Holographic measurement and synthesis of optical field using a spatial light modulator
Joonku Hahn
NCRCAPAS School of Electrical Engineering
Seoul National University
Introduction
Overview of digital holography
Real optical space where optical fields propagate
Synthesis with spatial light modulator
Measurement by phase-shift interferometry
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Introduction
Motivation of adaptive holographic technology
Real optical space
Designing hologram
Synthesizing technology
Measuringtechnology
Adaptive feedback
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Synthesis of optical fieldwithout adaptive feedback
Measurement of optical fieldbased on phase-shifting interferometry
Synthesis of optical fieldwith adaptive feedback
Synthesis of micro optical fieldby demagnification optics
Measurement of optical fieldbased on holographic microscopy
Digital holographic technologies
Holographic synthesis Holographic measurement
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Contents
I.
II.
III.
Synthesis of optical fieldwithout adaptive feedback
Measurement of optical fieldbased on phase-shifting interferometry
Synthesis of optical fieldwith adaptive feedback
Synthesis of micro optical fieldby demagnification optics
Measurement of optical fieldbased on holographic microscopy
Digital holographic technologies
Holographic synthesis Holographic measurement
I. Spatial light modulator with twisted nematic liquid crystal
1.1 Optimization of twisted nematic liquid crystal SLM
1.2 Wide viewing angle dynamic holographic stereogram
Synthesis of optical fieldwithout adaptive feedback
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I. Spatial light modulator with twisted nematic liquid crystal
1.1 Optimization of twisted nematic liquid crystal SLM
Input side Output side
Twist angle
Tilt angleTNLC Cell
Input Output
Ideal amplitude only modulation
Ideal phase only modulation
Typical TNLC modulation with two polarizers.
-1 1
i
-i
Re
Im
-1 1
i
-i
Re
Im
-1 1
i
-i
Re
Im
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x
zy
TN-LC Cell
Wave plate
Polarizer
Wave plate
Polarizer
fast axis
fast axis
director axis
twist angle
tilt angle
transmission axis
transmission axis
x
zy
TN-LC Cell
Wave plate
Polarizer
Wave plate
Polarizer
fast axis
fast axis
director axis
twist angle
tilt angle
transmission axis
transmission axis
I. Spatial light modulator with twisted nematic liquid crystal
1
2
1
2
: rotation angle of input polarizer: rotation angle of output polarizer: rotation angle of input wave plate: rotation angle of output wave plate
P
P
W
W
θθθθ
1.1 Optimization of twisted nematic liquid crystal SLM
Configuration of SLM with TNLC
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Polarization-state generator
Polarization-state detector
J. Hahn, H. Kim, and B. Lee, Appl. Opt. 47, pp. D87-D95 (2008).
TNLC cell
I. Spatial light modulator with twisted nematic liquid crystal
Eigenstates of twisted nematic liquid crystal
( )( )
( ) ( )
1 22
1 22
2 2
2 2E
iλ
α γ βγ
β γ γ βγ
⎡ ⎤+⎢ ⎥+ =⎢ ⎥+ +⎢ ⎥⎣ ⎦
( )( ) ( )
( )
1 22
1 22
2 2
2 2E
iλ
β γ γ βγ
α γ βγ
⎡ ⎤+ +⎢ ⎥− =⎢ ⎥− +⎢ ⎥⎣ ⎦
