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

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1 Holographic measurement and synthesis of optical field using a spatial light modulator Joonku Hahn NCRCAPAS School of Electrical Engineering Seoul National University

2 Introduction Overview of digital holography Synthesis with spatial light modulator Measurement by phase-shift interferometry Real optical space where optical fields propagate 1/56

3 Introduction Motivation of adaptive holographic technology Designing hologram Synthesizing technology Real optical space Adaptive feedback Measuring technology 2/56

4 Contents Digital holographic technologies Holographic synthesis Holographic measurement I. Synthesis of optical field without adaptive feedback II. Synthesis of optical field with adaptive feedback Measurement of optical field based on phase-shifting interferometry III. Synthesis of micro optical field by demagnification optics Measurement of optical field based on holographic microscopy 3/56

5 I. Spatial light modulator with twisted nematic liquid crystal Holographic synthesis Digital holographic technologies Holographic measurement 1.1 Optimization of twisted nematic liquid crystal SLM Synthesis of optical field without adaptive feedback Synthesis of optical field with adaptive feedback Measurement of optical field based on phase-shifting interferometry 1.2 Wide viewing angle dynamic holographic stereogram Synthesis of micro optical field by demagnification optics Measurement of optical field based on holographic microscopy 4/56

6 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Ideal amplitude only modulation Im i Ideal phase only modulation Im i Re -1 1 Re i -i TNLC Cell Tilt angle Typical TNLC modulation with two polarizers. Im i Input Twist angle Input side Output side Output Re i 5/56

7 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Configuration of SLM with TNLC transmission axis Polarizer Wave plate Polarization-state generator director axis TN-LC TNLC Cell cell fast axis Wave plate Polarization-state detector tilt angle Polarizer twist angle y x z fast axis transmission axis θ θ θ θ P1 P2 W1 W 2 : rotation angle of input polarizer : rotation angle of output polarizer : rotation angle of input wave plate : rotation angle of output wave plate J. Hahn, H. Kim, and B. Lee, Appl. Opt. 47, pp. D87-D95 (2008). 6/56

8 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Eigenstates of twisted nematic liquid crystal Lu and Saleh model Coy model E ( ) i 2 12 α ( 2γ + 2βγ) 2 ( β + γ) ( 2γ + 2βγ) λ + = 12 E λ = ( ) 2 ( β + γ) ( 2γ + 2βγ) 2 12 iα ( 2γ + 2βγ) 12 7/56

9 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Optimization of SLM with genetic optimization algorithm Polarization-state generator Polarization-state detector Polarizer λ 4 waveplate λ 4 waveplate Polarizer Positive lens CCD λ 4plate OPD TNLC TNLC SLM cell Beam splitter Expander Laser Motorized rotation stages Specifications of system SLM: SONY LCX016AL-6 (32um pixel pitch) CCD: KODAK MegaPlus ES1.0/MV (9um pixel pitch) Laser: Coherent Verdi V-5 (Nd:YAG 532nm) 8/56

10 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Schematics of optimization system Precision of measuring the phase modulation : 2π 50 9/56

11 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Genetic optimization algorithm Labview TM Matlab Start Motor control Phase modulation measurement Amplitude modulation measurement Motor control Phase modulation measurement Amplitude modulation measurement k k max No Create the initial population P 0 = { x i i = 0,1,, m } k = 0 Motor Driving P = { x i = 0,1,, m } P => P k k { 1 } = P k x i f i f i + sorting x i = x, x j = x j P k = Yes i = 0,, h 1, j = h,, m E lite : x k = k + 1 k i Select the fittest elite : x F ( x ) = max F ( P k ) Mutation Motor Driving P = { x i = 0,1,, m } k i Select the fittest ( ˆ ) = max ( k ) F x F P Select the new fittest N ew elite : x F ( x ) = max F ( x ), F ( x ˆ ) Reorganization of the population Genetic algorithm is programmed by Labview TM and Matlab. Main part of genetic algorithm is programmed in Matlab program. Four motorized rotation stages are controlled by Labview TM. 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 Labview TM. 10/56

12 I. Spatial light modulator with twisted nematic liquid crystal 1.1 Optimization of twisted nematic liquid crystal SLM Phase and amplitude modulations during evolutions Experimental results before and after genetic optimization Twin image Before the genetic optimization After the genetic optimization 11/56

13 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 The concave-shaped CGH designed by Benton (1966) Transfer lens Viewing windows Transfer lenses φ U φ U û Object ẑ Focal length Hologram Conventional planar hologram Hologram Focal length Object û Curved-shaped holographic stereogram ẑ 12/56

