November, 2000
David Andrews
University College
Third Year Science Third Year Science
Imaging Imaging
Holography
Holography
Introduction Introduction
Photograph Photograph
ÐImage intensity distribution of light .
++ Does not record direction.Does not record direction.
++ TwoTwo--dimensional image.dimensional image.
Hologram Hologram
ÐRecords intensity & direction of light.
++ Information in interference pattern.Information in interference pattern.
++ Reconstruct image by passing original light Reconstruct image by passing original light through hologram.
through hologram.
++ Need laser so that light interferes.Need laser so that light interferes.
Diffraction Grating Diffraction Grating
Series of very closely spaced slits Series of very closely spaced slits
f
d
dsinθ
θ
Diffraction Grating
Diffraction Grating
Diffraction Grating Diffraction Grating
N N narrow slits narrow slits
ÐWidth = a
ÐSeparation = d
Intensity diffraction pattern is Intensity diffraction pattern is
ÐA2 is diffraction pattern from each slit
( )
( )
2 2
2
sin sin
sin sin
∝ θ
θ I A Nkd
kd
( )
( )
2 1 2 2
1 2 2
sin sin θ
∝ ka
A
ka
Diffraction Grating Diffraction Grating
Intensity pattern Intensity pattern
Ðset of very sharp peaks
++ at angles given byat angles given by
ÐAmplitude of peaks
++ modulated by single slit patternmodulated by single slit pattern
sin θ = 0, , , , ± λ ± 2λ ± 3λ L
Nd Nd Nd
( )
( )
2 1 2 1 2
2
sin ka sin θ
ka
Diffraction Grating Diffraction Grating
Intensity, I
Single slit envelope
0 sinθ
λ Nd λ Nd
Nd −
− 2λ
2λ Nd
Diffraction peaks
Diffraction grating Diffraction grating
Can be used to display spectrum Can be used to display spectrum
ÐUsually use first order peak
ÐSince angle depends on wavelength
++ spectrum spread out.spectrum spread out.
sin θ = ± λ
Nd
Simple Hologram Simple Hologram
Two beams cross at an angle Two beams cross at an angle θ θ
Photographic plate Photographic plate
θθ
zz xx laser
laser beambeam aa
laser
laser beam b beam b
Simple Hologram Simple Hologram
Extra path is Extra path is
Displacements of two beams are Displacements of two beams are
zz θθ θθ
ll
= sin θ l z
( )
( )
( )
cos
cos sin
a o
b o
E E kx t
E E k x z t
= − ω
= + θ − ω
Thus displacement at film is: Thus displacement at film is:
ÐUsing the trig identity
ÐAmplitude varies as ÐIntensity varies as
( ) ( [ ] )
{ }
[ ]
( ) ( )
1 2
1 1
2 2
cos cos
2 cos cos
= + = − ω + + − ω
= + − ω
l
l l
o
o
E E E E kx t k x t
E k x t k
Simple Hologram Simple Hologram
( ) ( )
1 1
2 2
cos A + cos B = 2 cos A + B cos A B−
(
12)
cos kl
( ) ( )
2 1 2 1
2 2
cos cos sin
∝ l = θ
I k kz
Simple Hologram Simple Hologram
Plate is developed, and horizontal lines Plate is developed, and horizontal lines appear.
appear.
Beam a is shone through plate Beam a is shone through plate
Ð amplitude varies as cos2
(
12 kz sin θ)
Intensity
z
Sinusoidal Diffraction Grating
Sinusoidal Diffraction Grating
Amplitude of beam is: Amplitude of beam is:
ÐSince ÐAnd
Ðsince
Simple Hologram Simple Hologram
( ) ( )
( )
{ } ( )
2 1 2 1
2
cos sin cos
1 cos sin cos
= θ − ω
= + θ − ω
o
o
E E kz kx t
E kz kx t
( )
2 1
cos C = 2 1 cos 2+ C
( ) ( ) ( )
( ) ( ( ) )
( )
( )
1 1
2 0 2
1 1
0 0
2 4
1 4 0
cos cos sin cos
cos cos sin
cos sin
= − ω + θ − ω
= − ω + + θ − ω
+ − θ − ω
E E kx t Eo kz kx t
E kx t E k x z t
E k x z t
( ) ( )
1 1
2 2
cos Acos B = cos A+ B + cos A B−
Simple Hologram Simple Hologram
The three parts are: The three parts are:
ÐBeam continuing in direction of beam a ÐBeam in direction +θ.
ÐBeam in direction -θ.