1.1 Optimization of twisted nematic liquid crystal SLM
Lu and Saleh model Coy model
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I. Spatial light modulator with twisted nematic liquid crystal
Optimization of SLM with genetic optimization algorithm
1.1 Optimization of twisted nematic liquid crystal SLM
Specifications of systemSLM: SONY LCX016AL-6 (32um pixel pitch)CCD: KODAK MegaPlus ES1.0/MV (9um pixel pitch)Laser: Coherent Verdi V-5 (Nd:YAG 532nm)
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Laser
Expander
4 plateλ
Polarizer4 waveplateλ
4 waveplateλPolarizer
TNLC SLM
Beam splitter
Positive lensCCD
OPD
Motorized rotation stages
Polarization-state generator
Polarization-state detector
TNLC cell
I. Spatial light modulator with twisted nematic liquid crystal
1.1 Optimization of twisted nematic liquid crystal SLM
Schematics of optimization system
2 50πPrecision of measuring the phase modulation :
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I. Spatial light modulator with twisted nematic liquid crystal
Genetic optimization algorithm
Motor control
Amplitude modulation measurement
Phase modulation measurement
:E l i t e x
Yes
No
1k k= +
0k =
Motor Driving
Select the fittest
LabviewTM Matlab®
Mutation
k kP P ′= >
Reorganization of the population
sorting{ }1|k i i iP x f f +′ ′= ≥
, |
0 , , 1, , ,i j j
k
x x x xP
i h j h m
′= =⎧ ⎫= ⎨ ⎬
= − =⎩ ⎭
Start Create the initial population{ }0 | 0 , 1, ,iP x i m= =
{ }| 0 , 1 , ,k iP x i m= =
:e l i t e x( ) ( )m a x kF x F P= ⎡ ⎤⎣ ⎦
Motor control
Amplitude modulation measurement
Phase modulation measurement
Motor Driving
Select the fittest
{ }| 0 , 1 , ,k iP x i m′ = =
( ) ( )ˆ m a x kF x F P⎡ ⎤′= ⎣ ⎦
Select the new fittest
( ) ( ) ( )ˆm a x ,F x F x F x= ⎡ ⎤⎣ ⎦
:N e w e l i t e x
m a xk k≥
Motor control
Amplitude modulation measurement
Phase modulation measurement
:E l i t e x
Yes
No
1k k= +
0k =
Motor Driving
Select the fittest
LabviewTM Matlab®
Mutation
k kP P ′= >
Reorganization of the population
sorting{ }1|k i i iP x f f +′ ′= ≥
, |
0 , , 1, , ,i j j
k
x x x xP
i h j h m
′= =⎧ ⎫= ⎨ ⎬
= − =⎩ ⎭
Reorganization of the population
sorting{ }1|k i i iP x f f +′ ′= ≥
, |
0 , , 1, , ,i j j
k
x x x xP
i h j h m
′= =⎧ ⎫= ⎨ ⎬
= − =⎩ ⎭
Start Create the initial population{ }0 | 0 , 1, ,iP x i m= =
Create the initial population{ }0 | 0 , 1, ,iP x i m= =
{ }| 0 , 1 , ,k iP x i m= =
:e l i t e x( ) ( )m a x kF x F P= ⎡ ⎤⎣ ⎦
Motor control
Amplitude modulation measurement
Phase modulation measurement
Motor Driving
Select the fittest
{ }| 0 , 1 , ,k iP x i m′ = =
( ) ( )ˆ m a x kF x F P⎡ ⎤′= ⎣ ⎦
Select the new fittest
( ) ( ) ( )ˆm a x ,F x F x F x= ⎡ ⎤⎣ ⎦
:N e w e l i t e x
m a xk k≥
1.1 Optimization of twisted nematic liquid crystal SLM
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Genetic algorithm is programmed by LabviewTM and Matlab®.
Main part of genetic algorithm is programmed in Matlab® program.
Four motorized rotation stages are controlled by LabviewTM.
The phase modulation is calculated with interference pattern by a CCD and the amplitude modulation is measured by a OPD.
These data is delivered into Matlab® with the help of LabviewTM.