14 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 p a p p a p Pixels of SLM η ξ v u Spherical phase resulting from d Amplitude contour by sinc function +1 order diffraction on v-axis ( α, β ) c c f Central direction of local viewing angle d f Transfer lens Focal plane Constraint relation in the area and local viewing angles 2 WW u vθθ u v λ N M. 0 order diffraction θ v -1 order diffraction on v-axis θ u Local viewing angle 13/56

15 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 SLM η Backward vertical summit ξ λ f 2 ( ) 2 Mp + f d λ v Viewing volume λ f 2 ( ) 2 Mp f d u λ Frontward vertical summit SLM plane d Transfer lens f Focal plane Backward horizontal summit Total viewing angles in field of view 1 2tan Np λ d Θu 1 2f 2p f 2 λ f + ( ) 2 Np f d 14/56 λ λ f 2 Θu Θv Total viewing angle ( ) λ Frontward horizontal summit 2 Np f d

16 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 û ẑ n SLMs Local viewing angle by an individual SLM θ u Total viewing angle by a curved array of SLMs Θ u Total backward horizontal summit Transfer optics conflict with each other. Total forward horizontal summit Total viewing angles by a curved array of SLMs ( 1) 1 n Np Np λ d Θ u = + 2tan 1. f 2f 2p f J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, Opt. Express 16, pp (2008). 15/56

directions Central directions Transfer lens Transfer lens Focal plane Mirrors Focal plane Local viewing angles Local

17 I. Spatial light modulator with twisted nematic liquid crystal 1.2 Wide viewing angle dynamic holographic stereogram Equivalent fields of view Sub-SLMs Sub-SLMs Mirrors Central directions Central directions Transfer lens Transfer lens Focal plane Mirrors Focal plane Local viewing angles Local viewing angles Field of view by three sub-slms positioned at different vertical heights in contact with each other diagonally Field of view by effectively reformed SLM 16/56

18 I. Spatial light modulator with twisted nematic liquid crystal 1.2 Wide viewing angle dynamic holographic stereogram Embodiment of effectively reformed SLM Mirrors Upper arm SLM Polarizer TNLC Polarizer Transfer Lens lens Mirrors Lower arm Structure of effectively reformed SLM Alignment of some reformed SLMs 17/56

19 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 Curved array of SLMs Asymmetric diffusing screen Front lens Folding optics 4f optics Light source Rear lens array 18/56

the dynamic holographic stereogram Curved array of SLMs mounted

20 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 19/56

2 Wide viewing angle dynamic holographic stereogram Computer

50 50 50 100 100 100 150 150 150 200 200 200 250 250 250 200

Pictures of the implemented dynamic holographic stereogram

21 I. Spatial light modulator with twisted nematic liquid crystal 1.2 Wide viewing angle dynamic holographic stereogram Computer generated holograms and respective numerical reconstructions Pictures of the implemented dynamic holographic stereogram 1st view 19th view 36 th view This result is honored to be chosen as Image of the week, August 4th in OpticsInfoBase. 20/56

22 II. Adaptive holographic synthesis with phase-shifting interferometry Holographic synthesis Synthesis of optical field without adaptive feedback Digital holographic technologies Holographic measurement 2.1 Phase-shifting interferometry with unknown phase-shifts 2.2 Optical implementation of iterative fractional Fourier transform algorithm Synthesis of optical field with adaptive feedback Synthesis of micro optical field by demagnification optics Measurement of optical field based on phase-shifting interferometry Measurement of optical field based on holographic microscopy 2.3 Adaptive beam-shaping with a genetic feedback tuning loop 21/56

23 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 Variable beamsplitter Mirror Mirror Object wave Diverging lens Fourier lens Beam expander Cube beamsplitter CCD Reference wave Piezo driven mirror Object 22/56

24 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 Object and reference waves U = A exp( jϕ ) O O U = A exp( jα ) R R i i ith step interferogram 2 2 I = A + A + 2A A ˆ ϕ ˆ α i O R O R i Conventional 4-step phase-shifting interferometry ( ) *( ) U = I I A + j I I A O 1 3 R 4 2 R Base of phase-shifting interferometry U = a I O i 1 i1 i1 ( ) 2A ˆ ( ˆ ˆ Oϕ αi α j) I I I A ij i j R = General phase-shifting interferometry equation ˆ α j Im αˆ j αˆi αˆ j ˆi α ˆi α Re ˆ j α 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 J. Hahn, H. Kim, S.-W. Cho, and B. Lee, Appl. Opt. 47, pp (2008). 23/56

