HolographyHolography

• Dennis Gabor (1948, 1949, 1951) ••• Nobel Prize in Physics (1971)

holography

“whole recording”

- On-axis hologram

• E. N. Leith and J. Upatnieks (1962, 1963)

- Off-axis hologram

• Y. N. Denisyuk (1962, 1963, 1965)

HolographyHolography

Reference : http://oeqelab.snu.ac.kr

Recording Amplitude and PhaseRecording Amplitude and Phase

Object Beam

( ) ( ) ( )[ ]yxjyxayxa ,exp,, φ−=

Reference Beam

( ) ( ) ( )[ ]yxjyxAyxA ,exp,, ψ−=

Interference

( ) ( ) ( ) ( ) ( ) ( ) ( )[ ]yxyxyxayxAyxayxAyxI ,,cos,,2,,, 22 φψ −++=

Reconstruction of wavefrontReconstruction of wavefront

( ) ( )yxIyxtA ,, ∝ ( ) ( )∗∗ +++= AaaAatyxt bA2', β

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

( ) ( ) 4321''', , UUUUABaBaABaaBtyxtyxB bA +++=+++= ∗∗∗ βββ

AB =For

∗= ABFor

( ) ( )yxaAyxU ,', 23 β=

( ) ( )yxaAyxU ,', 24

∗= β

Original Referencing & Conjugate ReferencingOriginal Referencing & Conjugate Referencing

AB =For

∗= ABFor

( ) ( )yxaAyxU ,', 23 β=

( ) ( )yxaAyxU ,', 24

∗= β

Virtual image

real image

Image Formation by HolographyImage Formation by Holography

( ) ( )

−+−+ 2

02

0200 ˆˆexp yyxxzjka :

image Virtual

( ) ( )

−+−+−∗ 2

02

0200 ˆˆexp yyxxzjka :

image Real

GaborGabor Hologram : onHologram : on--axisaxis

( ) ( )2,, yxaAyxI +=

( ) ( ) ( )yxAayxaAyxaA ,,, 22 ∗∗ +++=

LeithLeith--UpatnieksUpatnieks Hologram : offHologram : off--axisaxis

( ) ( ) ( )yxayjAyxU ,2exp, +−= παλθα 2sin

=

( ) ( ) ( ) ( ) ( ) ( )yjyxAayjyxaAyxaAyxI παπα 2exp,2exp,,, 22 −+++= ∗∗

LeithLeith--UpatnieksUpatnieks HologramHologram

( ) ( )( ) ( ) ( ) yjx,yBAa Ux,yaBU

yjx,yaBA U B tU b

παββ

παβ

2exp''

2exp'

42

2

31

−==

==∗

∗

Requirement of Reference Beam AngleRequirement of Reference Beam Angle

( )λθ B3sin2 1min

−=

Holography of 3D Scenes (I)Holography of 3D Scenes (I)

Holography of 3D Scenes (II)Holography of 3D Scenes (II)

(a)

(b)

Parallax in HologramsParallax in Holograms

Image LocationImage Location

1

01

2

1

21−

±=

zzzz

rpi λ

λλλ

m

pp

ir

iii x

zzx

zzx

zzx +±=

01

20

01

2

λλ

λλ

m

pp

ir

iii y

zzy

zzy

zzy +±=

01

20

01

2

λλ

λλ

m

Image MagnificationImage Magnification

Transverse Magnification

Axial Magnification

1

2

010

01

2

00

1−

−==∂∂

=∂∂

=pr

iiit z

zzz

zz

yy

xxM

λλ

λλ

m

2

2

1

1

01

2

1

2

00

1t

rp

ia M

zzzzzzM

λλ

λλ

λλ

=

±

∂∂

=∂∂

=−

m

Fourier Hologram (I)Fourier Hologram (I)

(a)

(b)

Fourier Hologram (II)Fourier Hologram (II)

Lensless Fourier hologram

Image HologramImage Hologram

FraunhoferFraunhofer HologramHologram

OrthoscopicOrthoscopic and and PseudoscopicPseudoscopic ImagesImages

Transmission and Reflection Holograms (I)Transmission and Reflection Holograms (I)

• Reflection hologram

(a)

(b)

Transmission and Reflection Holograms (II)Transmission and Reflection Holograms (II)

Maximum Theoretical Diffraction EfficiencyMaximum Theoretical Diffraction Efficiency

Holographic StereogramHolographic Stereogram

(a) (b)

Rainbow Hologram (I)Rainbow Hologram (I)

(a)

(b)

Rainbow Hologram (II)Rainbow Hologram (II)

(b)(a)

Multiplex HologramMultiplex Hologram

(a)

(b)

Holographic Materials (I)Holographic Materials (I)

Holographic Materials (II)Holographic Materials (II)

ColorColor

Color HolographyColor Holography

CIE Chromaticity diagram

Incoherent HolographyIncoherent Holography

1

21 f

fM −=

2

12 f

fM −=

( ) ( )

+= 22

0 exp, yxz

jUyxUa λπ

( )

+

+

+

=

2

2

2

22

2

1

2

11 expexp,

My

Mx

zjU

My

Mx

zjUyxUb λ

πλπ

ComputerComputer--Generated Hologram (CGH)Generated Hologram (CGH)

Special film,

Special treatmentContinuous

Bleached photo on triple-emulsion film

ROACH

Phase only,

Special film treatment

Plot- continuous Final result-transparent

Bleached photo of plotter output

Kinoform

Phase onlyBinaryCRT displaySynthetic interferogram

Fourier hologramContinuousCRT displayDelay sampling

Both phase and amplitude are quantized

BinaryPlotter outputDetour phase

Limited number of pointsContinuousMulti-exposure photoSuperimposed FZP

CommentsGray levelsPreparationType

DetourDetour--Phase Hologram (I)Phase Hologram (I)

( ) ( )∑ ∑−

=

−

=

∆+∆=

1

0

1

0

2exp,X Y

pq

N

p

N

q

jpqf yqxup

fjeauU υλπυ φ

DetourDetour--Phase Hologram (II)Phase Hologram (II)

(a)

(b)

KinoformKinoform

InterferometryInterferometry

DoubleDouble--Exposure Holographic Exposure Holographic InterferometryInterferometry

(b)

(a)

Contour GenerationContour Generation

(a) (b)

Vibration AnalysisVibration Analysis

(a) (b)

Electronic Speckle Pattern Electronic Speckle Pattern InterferometryInterferometry (I)(I)

ESPI (II)ESPI (II)

Aberration CompensationAberration Compensation

Artificial Neural NetworksArtificial Neural Networks

(b)(a)

Holographic data storageHolographic data storage

From Lucent

Holographic data storageHolographic data storage

From Lucent