optics slides

7/29/2019 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

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)



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Electronics

Optics

Quantum

Electronics

QuantumOptics

Photonics

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

Electromagnetism


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Astronomical observatory, Hawaii, 4200m above sea level.


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Multi-segmentObjective mirror,

Keck Obsevatory


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Hubble Space Telescope, HST,

In orbit


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HST Deep Field

Oldest objects

in the Universe:

13 billion years


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HST Image: Gravitational lensing


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SEM Image:

Insect head


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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


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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P1

First

PrincipalPlane

Back

FocalPlane

Location of

equivalent thin lens

Thick lens or

compound lens


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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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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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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

Oxford Physics: Second Year Optics


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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

O f d Ph i S d Y Optics


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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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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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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

Optics


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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


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

O ti


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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)


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


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

Oxford Physics: Second Year, Optics Schlieren photography


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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

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