25 II. Adaptive holographic synthesis with phase-shifting interferometry 2.1 Phase-shifting interferometry with unknown phase-shifts Original object and twin image in hologram with Fourier optics Frontward focal plane ŷ ˆx Fourier transform lens with focal length f Original object Backward focal plane (Hologram plane) UO ( x, y; z 0 ) UO ( x, y;2f U ( x, y;2f ) ) twin Centro-symmetry ẑ Twin image U x y z twin (, ; 0 ) z = z 0 z = 0 z = z 0 z = f z = 2 f The degree of twin image noise can be evaluated by the evenness of reconstructed image on focal plane. Reconstructed images using only one base of phase-shifting interferometry 24/56

26 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 Chromosome Coefficients of baes in phase-shifting interferometry equation { Re { 21},Im{ 21},Re{ 31},Im{ 31},,Re{ 1},Im{ 1} } x = a a a a a a i N N Degree of twin image noise cost function = Cost function n m= 0, ± 2, ± 4 ± n n m=± 1, ± 3 ± n U U m n m n Genetic algorithm Create an initial population P0 = { xi i= 1, 2,, p} where x i = { 0, 1, 1,0,0,1} Evaluate the fitness function fmax = max cost ( xi ); i = 1, 2,, p 1 fave = cost ( xi ) m p fmax fave δ Sort the population P k = { x i fi fj} Exclude the poorest Pk = { x 1, x i + 1 i= 1,2,, p 1} Crossover { x i+ 1 i = 1, 2,, p 1} { yi+ 1 i = 1, 2,, p 1} Update the population Pk = { x 1, yi+ 1 i= 1,2,, p 1} k = k+ 1 Determine the elite cost ( x) = max cost ( xi ); i = 1, 2,, p Mutation Pk P k Determine new elite cost ( x ) = max cost ( x),cost ( x i ); i= 1,2,, p Sort the population P k = { x i fi f j} Protect the fittest Pk = { x, x i+ 1 i= 1,2,, p 1} k < k max Elite x m Where U n are modified real Zernike polynomials 25/56

27 II. Adaptive holographic synthesis with phase-shifting interferometry 2.1 Phase-shifting interferometry with unknown phase-shifts Experimental results with the genetic algorithm Before the genetic algorithm After the genetic algorithm 26/56

28 II. Adaptive holographic synthesis with phase-shifting interferometry 2.1 Phase-shifting interferometry with unknown phase-shifts Evolutions in the genetic algorithm Coefficients of phase-shift bases Genrations Fittest chromosome α 1r α 1i α 2r α 2i α 3r α 3i Ratios of evenness and oddness symmetric symmetric evenness coeffs. c antisymmetric antsymmetri oddness coeffs Genrations Resultant evenness and oddness in reconstructed images 27/56

29 II. Adaptive holographic synthesis with phase-shifting interferometry 2.1 Phase-shifting interferometry with unknown phase-shifts Resultant relationship among phase-shift bases I I 1 Im I1( α 1 = 2.79) I4( α 4 = 0.52) I3( α 3 = 0.47) Re I Optimized coefficients of the bases in phase-shifting interferometry. I I2( α 2 = 1.89) Resultant phase-shifts of interferograms 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 28/56

30 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 method Conventional method Simple filtering The proposed method Focused plane Defocused plane 29/56

31 II. Adaptive holographic synthesis with phase-shifting interferometry 2.2 Optical implementation of iterative fractional Fourier transform algorithm iterative fractional Fourier transform algorithm Input plane Phase hologram Output plane Diffraction image Input plane Hard constraint Functional relationship between phase and amplitude modulations W = A Φ exp jφ ( ) ( ) n n n a th order Forward Fresnel FRFT transform IFTA (2-a) th order FRFT Inverse Fresnel transform Output plane Soft constraint Amplitude and phase freedoms FRFT = fractional Fourier transform 30/56

32 II. Adaptive holographic synthesis with phase-shifting interferometry 2.2 Optical implementation of iterative fractional Fourier transform algorithm Optical implementation of the a th order and its complementary (2-a) th order two-dimensional FRFT Diverging spherical wave ( x y ) 1 exp j π λ R G ( x, y ) P ( x y ) ( 3, y 3 ) 1 1 2, F x 2 th th a order FRFT ( 2 a) order FRFT f FL f f FL f Associative and the communicative properties ( ) = ( ) = ( ) Fa 1 Fa2 f Fa2 Fa 1 f Fa 1+ a2 f FL: Fourier lens with a focal length f 31/56