Three beams emerge, one in direction Three beams emerge, one in direction 0, one at +
0, one at + θ θ and one at and one at - - θ θ . .
( )
( )
1
4 E0 cos k x − z sin θ − ωt
( )
1
2 E0 cos kx − ωt
( )
( )
1
4 E0 cos k x + z sin θ − ωt
Simple Hologram Simple Hologram
You will get: You will get:
Ð+θ recreation of beam b (virtual image) Ð-θ beam is real image
θθ
Developed Developed
Photographic plate
Photographic plate
θ θ laser beam a
laser beam a
++θθ
-θ-θ
Recording a Hologram Recording a Hologram
laser laser
beambeam splitter splitter
Mirror
reference beam
Mirror
object
beam Mirror
object
holographic plate
Reconstructing a hologram Reconstructing a hologram
Observer Image
In line Hologram In line Hologram
laser
holographic film
object
Hologram is interference pattern Hologram is interference pattern between direct beam and light
between direct beam and light scattered form object
scattered form object
In line Hologram In line Hologram
Hologram produced by developing film Hologram produced by developing film
ÐImage seen when original beam shone on hologram
laser
hologram
image
Holography Holography
Many different optical arrangements. Many different optical arrangements.
Recording requirements: Recording requirements:
ÐLaser light source(coherent light)
ÐHolographic film needs small grains.
ÐGood stability (no movements during exposure)
Reconstruction requirements: Reconstruction requirements:
ÐMuch less strict.
ÐSome do not need laser.
‘ ‘ Conventional’ light Conventional’ light
Short, random wave Short, random wave
trains (Incoherent) trains (Incoherent)
Intensity
Wavelength
Large spread in Large spread in
wavelengths wavelengths
Light emerges in Light emerges in manymany directionsdirections
Laser Light Laser Light
Long wave trains Long wave trains
(Coherent) (Coherent)
Small spread in Small spread in
wavelengths wavelengths
Narrow, intense Narrow, intense
light beam light beam
LASER LASER
Often plane Often plane
polarized polarized
Intensity
Wavelength
Coherence Coherence
Interference needs fixed relationship Interference needs fixed relationship between phases.
between phases.
ÐConventional light sources produce short wavetrains at random intervals.
++ Random variation of phaseRandom variation of phase
++ Little interferenceLittle interference
ÐLasers produce long wavetrains
++ Phase relation between light beams fairly Phase relation between light beams fairly constant.
constant.
++ Good interferenceGood interference
November 2000 David Andrews
Applications of Holography Applications of Holography
Artistic creations. Artistic creations.
Storing & transporting delicate images Storing & transporting delicate images
ÐRussian icons are shown as holograms.
Holographic Interferometry. Holographic Interferometry.
ÐStrain analysis of objects under stress ÐUsed for measuring shape of objects.
Data storage. Data storage.
ÐContain large amount of visual information
ÐSimilar technique for storing digital data
Holographic Interferometery Holographic Interferometery
Measures strain on an object. Measures strain on an object.
Two methods: Two methods:
ÐDouble exposure holographic interferometry.
ÐReal time holographic interferometry.
Holographic Interferometery Holographic Interferometery
Double exposure holographic Double exposure holographic interferometry.
interferometry.
ÐTwo holograms on photographic plate.
ÐObject is stressed between exposures.
ÐMovement of object appears as interference fringes.
++ Light & dark bands across image.Light & dark bands across image.
Holographic Interferometery Holographic Interferometery
Real time holographic interferometry. Real time holographic interferometry.
ÐStandard hologram of image made.
ÐReconstruct image on top of object.
ÐStress object & interference fringes appear.
Double Exposure Interference Double Exposure Interference
Holography Holography
Method is as follows Method is as follows
ÐSet up as for standard holography.
ÐTake one exposure of object.
ÐStress object.
ÐTake second exposure.
ÐDevelop hologram.
ÐReconstruct images.
Two images are on top of each other. Two images are on top of each other.
Analysis Analysis
From each point on two images, light From each point on two images, light will have the displacements.
will have the displacements.
Ð∆x is movement of that point when object was stressed.
ÐResultant displacement is sum of the two:
( )
( )
( )
1
2
cos cos
o
o
E E kx t
E E k x x t
= − ω
= + ∆ − ω
( ) ( ( ) )
{ }
1 2
2 2
cos cos
cos cos
o
o
E E E E kx t k x x t
x x k x
E k t
= + = − ω + + ∆ − ω
+ ∆ ∆
= − ω
Analysis Analysis
Intensity varies as Intensity varies as
ÐIntensity shows how much (∆x) object has moved.
2
cos k x∆2
