optics slides
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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, OpticsLipson, Lipson and Lipson, Optical Physics
Brooker, Modern Classical Optics
Problems: Material for four tutorials plus pastFinals papers A2
Practical Course: Manuscripts and Experience
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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)
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Electronics
Optics
Quantum
Electronics
QuantumOptics
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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Multi-segmentObjective 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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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 computingUltra-cold atoms
Laser nuclear ignition
Medical applications
EngineeringChemistry
Environmental sensing
Metrology etc.!
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CD/DVD Player: optical tracking assembly
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Astronomy and Cosmology
Microscopy Spectroscopy and Atomic Theory
Quantum Theory
Relativity Theory
Lasers
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Optics in Physics
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Geometrical Optics
Ignores wave nature of light
Basic technology for optical instruments
Fermats principle:
Light propagating between two points
follows a path, or paths,for which the time taken is an extremum
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Ray tracing - revision
axis
Focal point
Focal point
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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.
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Oxford Physics: Second Year, Optics
P1
First
PrincipalPlane
Back
FocalPlane
Location of
equivalent thin lens
Thick lens or
compound lens
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Oxford Physics: Second Year, Optics
2
SecondPrincipalPlane
FrontFocalPlane
Thick lens or
compound lens
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PrincipalPlane
FocalPlane
fT
Telephoto lens
Equivalent thin lens
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rncpaPlane
ocaPlane
fW
Wide angle lens
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fO fE
b
angular magnification = b/a
Astronomical Telescope
= fo/fE
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angular magnification = b/a
Galilean Telescope
=
fo/fE
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b
fo
fE
angular
magnification
= b/a
Newtonian Telescope
= fo/fE
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The compound microscope
Objective magnification = v/uEyepiece magnifies real image of object
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Image o o ect vein eyepiece
Aperture stop
What size to make the lenses?
Eye piece ~ pupil size
Objective: Image in eye-piece ~ pupil size
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(a) (b)
Field stop
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ILLUMINATION OFOPTICAL INSTRUMENTS
f/no. : focal lengthdiameter
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Lecture 2: Waves and Diffraction
Interference
Analytical method Phasor method
Diffraction at 2-D apertures
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u
t, x
T
Time
or distanceaxis
t,z
u
Phase change of 2p
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dsinq
d q
r1
r2
P
D
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Real
Imaginary
u
Phasor diagram
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/u /roup
u /ro
Phasor diagram for 2-slit interference
uo
r
uor
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ysinq
+a/2
-a/2
q r
r y+ sinq
P
D
dy
Diffraction from a single slit
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-10 -5 0 5 10
0.0
0.2
0.4
0.6
0.8
1.0
pp p ppp
sinc2(b)
b
Intensity pattern from
diffraction at single slit
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asinq
+a/2
-a/2
qr
P
D
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q0
q0/
RO
R
R =
P
P
Phasors and resultant
at different angles q
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RR
P
/
R sin /2
R
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Phasor arc tofirst minimum
Phasor arc tosecond minimum
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y
x
z
q
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Diffraction from a rectangular aperture
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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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Lecture 3: Diffraction theory
and wave propagation
Fraunhofer diffraction
Huygens-Fresnel theory of
wave propagation
Fresnel-Kirchoff diffraction
integral
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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
observation point is a
linear function of the positionfor all points in the diffracting
aperture is Fraunhofer diffraction
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R
R R
R
a a
r r
diffractingaperture
source observingpoint
r < /0
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Fraunhofer Diffraction
A diffraction pattern formed in the image
plane of an optical system is
Fraunhofer diffraction
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O
P
A
BC
f
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u v
Equivalent lenssystem
Fraunhofer diffraction: in image plane of system
Diffractedwaves
imaged
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(a)
(b)
O
O
P
P
Equivalent lens system:
Fraunhofer diffraction is independent of aperture position
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Fresnels Theory of wave propagation
O ti
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dS
n
r
P
z-z 0
Plane wave
surface
Huygens secondary sources on wavefront at -z
radiate to point P on new wavefront atz = 0
unobstructed
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rn
q
rn
P
Construction of elements of equal area on wavefront
rn
q
rn
O ti
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(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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rp
