffraction Integral

ikr

  • p

e r S u i u ) r n, ( d     

Phase at observation is linear function of position in aperture:  = k sinq y

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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

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Oxford Physics: Second Year, Optics

ikr

  • p

e r n r u i u ) . ( dS     x e x u A u

x i p

d ) ( ) (

b

a b

  

 

Fresnel-Kirchoff diffraction integral: Simplifies to: where b = ksinq

Note: A(b) is the Fourier transform of u(x)

The Fraunhofer diffraction pattern is the Fourier transform

  • f the amplitude function in the diffracting aperture
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Oxford Physics: Second Year, Optics

' d ). ' ( ). ' ( ) ( ) ( ) ( x x x g x f x g x f x h

  

   

The Convolution function: The Convolution Theorem:

The Fourier transform, F.T., of f(x) is F(b) F.T., of g(x) is G(b) F.T., of h(x) is H(b) H(b) = F(b).G(b) The Fourier transform of a convolution of f and g is the product of the Fourier transforms of f and g

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Oxford Physics: Second Year, Optics

b Monochromatic Wave Fourier Transform T

.bo  p/T

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Oxford Physics: Second Year, Optics

xo x b V(x) V( ) b

-function Fourier transform Power spectrum V(b)V(b)* = V2 = constant V

b

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Oxford Physics: Second Year, Optics

xS x b V(x) V( ) b

Comb of -functions Fourier transform

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g(x-x’) f(x) h(x)

Constructing a double slit function by convolution

Oxford Physics: Second Year, Optics

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g(x-x’) f(x) h(x)

Triangle as a convolution of two “top-hat” functions This is a self-convolution or Autocorrelation function

Oxford Physics: Second Year, Optics

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Joseph Fourier (1768 –1830)

Oxford Physics: Second Year, Optics

  • Heat transfer theory:
  • greenhouse effect
  • Fourier series
  • Fourier synthesis and analysis
  • Fourier transform as analysis
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Oxford Physics: Second Year, Optics

Lecture 6: Theory of imaging

  • Fourier methods in optics
  • Abbé theory of imaging
  • Resolution of microscopes
  • Optical image processing
  • Diffraction limited imaging
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Oxford Physics: Second Year, Optics

ikr

  • p

e r n r u i u ) . ( dS     x e x u A u

x i p

d ) ( ) (

b

a b

  

 

Fresnel-Kirchoff diffraction integral: Simplifies to: where b = ksinq

Note: A(b) is the Fourier transform of u(x)

The Fraunhofer diffraction pattern is the Fourier transform

  • f the amplitude function in the diffracting aperture
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Ernst Abbé (1840 -1905)

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Oxford Physics: Second Year, Optics

a d d’ f D u v u(x) v(x)

Fourier plane

q

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Oxford Physics: Second Year, Optics

The compound microscope

Objective magnification = v/u Eyepiece magnifies real image of object

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Diffracted orders from high spatial frequencies miss the objective lens

So high spatial frequencies are missing from the image.

qmax defines the numerical aperture… and resolution

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Oxford Physics: Second Year, Optics

Fourier plane Image plane Image processing

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Oxford Physics: Second Year, Optics

Optical simulation of “X-Ray diffraction”

a b a’ b’

(a) and (b) show objects: double helix at different angle of view Diffraction patterns of (a) and (b) observed in Fourier plane Computer performs Inverse Fourier transform To find object “shape”

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PIV particle image velocimetry

Oxford Physics: Second Year, Optics

  • Two images recorded

in short time interval

  • Each moving particle gives

two point images

  • Coherent illumination
  • f small area produces

“Young’s” fringes in Fourier plane of a lens

  • CCD camera records

fringe system – input to computer to calculate velocity vector

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PIV particle image velocimetry

Oxford Physics: Second Year, Optics

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Oxford Physics: Second Year, Optics

a d d’ f D u v u(x) v(x)

Fourier plane

q

phase object amplitude object

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Oxford Physics: Second Year, Optics

Schlieren photography

Source Collimating Lens Imaging Lens Knife Edge Image Plane Refractive index variation

Fourier Plane

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Schleiren photography in i.c.engine

Schlieren film of autoignition Courtesy of Prof CWG Sheppard University of Leeds

Spark plug

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Oxford Physics: Second Year, Optics

Intensity y x

Diffraction pattern from circular aperture

Point Spread Function, PSF

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Oxford Physics: Second Year, Optics

Lecture 7: Optical instruments and Fringe localisation

  • Interference fringes
  • What types of fringe?
  • Where are fringes located?
  • Interferometers
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Oxford Physics: Second Year, Optics

non-localised fringes

Plane waves

Young’s slits

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Z

Oxford Physics: Second Year, Optics

Diffraction grating

q q to 8 f

Plane waves

Fringes localised at infinity: Fraunhofer

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Oxford Physics: Second Year, Optics

P’ P O

Wedged reflecting surfaces Point source

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Oxford Physics: Second Year, Optics

O P P’ q q’

Parallel reflecting surfaces Point source

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Oxford Physics: Second Year, Optics

P’ P R O S R’

Wedged Reflecting surfaces Extended source

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Oxford Physics: Second Year, Optics

t 2t=x source images 2t=x a path difference cos x a circular fringe constant a

Parallel reflecting surfaces Extended source

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Oxford Physics: Second Year, Optics

Wedged Parallel Point Source Non-localised Equal thickness Non-localised Equal inclination Extended Source Localised in plane

  • f Wedge

Equal thickness Localised at infinity Equal inclination

Summary: fringe type and localisation