I. Spatial light modulator with twisted nematic liquid crystal
1.1 Optimization of twisted nematic liquid crystal SLM
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After the genetic optimizationBefore the genetic optimization
Phase and amplitude modulations during evolutions
Experimental results before and after genetic optimization
Twin image
z
u
Uφ
z
u
Viewing windowsTransfer lensesTransfer lens
Hologram
Hologram
Object Object
Focal length Focal len
gth
Uφ
I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Angular spectrum of object wave and their recording positions
Conventional planar hologram Curved-shaped holographic stereogram
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The concave-shaped CGH designed by Benton (1966)
I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Local viewing angles in field of view displayed by a single SLM
f
duθ
p
p
ap
ap
u
v
ξ
η
vθ
Transfer lens
Focal plane
0 order diffraction
-1 order diffractionon v-axis
+1 order diffraction on v-axis
Local viewing angle
Spherical phase resulting from
Amplitude contour by sinc function
Pixels of SLM
d f≠
( ),c cα β
Central direction of local viewing angle
2 .u v u vW W N Mθ θ λ ≈ ×Constraint relation in the area and local viewing angles
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I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Total viewing angles in field of view displayed by a single SLM
f
d
u
v
ξ
η
uΘ vΘ
Total viewing angle
( )2
2
fNp f d
λλ− −( )
2
2
fNp f d
λλ+ −
( )2
2
fMp f d
λλ− −
( )2
2
fMp f d
λλ+ −
SLM plane
Transfer lensFocal plane
Frontward horizontal summit
Frontward vertical summit
Backward horizontal summit
Backward vertical summit Viewing volume
SLM
12 tan 12 2uNp d
f p fλ− ⎡ ⎤⎛ ⎞
Θ ≈ − −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦
Total viewing angles in field of view
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I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Field of view defined by a curved array of SLMs
z
u
uθ ′
Total backward horizontal summit
Total forward horizontal summit
Local viewing angle by an individual SLM
Total viewing angle by a curved array of SLMs u′Θ
SLMsn×
( ) 112 tan 1 .
2 2u
n N p N p df f p f
λ−′ ⎡ ⎤− ′ ⎛ ⎞′Θ = + − −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦
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Total viewing angles by a curved array of SLMs
Transfer optics conflict with each other.
J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, Opt. Express 16, pp. 12372-12386 (2008).
I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
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Sub-SLMs
Transfer lensFocal plane
Local viewing angles
Central directions
Sub-SLMs
Mirrors
Mirrors
Transfer lens
Focal plane
Local viewing angles
Central directions
Equivalent fields of view
Field of view by effectively reformed SLMField of view by three sub-SLMs positioned at different vertical heightsin contact with each other diagonally
I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Polarizer
Polarizer
TNLC Lens
Mirrors
Mirrors
Upper arm
Lower arm
SLM
Transfer lens
Polarizer
Polarizer
TNLC Lens
Mirrors
Mirrors
Upper arm
Lower arm
SLM
Transfer lens
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Embodiment of effectively reformed SLM
Alignment of some reformed SLMsStructure of effectively reformed SLM
I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Schematics of the proposed wide viewing angle dynamic holographic stereogram
Asymmetric diffusing screen
Curved array of SLMs
4f optics
Rear lens array
Light source
Front lens
Folding optics
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I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Pictures of the dynamic holographic stereogram
Curved array of SLMs mounted without upper arms Whole system with electronic controllers
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I. Spatial light modulator with twisted nematic liquid crystal
1.2 Wide viewing angle dynamic holographic stereogram
Computer generated holograms and respective numerical reconstructions
200 400 600 800 1000
50
100
150
200
250200 400 600 800 1000
50
100
150
200
250200 400 600 800 1000
50
100
150
200
250
Pictures of the implemented dynamic holographic stereogram
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36th view1st view 19th view
This result is honored to be chosen as ‘Image of the week’ , August 4th in OpticsInfoBase.
