Photography Records intensity distribution of light .

Does not record direction.Two-dimensional image.

Holography = “whole + writing” Records intensity & direction of light.

Information in interference pattern.Reconstruct image by passing original light through hologram.Need laser so that light interferes.

16. Holography

http://en.wikipedia.org/wiki/Hologram

Dennis Gabor (1947) ••• Nobel Prize in Physics (1971)

Recording

Reconstructing

Photograph of the recorded interference pattern in an amplitude-modulation hologram

Holography vs. photography (from http://en.wikipedia.org/wiki/Hologram)

Each point in the holographic recording includes light scattered from every point in the scene, whereas each point in a photograph has light scattered only from a single point in the scene.

A hologram differs from a photograph in several ways:

The hologram allows the recorded scene to be viewed from a wide range of angles.The photograph gives only a single view.

The reproduced range of a hologram adds many of the same depth perception cues that were present in the original scene, which are again recognized by the human brain and translated into the same perception of a three-dimensional image as when the original scene might have been viewed.

The photograph is a flat two-dimensional representation.The developed hologram surface itself consists of a very fine, seemingly random pattern, which appears to bear no relationship to the scene which it has recorded.

A photograph clearly maps out the light field of the original scene.When a hologram is cut in pieces, the whole scene can still be seen in each piece.

When a photograph is cut in pieces, each piece shows only part of the scene. Holograms can only be viewed with very specific forms of illumination,

whereas a photograph can be viewed in a wide range of lighting conditions.

Recording Amplitude and Phase

Object Beam

( ) ( ) ( )[ ]yxjyxayxa ,exp,, φ−=

Reference Beam

( ) ( ) ( ), , exp ,A x y A x y j x yψ= −⎡ ⎤⎣ ⎦

Interference

( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

2

2 2 * *

2 2

, , ,

, , 2 , , cos , ,

I x y A x y a x y

A a A a Aa

A x y a x y A x y a x y x y x yψ ϕ

= +

= + + +

= + + −⎡ ⎤⎣ ⎦

Reconstruction of wavefront

( ) ( )yxIyxtA ,, ∝ ( ) ( )2 2,At x y A a A a Aaβ ∗ ∗= + + +

( ),, of beam (probe) reading For the yxB

( ) ( ) *1 2 3 4, ,AB x y t x y AA B aa B A Ba ABa U U U Uβ β β β∗ ∗ ∗= + + + = + + +

AB =For

∗= ABFor

( ) ( )23 , ,U x y A a x yβ=

( ) ( )24 , ,U x y A a x yβ ∗=

Original Referencing & Conjugate Referencing

AB =For

∗= ABFor

( ) ( )23 , ,U x y A a x yβ=

( ) ( )24 , ,U x y A a x yβ ∗=

Virtual image

real image

*4 ~U a

Hologram

Simple Hologram

Simple HologramConsider Two beams cross at an angle θ

Photographic plate

θz

x

beam 1

Simple Hologram

Extra path of beam 2 isDisplacements of two beams are

zθ

θ

l

sin= θl z

( )( )

1

2

= − ω

⎡ ⎤= + θ − ω⎣ ⎦

cos

cos sino

o

E E kx t

E E k x z t

beam 1

x

Thus displacement at film is:

Using the trig identity

Amplitude varies asIntensity varies as

( ) [ ]( ){ }1 2 cos cosoE E E E kx t k x t= + = −ω + + −ωl

Simple Hologram

( ) ( )1 12 2cos cos 2cos cosA B A B A B+ = + −

( )12cos lk

( ) ( )2 2 21 12 2cos cos sinI E k kz= ∝ = θl

( ) [ ]( )1 12 22 cos cosoE E k k x t= + −ωl l

Simple HologramAfter the film is developed, lines (sinusoidal diffraction grating) appear on film.

( )2 12cos sin θkz

zbeam 1

When the beam 1 is shone on the developed film:

Simple Hologram

( ) ( )( ){ } ( )

2 12

12

cos sin cos

1 cos sin cos

= θ −ω

= + θ −ωo

o

E E kz kx t

E kz kx t

( )2 12cos 1 cos 2C C= +

( ) ( ) ( )( ) ( )( )

( )( )

1 102 2

1 10 02 4

104

cos cos sin cos

cos cos sin

cos sin

= −ω + θ −ω

= −ω + + θ −ω

+ − θ −ω

oE E kx t E kz kx t

E kx t E k x z t

E k x z t

( ) ( )1 12 2cos cos cos cosA B A B A B= + + −

beam 1 ?

Simple HologramThe three parts are:

Beam continuing in direction of beam 1

Beam in direction +θ.

Beam in direction -θ.Three beams emerge, one in direction 0, one at +θ and one at -θ.

( )( )104 cos sin− θ −ωE k x z t

( )102 cos −ωE kx t

( )( )104 cos sin+ θ −ωE k x z t

Simple HologramYou will get:

+θ recreation of beam 2 (virtual image)-θ beam is real image

θ

Developed Photographic plate θ

beam 1

+θ

-θ

virtual

real

Holography of 3D Scenes

(a)

(b)

Parallax in Holograms

HolographyMany different optical arrangements.Recording requirements:

Laser light source(coherent light)Holographic film needs small grains.Good stability (no movements during exposure)

Reconstruction requirements:Much less strict.Some do not need laser.

Applications of HolographyArtistic creations.Storing & transporting delicate images

Russian icons are shown as holograms.Holographic Interferometry.

Strain analysis of objects under stressUsed for measuring shape of objects.

Data storage.Contain large amount of visual informationSimilar technique for storing digital data.

Holographic InterferometeryDouble exposure holographic interferometry.

Two holograms on photographic plate.Object is stressed between exposures.Movement of object appears as interference fringes

Real time holographic interferometry.Standard hologram of image made.Reconstruct image on top of object.Stress object & interference fringes appear.

From each point on two images, light will have the displacements.

Δx is movement of that point when object was stressed.Resultant displacement is sum of the two:

( ) ( )1 2 ⎡ ⎤= − ω = + Δ −ω⎣ ⎦cos coso oE E kx t E E k x x t

( ) ( )( ){ }1 2

2 2

= + = − ω + + Δ −ω

⎡ ⎤+ Δ Δ⎛ ⎞ ⎛ ⎞= − ω⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

cos cos

cos cos

o

o

E E E E kx t k x x t

x x k xE k t

Holographic Interferometery

Intensity varies as

Intensity shows how much (Δx) object has moved.

2

2Δ⎛ ⎞∝ ⎜ ⎟

⎝ ⎠cos k xI

Contour GenerationDouble exposure hologram at the same time

Vibration AnalysisDouble exposure hologram in sequence

Electronic Speckle Pattern Interferometry (ESPI)

Computer-generated hologram (CGH)1. Detour-Phase CGH : amplitude pattern

( ) ( )∑ ∑−

=

−

=⎥⎦

⎤⎢⎣

⎡Δ+Δ=

1

0

1

0

2exp,X Y

pq

N

p

N

q

jpqf yqxup

fjeauU υλπυ φ

Computer-generated hologram (CGH)2. Kinoform CGH: phase-only pattern

Aberration Compensation

Artificial Neural Networks

(b)(a)

Holographic data storage

Holographic data storage

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