PC20312 Wave Optics

Section 3:
Interference
Interference fringes

2 I1I 2

2 I1I 2
I1 + I 2

Image adapted from Wikipedia

Temporal coherence

Phase relationship changes over a

characteristic time

1
Coherence time: c 
 Image adapted from Wikipedia
 Spatial coherence

Wave with infinite temporal Wave with finite temporal and

Wave with infinite temporal
coherence but finite spatial spatial coherence
and spatial coherence coherence

A pinhole isolates part of

the wavefront and thus
increases spatial
coherence. Coherence
length is unaffected.
Images adapted from Wikipedia
Types of interference
Wavefront division Amplitude division

e.g. Michelson interferometer

e.g. Young’s slits
Thomas Young
• “The Last Man Who Knew Everything “
• Learned 13 languages by age 14
• Comparative study of 400 languages
• Translated the Rosetta stone
• PhD in physics & medical doctor
• Young’s slits
• Young’s modulus
• Founded physiological optics:
• colour vision
• astigmatism
• accommodation of the eye
• Seminal work on haemodynamics
• Secretary to the Board of Longitude
Thomas Young (1773-1829)
• Superintendent of the HM Nautical Almanac Office.
Image from Wikipedia
Young’s slits 1
Poor spatial Good spatial
coherence coherence

Single slit isolates part Double slits act To distant

of wavefront as two coherent screen
sources
Young’s slits 1
Young’s original diagram presented to Royal Society in 1803

http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm

Image from Wikipedia

Young’s slits 3


r2

y
r1

r

s >> a
Lloyd’s mirror

r1
source

l2 y
l1
i r2 = l1+l2

t

image of Phase change on reflection

source

Rev. Humphrey Lloyd (1800-1881) Trinity College Dublin

Multiple slits
P
S0

S1
a
S2

S3

S4

r
S5
2r
S6
3r
s>>a
 Interference pattern for multiple slits




N=10
N=3
 N=5
Intensity, I













 ka 
          
2
 Michelson Interferometer
Mirror, M2 d2


d1
compensator
plate

light
source beamsplitter
Mirror, M1

lens
d = 2(d1- d2)
Albert Abraham Michelson
screen (1852-1931)
Image from Wikipedia
The compensator plate
Rays to M1 pass
thru BS once

Without compensator:
• Unequal paths thru glass
NB nglass= f()
Rays to M2 pass •  path length diff. = f()
thru BS three
times With compensator:
• Equal paths thru glass
• path length diff.  f()
 Equivalent diagram for Michelson
interferometer Images of S
in M1 and M2

S S1 d S2
 

focal lens source plane M1 plane M2 plane

plane
Fringe patterns

White light
Sodium lamp

Images from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/michel.html#c1

Fourier Transform Spectroscopy
d2
I(d) monochromatic
2

1.5
d1
compensator 1
plate 0.5

0
0 2 4 6 8 10 12 14
d
beamsplitter I(d) polychromatic
Movable
mirror
lens

detector
d
Thin films
A
i
nt ni
ni
source

D
A i
t
D
B
i

C
C A
t

t
B s
lens
s C
Thin film applications

Dichroic mirrors – high reflectivity

for narrow bandwidth only Anti-reflection coatings –
reduces glare from lenses

Images from Wikipedia

Thin films in nature

Oil on water – oil layer thickness varies Soap bubbles – thickness and angle of film
giving a rainbow effect in white light varies to give rainbow

The tapetum
The ‘Tapetum lucidum’ is lucidium in a
found behind the retina of calf’s eye
many animals (not humans) –
it enhances night vision

Images from Wikipedia and Google Image

 Multibeam interference

source

Er0
Et0
Er1
Et1
Er2
Et2
Er3
Et3
Er4
Et4
Er5 Er
Et Et5
Er6

lens s
lens
 Stokes’ relations
A) rE B) E rE
E

tE tE

r2E+ttE rE
C) • B) is time-reverse of A)
• Comparing B) and C):
Sir George Gabriel Stokes
r2 + tt=1 (1819-1903)

rtE+trE r = -r
tE

Images from Wikipedia

 The Airy function

1

F=2
F=10
0.8
F=50
Transmission

0.6


0.4

0.2

0
0 1 2 3 4 5 6 7 8 9 10
Frequency

Finesse, F = Free Spectral Range,  Sir George Biddell Airy

Resolution,  (1801-1892)

Image from Wikipedia

 F  R

2 1  R 

Image from Wikipedia

 Fabry-Pérot Etalons 1

source

Charles Fabry (1867-1945)

Outer
surfaces are lens
non-parallel
f
2 highly reflecting
parallel surfaces

Alfred Pérot (1863-1925)

Potrait images from http://www-obs.cnrs-mrs.fr/tricent/astronomes/fabry.htm
Fabry-Pérot Etalons 2

4500
4000 FSR

3500
Intensity (Arb. units)
3000
2500
2000
1500
1000
500
0
0 5 10 15 20 25 30
Frequency (GHz)

Images from Google image Data from D. Binks PhD thesis