Synthesis of optical fieldwithout adaptive feedback
Measurement of optical fieldbased on phase-shifting interferometry
Synthesis of optical fieldwith adaptive feedback
Synthesis of micro optical fieldby demagnification optics
Measurement of optical fieldbased on holographic microscopy
Digital holographic technologies
Holographic synthesis Holographic measurement
Synthesis of optical fieldwith adaptive feedback
Measurement of optical fieldbased on phase-shifting interferometry
II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
2.2 Optical implementation of iterative fractional Fourier transform algorithm
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
Optical configuration for phase-shifting interferometry in Fourier optics
Laser
Mirror
Mirror
Variable beamsplitter
Cube beamsplitter
CCDPiezo driven mirror
Diverging lens
Fourier lens
Object
Object wave
Reference wave
Beam expander
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
The relation between two phases of interferograms in the complex plane
2 2 ˆ ˆ2i O R O R iI A A A A ϕ α= + + ⋅
( )expO OU A jϕ=
( )expiR R iU A jα=
( )( )ˆ ˆ ˆ2
ij i j R
O i j
I I I A
A ϕ α α
≡ −
= ⋅ −
1 11O i iiU a I
≠′ = ∑
Object and reference waves
ith step interferogram
Base of phase-shifting interferometry
General phase-shifting interferometry equation
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J. Hahn, H. Kim, S.-W. Cho, and B. Lee, Appl. Opt. 47, pp.4068-4076 (2008).
ˆiα
ˆ jα
ˆiα
ˆ jα
ˆ jα−
Re
Im
ˆiα ˆ jα−
Conventional 4-step phase-shifting interferometry
( ) ( )1 3 4 2*O R RU I I A j I I A′ = − + −
If the difference between two arguments decreases, the magnitude of the base will decrease.This relationship affects the coefficients of bases in phase-shifting interferometry equation
Original object and twin image in hologram with Fourier optics
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
Reconstructed images using only one base of phase-shifting interferometry
The degree of twin image noise can be evaluated by the evenness of reconstructed image on focal plane.
2z f=0z =
Fourier transform lenswith focal length f
(Hologram plane)
Frontward focal plane
z f=
Backward focal plane
( )0, ;OU x y z ( ), ;2OU x y fOriginal object
z
x
y ( ), ;2twinU x y f
( )0, ;twinU x y z−Twin image
Centro-symmetry
0z z=0z z= −
Genetic algorithmChromosome
Cost function
II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
The flow of the micro-genetic algorithm to eliminate a twin image
Create an initial population
Evaluate the fitness function
Determine the elite
Mutation
Determine new elite
Sort the population
Exclude the poorest
Elite
{ }0 1,2, ,iP x i p= =
( )max max cost ; 1,2, ,if x i p= =⎡ ⎤⎣ ⎦( )1 costave im
f xp
= ∑
max avef f δ− ≤
Crossover
Update the population
{ }k i i jP x f f′ ′= ≥
{ }1 1, 1,2, , 1k iP x x i p+′ ′= = −
{ } { }1 11, 2, , 1 1, 2, , 1i ix i p y i p+ +′ = − ⇒ = −
{ }1 1, 1,2, , 1k iP x y i p+′= = −
( ) ( )cost max cost ; 1, 2, ,ix x i p= =⎡ ⎤⎣ ⎦
k kP P′⇒
( ) ( ) ( )cost max cost ,cost ; 1,2, ,ix x x i p′= =⎡ ⎤⎣ ⎦
1k k= +
maxk k<
Sort the population
Protect the fittest{ }k i i jP x f f′′ ′′= ≥
{ }1, 1,2, , 1k iP x x i p+′′= = −
x
{ }where 0, 1, 1,0,0,1ix = − −
0, 2, 4
1, 3
cost functionmnn m n
mnn m n
U
U= ± ± ±
=± ± ±
= −∑ ∑∑ ∑
Degree of twin image noise
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{ } { } { } { } { } { }{ }21 21 31 31 1 1Re , Im , Re , Im , , Re , Imi N Nx a a a a a a=
Where are modified real Zernike polynomials mnU
Coefficients of baes in phase-shifting interferometry equation
II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
Experimental results with the genetic algorithm
After the genetic algorithmBefore the genetic algorithm
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2.1 Phase-shifting interferometry with unknown phase-shifts
Evolutions in the genetic algorithm
0 20 40 60 80 100-1.0
-0.5
0.0
0.5
1.0
α1rα1iα2rα2iα3rα3i
Genrations
Coe
ffici
ents
of p
hase
-shi
ft ba
ses
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
symmetric coeffs.antisymmetric coeffs.