/2
q
q
P
O
Phase difference of/2
at edge of 1st HPZ
O
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As na infinity resultanta diameter of 1st HPZ
Rp
O ti
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Fresnel-Kirchoff diffraction integral
ikrop e
rSuiu )rn,(d
O ti
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Babinets Principle
O ti
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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
O ti
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Oxford Physics: Second Year, Optics
Gustav Robert Kirchhoff
(18241887)
Joseph Fraunhofer
(1787 - 1826)
Augustin Fresnel
(1788 - 1827)
Fresnel-Kirchoff Diffraction Integral
ikrop e
r
Suiu )rn,(
d
Phase at observation is
linear function of position
in aperture: = k sinq y
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Lecture 4: Fourier methods
Fraunhofer diffraction as a
Fourier transform
Convolution theoremsolving difficult diffraction problems
Useful Fourier transformsand convolutions
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ikrop ern
r
uiu ).(dS
xexuAu xip d)()(bab
Fresnel-Kirchoff diffraction integral:
Simplifies to:
whereb= ksinq
Note:A(b) is the Fourier transform ofu(x)
The Fraunhofer diffraction pattern is the Fourier transformof the amplitude function in the diffracting aperture
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'd).'().'()()()( xxxgxfxgxfxh
The Convolution function:
The Convolution Theorem:
The Fourier transform, F.T., off(x) isF(b)F.T., ofg(x) is G(b)
F.T., ofh(x) isH(b)
H(b) = F(b).G(b)The Fourier transform of a convolution offand gis the product of the Fourier transforms offand g
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b
Monochromatic
Wave
Fourier
Transform
T
.bo p/T
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xo x
b
V(x)
V( )b
-function
Fourier transform
Power spectrumV(b)V(b)* = V2
= constant
V
b
Optics
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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
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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
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Joseph Fourier(17681830)
Oxford Physics: Second Year, Optics
Heat transfer theory:
- greenhouse effect
Fourier series
Fourier synthesis and analysis
Fourier transform as analysis
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Lecture 6: Theory of imaging
Fourier methods in optics
Abb theory of imaging Resolution of microscopes
Optical image processing
Diffraction limited imaging
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ikrop ern
r
uiu ).(dS
xexuAu xip d)()(bab
Fresnel-Kirchoff diffraction integral:
Simplifies to:
whereb= ksinq
Note:A(b) is the Fourier transform ofu(x)
The Fraunhofer diffraction pattern is the Fourier transformof the amplitude function in the diffracting aperture
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Ernst Abb (1840 -1905)
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a
dd
f Du v
u(x) v(x)
Fourier plane
q
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The compound microscope
Objective magnification = v/uEyepiece magnifies real image of object
Diffracted orders from high spatial frequencies miss
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Diffracted orders from high spatial frequencies missthe objective lens
So high spatial frequencies are
missing from the image.
qmax defines the numerical aperture and resolution
Oxford Physics: Second Year, Optics Image processing
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y , p
Fourierplane
Image
plane
Image processing
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Optical simulation ofX-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 planeComputer performsInverse Fourier transformTo find object shape
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PIV particle image velocimetry
p
Two images recordedin short time interval
Each moving particle gives
two point images
Coherent illumination
of small area produces
Youngs fringes in
Fourier plane of a lens
CCD camera recordsfringe system
input to computer
to calculate velocity vector
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PIV particle image velocimetry
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a
dd
f Du v
u(x) v(x)
Fourier plane
q
phase object
amplitude object
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Sc e e p otog ap y
Source
CollimatingLens
ImagingLens
KnifeEdge
ImagePlane
e ract ve
indexvariation
FourierPlane
Schleiren photography in i.c.engine
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Schlieren film of autoignition
Courtesy of Prof CWG Sheppard
University of Leeds
Spark
plug
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Intensity
y
x
Diffraction pattern from circular aperture
Point Spread Function, PSF
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Lecture 7: Optical instruments and
Fringe localisation
Interference fringes
What types of fringe?
Where are fringes located?
Interferometers
Oxford Physics: Second Year, Optics Youngs slits
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y p
non-localisedfringes
Plane
waves
Young s slits
Oxford Physics: Second Year, Optics Diffraction grating
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Z
g g
q q
to8
f
Planewaves
Fringes localised at infinity: Fraunhofer
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p
P
P
O
Wedgedreflecting surfaces
Point
source
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OPP
q
qParallel
reflecting surfaces
Pointsource
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P
P
R
OS
R
Wedged
Reflecting surfaces
Extended source
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2t=x
sourceimages
2t=x
a
path difference cosx a
circular fringe
constant a
Parallel
reflectingsurfaces
Extended
source
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Wedged Parallel
PointSource
Non-localisedEqual thickness
Non-localisedEqual inclination
Extended
Source
Localised in plane
of Wedge
Equal thickness
Localised at infinity
Equal inclination
Summary: fringe type and localisation