# Introduction Introduction

## Full text

(1)

November, 2000

David Andrews

University College

## Holography

(2)



### 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.

(3)



f

d

dsinθ

θ

(4)

(5)



ÐWidth = a

ÐSeparation = d



### Intensity diffraction pattern isIntensity 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

(6)



### Intensity patternIntensity 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

2 1 2 1 2

2

(7)

### Diffraction GratingDiffraction Grating

Intensity, I

Single slit envelope

0 sinθ

λ Nd λ Nd

Nd

Nd

Diffraction peaks

(8)



### Can be used to display spectrumCan be used to display spectrum

ÐUsually use first order peak

ÐSince angle depends on wavelength

sin θ = ± λ

Nd

(9)



### 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

(10)





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

(11)



### 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

### ( ) ( )

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

(12)





### Beam a is shone through plateBeam a is shone through plate

Ð amplitude varies as cos2

12 kz sin θ

Intensity

z

(13)

(14)



ÐSince ÐAnd

Ðsince

### { } ()

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

(15)



### The three parts are:The three parts are:

ÐBeam continuing in direction of beam a ÐBeam in direction +θ.

ÐBeam in direction -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

(16)



### 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

++θθ

-θ

(17)

### Recording a HologramRecording a Hologram

laser laser

beambeam splitter splitter

Mirror

reference beam

Mirror

object

beam Mirror

object

holographic plate

(18)

Observer Image

(19)

laser

holographic film

object



(20)



### Hologram produced by developing filmHologram produced by developing film

ÐImage seen when original beam shone on hologram

laser

hologram

image

(21)





### 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.

(22)

### ‘‘Conventional’ lightConventional’ light

Short, random wave Short, random wave

trains (Incoherent) trains (Incoherent)

Intensity

Wavelength

wavelengths wavelengths

Light emerges in Light emerges in manymany directionsdirections

(23)

### Laser LightLaser Light

Long wave trains Long wave trains

(Coherent) (Coherent)

wavelengths wavelengths

Narrow, intense Narrow, intense

light beam light beam

LASER LASER

Often plane Often plane

polarized polarized

Intensity

Wavelength

(24)



### 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

(25)

November 2000 David Andrews





### Storing & transporting delicate imagesStoring & 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

(26)





### Two methods:Two methods:

ÐDouble exposure holographic interferometry.

ÐReal time holographic interferometry.

(27)



### 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.

(28)



### Real time holographic interferometry.Real time holographic interferometry.

ÐReconstruct image on top of object.

ÐStress object & interference fringes appear.

(29)



### Method is as followsMethod is as follows

ÐSet up as for standard holography.

ÐTake one exposure of object.

ÐStress object.

ÐTake second exposure.

ÐDevelop hologram.

ÐReconstruct images.



(30)



### 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   

(31)



### Intensity varies asIntensity varies as

ÐIntensity shows how much (∆x) object has moved.

2

cos  k x∆2 

 

 

Updating...

## References

Related subjects :