symmetric cantsymmetrievennessoddness .evennessoddness
Genrations
Rat
ios o
f eve
nnes
s and
odd
ness
Fittest chromosome Resultant evenness and oddness in reconstructed images
II. Adaptive holographic synthesis with phase-shifting interferometry
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
Resultant relationship among phase-shift bases
1I2I
3I 4I
1.00000.2
759
0.6857
0.1850
0.6706
0.26
98
( )1 1 2.79I α =
( )2 2 1.89I α = −
( )3 3 0.47I α =( )4 4 0.52I α =
Im
Re
Optimized coefficients of the basesin phase-shifting interferometry.
Resultant phase-shifts of interferograms
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As the difference between two arguments decreases, the magnitude of the base also decreases.This relationship affects the coefficients of bases in phase-shifting interferometry equation
II. Adaptive holographic synthesis with phase-shifting interferometry
2.1 Phase-shifting interferometry with unknown phase-shifts
Comparison of the proposed method with simple filtering methodThe proposed methodConventional method
Focused plane
Defocused plane
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Simple filtering
II. Adaptive holographic synthesis with phase-shifting interferometry
2.2 Optical implementation of iterative fractional Fourier transform algorithm
iterative fractional Fourier transform algorithm
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Soft constraint
Amplitude and phase freedoms
Hard constraint
Functional relationship between phase and
amplitude modulations( ) ( )expn n nW A j= Φ Φ
Input plane
Diffraction imagePhase hologram
Forward Fresneltransform
Inverse Fresneltransform
Output plane
IFTA
Input plane Output plane
ath order FRFT
(2-a)th orderFRFT
FRFT = fractional Fourier transform
FL: Fourier lens with a focal length f
FL FLf f f f
order FRFTtha ( )2 order FRFTtha−( )1 1,G x y ( )2 2,P x y ( )3 3,F x y
FL: Fourier lens with a focal length f
FL FLf f f f
order FRFTtha ( )2 order FRFTtha−( )1 1,G x y ( )2 2,P x y ( )3 3,F x y
( )2 21 1exp
x yj
Rπ
λ
⎛ ⎞+⎜ ⎟⎜ ⎟⎝ ⎠
Diverging spherical wave
FL: Fourier lens with a focal length f
FL FLf f f f
order FRFTtha ( )2 order FRFTtha−( )1 1,G x y ( )2 2,P x y ( )3 3,F x y
FL: Fourier lens with a focal length f
FL FLf f f f
order FRFTtha ( )2 order FRFTtha−( )1 1,G x y ( )2 2,P x y ( )3 3,F x y
( )2 21 1exp
x yj
Rπ
λ
⎛ ⎞+⎜ ⎟⎜ ⎟⎝ ⎠
Diverging spherical wave
II. Adaptive holographic synthesis with phase-shifting interferometry
2.2 Optical implementation of iterative fractional Fourier transform algorithm
Optical implementation of the ath order and its complementary (2-a)th order two-dimensional FRFT
( ) ( ) ( )1 2 2 1 1 2a a a a a aF F f F F f F f+= =⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
Associative and the communicative properties
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.2 Optical implementation of iterative fractional Fourier transform algorithm
