Two-dimensional image.

‹ Photography

Ð Records intensity distribution of light .

+

Does not record direction.

+

Two-dimensional image.

‹ Holography = “whole + writing”

Ð 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

( ) ( ) ^{x y a x y} [ ^j ( ) ^{x y} ]

a , = , exp − φ ,

Reference Beam

( ) ^, ( ) ^{, exp} ( ) ^,

A x y = A x y ⎡ ⎣ − j ψ x y ⎤ ⎦

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 ψ x y ϕ x y

= +

= + + +

= + + ⎡ ⎣ − ⎤ ⎦

Reconstruction of wavefront

( ) ( ) ^{x y I x y}

t

, ∝ , ^t

( ) ^{x y , = β} ( ^A

^{+ a}

^{+ A a}

^{+ Aa}

)

( ) ^{, ,}

of beam (probe)

reading

For the B x y

( ) ( ) ,

,

B x y t x y = β AA B + β aa B

+ β A Ba

+ β ABa

= U + U + U + U

A B =

For

= A ∗

B For

( ) ² ( )

3 , ,

U x y = β A a x y

( ) ² ( )

4 , ,

U x y = β A a ^∗ x y

Original Referencing & Conjugate Referencing

A B = For

= A

B For

( )

( )

3

, ,

U x y = β A a x y

( )

( )

4

, ,

U x y = β A a

x y

Virtual image

real image

* 4 ~ U a

Hologram

Simple Hologram

Simple Hologram

‹ Consider Two beams cross at an angle θ

Photographic plate

θ

z

x

beam 1

Simple Hologram

‹ Extra path of beam 2 is

‹ Displacements of two beams are

θ z

θ

l

= sin θ l z

( )

( )

1

2

= − ω

⎡ ⎤

= ⎣ + θ − ω ⎦

cos

cos sin

o

o

E E kx t

E E k x z t

beam 1

x

‹ Thus displacement at film is:

ÐUsing the trig identity

ÐAmplitude varies as ÐIntensity varies as

( ) ( [ ] )

{ }

1 2 _o

cos cos

E = E + E = E kx − ω + t k x + − ω l t

Simple Hologram

( ) ( )

1 1

2 2

cos A + cos B = 2 cos A + B cos A B −

(

)

cos k l

( ) ( )

2 2 1 2 1

2 2

cos cos sin

I = E ∝ k l = kz θ

(

) ( [

] )

2

cos cos

E = E k l k x + l − ω t

Simple Hologram

‹

After the film is developed,

‹

lines (sinusoidal diffraction grating) appear on film.

( )

2 1

cos

kz sin θ

z

beam 1

‹ When the beam 1 is shone on the developed film:

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 =

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 E

kz kx t

E kx t E k x z t

E k x z t

( ) ( )

1 1

2 2

cos A cos B = cos A + B + cos A − B

beam 1

?

Simple Hologram

‹ The three parts are:

ÐBeam continuing in direction of beam 1

ÐBeam in direction +θ.

ÐBeam in direction -θ.

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

( )

( )

1

4

E

cos k x − z sin θ − ω t

( )

1

2

E

cos kx − ω t

( )

( )

1

4

E

cos k x + z sin θ − ω t

Simple Hologram

‹ You will get:

Ð+θ recreation of beam 2 (virtual image) Ð-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

Holography

‹ Many different optical arrangements.

‹ Recording requirements:

ÐLaser light source(coherent light)

ÐHolographic film needs small grains.

ÐGood stability (no movements during exposure)

‹ Reconstruction requirements:

ÐMuch less strict.

ÐSome do not need laser.

Applications of Holography

‹ Artistic creations.

‹ Storing & transporting delicate images ÐRussian icons are shown as holograms.

‹ Holographic Interferometry.

ÐStrain analysis of objects under stress ÐUsed for measuring shape of objects.

‹ Data storage.

ÐContain large amount of visual information

ÐSimilar technique for storing digital data.

Holographic Interferometery

‹ Double exposure holographic interferometry.

ÐTwo holograms on photographic plate.

ÐObject is stressed between exposures.

ÐMovement of object appears as interference fringes

‹ Real time holographic interferometry.

ÐStandard hologram of image made.

ÐReconstruct image on top of object.

ÐStress object & interference fringes appear.

‹

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

Ð Δx is movement of that point when object was stressed.

Ð Resultant displacement is sum of the two:

( ) ( )

1

=

cos − ω

=

cos ⎡ ⎣ + Δ − ω ⎤ ⎦

E 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 x

E k t

Holographic Interferometery

‹ Intensity varies as

Ð Intensity shows how much (Δx) object has moved.

2

2

⎛ Δ ⎞

∝ cos ⎜ ⎝ k x ⎟ ⎠

I

Contour Generation

Double exposure hologram at the same time

Vibration Analysis

Double exposure hologram in sequence

Electronic Speckle Pattern Interferometry (ESPI)

Computer-generated hologram (CGH)

1. Detour-Phase CGH : amplitude pattern

( ) ∑ ∑

( )

=

−

=

⎥

⎦

⎢ ⎤

⎣

⎡ Δ + Δ

=

0

1

0

exp 2 ,

X Y

pq

N

p N

q

j pq

f

up x q y

j f e

a u

U υ

λ

υ

π

Computer-generated hologram (CGH)

2. Kinoform CGH: phase-only pattern

Aberration Compensation

Artificial Neural Networks

(b) (a)

Holographic data storage

Holographic data storage

From Lucent