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PC20312 Wave Optics
Section 3:
Interference
Interference fringes
212 II
212 III1 + I2
Image adapted from Wikipedia
Temporal coherence
Phase relationship changes over a characteristic time
1
cCoherence time:Image adapted from Wikipedia
Spatial coherence
Wave with infinite temporal and spatial coherence
Wave with infinite temporal coherence but finite spatial
coherence
Wave with finite temporal and spatial 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
e.g. Young’s slits
Amplitude division
e.g. Michelson interferometer
Thomas Young
Thomas Young (1773-1829)
• “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
• Superintendent of the HM Nautical Almanac Office. Image from Wikipedia
Young’s slits 1
Poor spatial coherence
Good spatial coherence
Single slit isolates part of wavefront
Double slits act as two coherent
sources
To distant screen
Young’s slits 1Young’s original diagram presented to Royal Society in 1803
Image from Wikipedia
http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm
Young’s slits 3
a
y
r2
r1
r
s
s >> a
Lloyd’s mirror
i
y
r1
l1l2
Phase change on reflection
source
image of source
r2 = l1+l2
t
Rev. Humphrey Lloyd (1800-1881) Trinity College Dublin
Multiple slits
S0
S3
S4
S5
S6
S1
S2
a
r
2r
3r
s>>a
P
Interference pattern for multiple slits
Inte
nsity
, I
N=10N=3N=5
ka2
Michelson Interferometer
Albert Abraham Michelson (1852-1931)
d1
d2
beamsplitter
Mirror, M1
Mirror, M2
compensator plate
lens
screen
light source
d = 2(d1- d2)
Image from Wikipedia
The compensator plate
Without compensator:
• Unequal paths thru glass
• path length diff. = f()
With compensator:
• Equal paths thru glass
path length diff. f()
Rays to M1 pass thru BS once
Rays to M2 pass thru BS three
times
NB nglass= f()
Equivalent diagram for Michelson interferometer
source plane M1 plane M2 plane
d
d cos()
S S1 S2
Images of S in M1 and M2
lens
f
focal plane
Fringe patterns
Sodium lamp
Images from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/michel.html#c1
White light
Fourier Transform Spectroscopy
d1
d2
beamsplitter
compensator plate
lens
detector
Movable mirror
0 2 4 6 8 10 12 140
0.5
1
1.5
2
d
I(d) monochromatic
d
I(d) polychromatic
Thin films
nt nini
BD
C
A
s
source
lens
i
t
A
C
D
i
i
A
C
B st
t
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 giving a rainbow effect in white light
Soap bubbles – thickness and angle of film varies to give rainbow
The ‘Tapetum lucidum’ is found behind the retina of many animals (not humans) – it enhances night vision
The tapetum lucidium in a
calf’s eye
Images from Wikipedia and Google Image
Multibeam interference
Er
s
source
Et0
Et1
Et3
Et2
Et5
Et4
Er0
Er1
Er3
Er2
Er5
Er4
Er6
lenslens
Et
Stokes’ relations
Sir George Gabriel Stokes (1819-1903)
r2E+ttE
E rE
tE
E rE
tE
rE
tErtE+trE
A) B)
C) • B) is time-reverse of A)
• Comparing B) and C):
r2 + tt=1
r = -r
Images from Wikipedia
The Airy function
Sir George Biddell Airy (1801-1892)
Finesse, F = Free Spectral Range, Resolution,
Image from Wikipedia
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
Frequency
Tra
nsm
issi
on
F=2F=10F=50
RRF
12
Image from Wikipedia
Fabry-Pérot Etalons 1
Potrait images from http://www-obs.cnrs-mrs.fr/tricent/astronomes/fabry.htm &Wikipedia
Charles Fabry (1867-1945)
Alfred Pérot (1863-1925)
s
r
source
lens
f2 highly reflecting parallel surfaces
Outer surfaces are non-parallel
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 5 10 15 20 25 30
Frequency (GHz)
Inte
nsi
ty (
Arb
. u
nit
s)
FSR
Images from Google image Data from D. Binks PhD thesis
Fabry-Pérot Etalons 2