Optical implementation of the iterative FRFT algorithm
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Laser
Beam expander
Beam splitters
Beam splitter
Beam splitters
Negative lens
Mechanical shutters
Polarizers
TNLC
Patterned maskMirrors
FT lens
CCD
Patterned mask
4f zoom system
Positive lens
PZT
Laser
Beam expander
Beam splitters
Beam splitter
Beam splitters
Negative lens
Mechanical shutters
Polarizers
TNLC
Patterned maskMirrors
FT lens
CCD
Patterned mask
4f zoom system
Positive lens
PZT
f
J. Hahn, H. Kim, and B. Lee, Opt. Express 14, pp. 11103-11112 (2006).
II. Adaptive holographic synthesis with phase-shifting interferometry
2.2 Optical implementation of iterative fractional Fourier transform algorithm
Schematics of the optical iterative FRFT system
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BS: Beam splitterM: MirrorP: PolarizerBE: Beam expanderFL: Fourier lens with a focal length f
PL: Positive lensNL: Negative lensTNLC: Twisted nematic liquid crystalS: Mechanical shutterAtt.: Optical attenuatorPM: Patterned mask
Measurement part: phase shifting digital holography
4f-system for matching scaling factors
1st beam path
2nd beam path
Drive the piezo stage
Detect the phase profiles
Control the shutters
Encode the phase profiles
Laser
S
SBSBEf f
PM P
M
M
M
BS
BS
BS
FL
SLM
P PTNLC
Piezostage
Att.Att. BS
CCD
PLNL
f1 f1 f2 f2
4-f system
BS: Beam splitterM: MirrorP: PolarizerBE: Beam expanderFL: Fourier lens with a focal length f
PL: Positive lensNL: Negative lensTNLC: Twisted nematic liquid crystalS: Mechanical shutterAtt.: Optical attenuatorPM: Patterned mask
Measurement part: phase shifting digital holography
4f-system for matching scaling factors
1st beam path
2nd beam path
Drive the piezo stage
Detect the phase profiles
Control the shutters
Encode the phase profiles
Laser
S
SBSBEf f
PM P
M
M
M
BS
BS
BS
FL
SLM
P PTNLC
Piezostage
Att.Att. BS
CCD
PLNL
f1 f1 f2 f2
4-f systemf
f
II. Adaptive holographic synthesis with phase-shifting interferometry
d2-f=180㎜d2-f=90㎜
d2-f=45㎜d2-f=0㎜
Multiplexing four DOE phase profiles and their diffraction images
2.2 Optical implementation of iterative feedback loop
Patterned masks
Applied spherical phase profiles
R = ∞ 485R mm= 247R mm= 121R mm=
Diffraction images of the multiplexed DOE captured by a CCD
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
Schematics of the system
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J. Hahn, H. Kim, K. Choi, and B. Lee, Appl. Opt. 45, pp. 915-924 (2006).
Laser
Beam expander
Polarizers
TNLC
FT lens
CCD
Genetic feedback loop
Capturingdiffractionimages
Encoding phaseholograms
II. Adaptive holographic synthesis with phase-shifting interferometry
DOE phaseprofile
A. Diffraction image
B. Targetimage
Difference image between A and B
Phase modulationcurve
Coefficients of Zernike polynomial
Cost valueof the elite
Zernike polynomials
DOE phaseprofile
A. Diffraction image
B. Targetimage
Difference image between A and B
Phase modulationcurve
Coefficients of Zernike polynomial
Cost valueof the elite
Zernike polynomials
Program panel
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
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Phase profilein hologram
Encoding index Encoding index
II. Adaptive holographic synthesis with phase-shifting interferometry
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
Optimization of encoding index in SLM
SLM: SONY LCX016AL-6 (32um pixel pitch)
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0
50
100
150
200
250
0 0.5 1 1.5 2
1st43rd299th
II. Adaptive holographic synthesis with phase-shifting interferometry
Experimental results for optimized encoding index
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
Diffraction image by the SLM with the optimized encoding index
Diffraction image by the SLM with the linear encoding index
Designed phase modulation( π unit rad. )
Enco
ding
inde
x
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10o 10o
