holographic measurement and synthesis of optical field using a spatial light modulator

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

1/56

Introduction

Motivation of adaptive holographic technology

Real optical space

Designing hologram

Synthesizing technology

Measuringtechnology

Adaptive feedback

2/56

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.








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


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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

5/56

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


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


Configuration of SLM with TNLC

6/56

Polarization-state generator

Polarization-state detector

J. Hahn, H. Kim, and B. Lee, Appl. Opt. 47, pp. D87-D95 (2008).

TNLC cell


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

⎡ ⎤+ +⎢ ⎥− =⎢ ⎥− +⎢ ⎥⎣ ⎦


Lu and Saleh model Coy model

7/56


Optimization of SLM with genetic optimization algorithm


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



Schematics of optimization system

2 50πPrecision of measuring the phase modulation :

9/56


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



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



:E l i t e x

Yes

No

1k k= +

0k =

Motor Driving

Select the fittest

LabviewTM Matlab®

Mutation

k kP P ′= >



, |

0 , , 1, , ,i j j

k

x x x xP

i h j h m

′= =⎧ ⎫= ⎨ ⎬

= − =⎩ ⎭



, |

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



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≥


10/56

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.



11/56

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



Angular spectrum of object wave and their recording positions

Conventional planar hologram Curved-shaped holographic stereogram

12/56

The concave-shaped CGH designed by Benton (1966)



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

13/56



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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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 = + − −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

15/56

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).



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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



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

17/56

Embodiment of effectively reformed SLM

Alignment of some reformed SLMsStructure of effectively reformed SLM



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

18/56



Pictures of the dynamic holographic stereogram

Curved array of SLMs mounted without upper arms Whole system with electronic controllers

19/56



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

20/56

36th view1st view 19th view

This result is honored to be chosen as ‘Image of the week’ , August 4th in OpticsInfoBase.










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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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

22/56



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

23/56

J. Hahn, H. Kim, S.-W. Cho, and B. Lee, Appl. Opt. 47, pp.4068-4076 (2008).

îα

ˆ jα

îα

ˆ jα

ˆ jα−

Re

Im

îα 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

24/56



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



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

25/56

{ } { } { } { } { } { }{ }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



Experimental results with the genetic algorithm

After the genetic algorithmBefore the genetic algorithm

26/56


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


27/56



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

28/56

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



Comparison of the proposed method with simple filtering methodThe proposed methodConventional method

Focused plane

Defocused plane

29/56

Simple filtering



iterative fractional Fourier transform algorithm

30/56

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 FLf f f f


( )2 21 1exp

x yj

Rπ

λ

⎛ ⎞+⎜ ⎟⎜ ⎟⎝ ⎠

Diverging spherical wave


FL FLf f f f



FL FLf f f f


( )2 21 1exp

x yj

Rπ

λ

⎛ ⎞+⎜ ⎟⎜ ⎟⎝ ⎠

Diverging spherical wave



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

31/56



Optical implementation of the iterative FRFT algorithm

32/56

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).



Schematics of the optical iterative FRFT system

33/56

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


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

34/56



Schematics of the system

35/56

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


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


36/56

Phase profilein hologram

Encoding index Encoding index



Optimization of encoding index in SLM

SLM: SONY LCX016AL-6 (32um pixel pitch)

37/56

0

50

100

150

200

250

0 0.5 1 1.5 2

1st43rd299th


Experimental results for optimized encoding index


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

38/56

10o 10o

Distorted diffraction Image in the tilted optics

Diffraction image obtained in the aligned optics



Experiments for compensation of aberration

39/56



Experimental results for compensation of aberration

Target diffraction image Evolution of the diffraction image Resultant Zernike phase profile

40/56



Experimental results for compensation of aberration

Diffraction image with aberration Compensated diffraction image

41/56

III. Holographic synthesis and measurement in micrometer scale

3.1 Micro field synthesis

42/56










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

43/56

Fourier optics 4f optics


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)


44/56


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

45/56

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



Holographic measurement of micro optical field with SLM

46/56

Reference arm

Signal arm

Microscopy

SLM

Expander

ExpanderPZT

Telecentriclens

Negativelens

CCD

Polarizer



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

47/56

104 mµ

7.5 mµ



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

48/56



Holographic microscopy for analyzing angular spectrum

High N.A.objective

49/56



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

50/56


Holographic microscopy for analyzing angular spectrum


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)



Transmission profile of objective (MPLAN FLN-BDP 100x) for compensation

51/56

Holographic measurement of angular spectrum

Interferogram Phase profile

52/56



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

53/56



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

54/56



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

55/56

Technical relation of my researches in digital holography

Summary

56/56

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.

holographic measurement and synthesis of optical field using a spatial light modulator

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