Distorted diffraction Image in the tilted optics
Diffraction image obtained in the aligned optics
II. Adaptive holographic synthesis with phase-shifting interferometry
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
Experiments for compensation of aberration
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
Experimental results for compensation of aberration
Target diffraction image Evolution of the diffraction image Resultant Zernike phase profile
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II. Adaptive holographic synthesis with phase-shifting interferometry
2.3 Adaptive beam-shaping with a genetic feedback tuning loop
Experimental results for compensation of aberration
Diffraction image with aberration Compensated diffraction image
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III. Holographic synthesis and measurement in micrometer scale
3.1 Micro field synthesis
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Synthesis of optical fieldwithout adaptive feedback
Measurement of optical fieldbased on phase-shifting interferometry
Synthesis of optical fieldwith adaptive feedback
Synthesis of micro optical fieldby demagnification optics
Measurement of optical fieldbased on holographic microscopy
Digital holographic technologies
Holographic synthesis Holographic measurement
Synthesis of micro optical fieldby demagnification optics
Measurement of optical fieldbased on holographic microscopy
3.2 Holographic angular spectrum analyzer
Demagnification of optical field without speckle noise
f f
: pixel pitchN: pixel numberp : Nyquist width
: resolutionNW
δ
SLM Optical fieldFT lens
f
: pixel pitchN: pixel numberp
Blurred imagewith the same resolution
SLM Optical field4f system
f f f
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Fourier optics 4f optics
III. Holographic synthesis and measurement in micrometer scale
3.1 Micro field synthesis by demagnification
polarizers
waveplates
TNLCwith double slits
telecentric lens
CCD
convex lens
Collimated light source
Demagnification of optical field by SLM in with telecentric lens
Specifications of systemTelecentric lens: Edmund gold series 0.09xSLM: Epson device L3P06X (12um pixel pitch)CCD: KODAK MegaPlus ES1.0/MV (9um pixel pitch)Laser: Coherent Verdi V-5 (Nd:YAG 532nm)
III. Holographic synthesis and measurement in micrometer scale
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3.1 Micro field synthesis by demagnification
J. Hahn, Y. Lim, H. Kim, and B. Lee, J. of Holography and Speckle (accepted for publication) (Invited paper).
Holographic measurement for micro optical field
Specifications of systemTelecentric lens: Edmund gold series 0.09xSLM: Epson device L3P06X (12um pixel pitch)CCD: KODAK MegaPlus ES1.0/MV (9um pixel pitch)Laser: Coherent Verdi V-5 (Nd:YAG 532nm)Objective: LMPlanFLN-BD 10x N.A. 0.25PZT: Piezo system Jena XYZ-38
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x10
BS
PZT
CC
D
Lase
r
BSBS
Mirror MirrorND filter Polarizer
Half waveplate
Microscopy
Expander
Telecentriclens
SLM
Negative lens
ExpanderShutter
Ref
eren
ce a
rm
Sign
al a
rm
x10
BS
PZT
CC
D
Lase
r
BSBS
Mirror MirrorND filter Polarizer
Half waveplate
Microscopy
Expander
Telecentriclens
SLM
Negative lens
ExpanderShutter
Ref
eren
ce a
rm
Sign
al a
rmMicroscope
Shutter
III. Holographic synthesis and measurement in micrometer scale
3.1 Micro field synthesis by demagnification
Holographic measurement of micro optical field with SLM
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Reference arm
Signal arm
Microscopy
SLM
Expander
ExpanderPZT
Telecentriclens
Negativelens
CCD
Polarizer
III. Holographic synthesis and measurement in micrometer scale
3.1 Micro field synthesis by demagnification
Micro optical field with SLM in the amplitude modulation condition
Focused signal wave Defocused signal wave
Phase profile of defocused signal wave
Numerically reconstructed wave
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104 mµ
7.5 mµ
III. Holographic synthesis and measurement in micrometer scale
3.1 Micro field synthesis by demagnification
Micro optical field with SLM in the phase modulation condition
Phase profile of signal wave Numerically reconstructed wave at 6.89mm
Spherical lens with focal length 6.78mm
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III. Holographic synthesis and measurement in micrometer scale
3.1 Micro field synthesis by demagnification
Holographic microscopy for analyzing angular spectrum
High N.A.objective
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3.2 Holographic angular spectrum analyzer
III. Holographic synthesis and measurement in micrometer scale
BS
PZT
CC
D
BSBS
Mirror MirrorND filter
Microscope
Micro structure
Expander
Shutter
Ref
eren
ce a
rm
Sign
al a
rm
Expander
x100
Laser
Pinhole
Focal plane
Specifications of systemCCD: SONY XCD-SX90 (3.75um pixel pitch)Laser: Coherent Verdi V-5 (Nd:YAG 532nm)Pinhole: Newport 5um apertureObjective: MPlanFLN-BDP 100x N.A. 0.9PZT: Piezo system Jena XYZ-38
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III. Holographic synthesis and measurement in micrometer scale
Holographic microscopy for analyzing angular spectrum
3.2 Holographic angular spectrum analyzer
Transmission characteristics of objectives
Products Magnification N.A. W.D. ( mm ) Resolution ( mµ )
MPLAN FLN-BDP 100x 0.9 1.0 0.37
LMPLAN FLN-BD 100x 0.8 3.3 0.42
LMPLAN FLN-BD 50x 0.5 10.6 0.67
200 400 600 800 1000 1200
0
100
200
300
400
500
600
700
800
9000.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
52 degree
200 400 600 800 1000 1200
0
100
200
300
400
500
600
700
800
9000.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
52 degree52 degreeMPLAN FLN-BDP 100x LMPLAN FLN-BD 100x LMPLAN FLN-BD 50x
MPLAN FLN-BDP 100x LMPLAN FLN-BD 100x LMPLAN FLN-BD 50x
Incident angle
Tran
smitt
ance
Tran
smitt
ance
(a.u
.)
Incident angle (degree)
III. Holographic synthesis and measurement in micrometer scale
3.2 Holographic angular spectrum analyzer
Transmission profile of objective (MPLAN FLN-BDP 100x) for compensation
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Holographic measurement of angular spectrum
Interferogram Phase profile
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III. Holographic synthesis and measurement in micrometer scale
3.2 Holographic angular spectrum analyzer
SEM images of pyramidal shape structureBottom side =Height =
47.5 mµ3.4 mµ
Fresnel domain filter at stop plane
Object plane
Stop plane
Hologram plane
Objectivelens Imaging
optics
Microscope
At this position, Fresnel domain filter is located
CCDBS
Pinhole
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III. Holographic synthesis and measurement in micrometer scale
3.2 Holographic angular spectrum analyzer
Before filtering After filtering
Undesirable diffraction from the optical stop
Perspective views with local angular spectrums
Original view Top view
Bottom viewLeft view
Right view
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III. Holographic synthesis and measurement in micrometer scale
3.2 Holographic angular spectrum analyzer
Optimization of SLM
Holographicstereogram
Adaptive optical systems
Micro field synthesis
Optical IFRFTA
Adaptive beam shaping
Holographic synthesis
Phase-shifting interferometry
Holographic microscopy
Angular spectrum analyzer
Holographic measurement
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Technical relation of my researches in digital holography
Summary
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Work in progress
Phase-shifting interferometry with three CCDs
CCD
BS
Mirror
Object wave
Reference wave
CCD
BS
Mirror
Object wave
Reference wave
Reconstructed image from the experiments under longitudinal vibrations
Reconstructed image from the experiments under transversal vibrations
The effects of longitudinal and transversal displacement in interferograms
J. Hahn, H. Kim, E.-H. Kim, J. Park, and B. Lee, Proc. SPIE, 7056, pp. 7056-66, 2008.