33 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 PZT Beam splitters CCD Mirrors Mechanical shutters Patterned mask Positive lens Beam splitters Laser Beam expander Negative lens Beam splitter FT lens 4f f zoom system Polarizers TNLC Patterned mask J. Hahn, H. Kim, and B. Lee, Opt. Express 14, pp (2006). 32/56

34 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 Measurement part: phase shifting digital holography M BS S Att. Att. PL M NL P TNLC P 4f-system f for matching scaling factors FL 4-f f system BS M Piezo stage Laser CCD BE 1 st beam path BS S PM BS SLM f 1 f 1 f 2 f 2 f f BS P 2 nd beam path Encode the phase profiles Detect the phase profiles BS: Beam splitter M: Mirror P: Polarizer BE: Beam expander FL: Fourier lens with a focal length f Control the shutters PL: Positive lens NL: Negative lens TNLC: Twisted nematic liquid crystal S: Mechanical shutter Att.: Optical attenuator PM: Patterned mask Drive the piezo stage 33/56

$Multiplexing four DOE phase profiles and their diffraction$ images Patterned masks d 2 -f=0 mm d2-f=45 mm Applied spherical

35 II. Adaptive holographic synthesis with phase-shifting interferometry 2.2 Optical implementation of iterative feedback loop Multiplexing four DOE phase profiles and their diffraction images Patterned masks d 2 -f=0 mm d2-f=45 mm Applied spherical phase profiles R = R = 485mm R = 247mm R = 121mm d2-f=90 mm d2-f=180 mm Diffraction images of the multiplexed DOE captured by a CCD 34/56

$3 Adaptive beam-shaping with a genetic feedback tuning loop Schematics of the system Genetic feedback loop Capturing diffraction images Encoding phase holograms CCD Laser FT lens$

36 II. Adaptive holographic synthesis with phase-shifting interferometry 2.3 Adaptive beam-shaping with a genetic feedback tuning loop Schematics of the system Genetic feedback loop Capturing diffraction images Encoding phase holograms CCD Laser FT lens Polarizers TNLC Beam expander J. Hahn, H. Kim, K. Choi, and B. Lee, Appl. Opt. 45, pp (2006). 35/56

37 II. Adaptive holographic synthesis with phase-shifting interferometry 2.3 Adaptive beam-shaping with a genetic feedback tuning loop Program panel DOE Phase phase profile profile in hologram Zernike polynomials Cost value of the elite A. Diffraction image Phase modulation curve B. Target image Coefficients of Zernike polynomial Difference image between A and B 36/56

38 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 Encoding index Encoding index SLM: SONY LCX016AL-6 (32um pixel pitch) 37/56

39 II. Adaptive holographic synthesis with phase-shifting interferometry 2.3 Adaptive beam-shaping with a genetic feedback tuning loop Experimental results for optimized encoding index Encoding index st 43rd 299th Designed phase modulation ( π unit rad. ) Diffraction image by the SLM with the linear encoding index Diffraction image by the SLM with the optimized encoding index 38/56

$for compensation of aberration 10 o 10 o Diffraction image obtained in$

40 II. Adaptive holographic synthesis with phase-shifting interferometry 2.3 Adaptive beam-shaping with a genetic feedback tuning loop Experiments for compensation of aberration 10 o 10 o Diffraction image obtained in the aligned optics Distorted diffraction Image in the tilted optics 39/56

$3 Adaptive beam-shaping with a genetic feedback tuning loop Experimental results for compensation of aberration Target diffraction image$

41 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 40/56

$Experimental results for compensation of aberration Diffraction$

42 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 41/56

43 III. Holographic synthesis and measurement in micrometer scale Digital holographic technologies 3.1 Micro field synthesis Holographic synthesis Holographic measurement Synthesis of optical field without adaptive feedback 3.2 Holographic angular spectrum analyzer Synthesis of optical field with adaptive feedback Measurement of optical field based on phase-shifting interferometry Synthesis of micro optical field by demagnification optics Measurement of optical field based on holographic microscopy 42/56

44 III. Holographic synthesis and measurement in micrometer scale 3.1 Micro field synthesis by demagnification Demagnification of optical field without speckle noise Fourier optics 4f optics SLM FT lens Optical field SLM 4f system Optical field Blurred image p : pixel pitch N: pixel number f f W N : Nyquist width δ : resolution p : pixel pitch N: pixel number f f f f with the same resolution 43/56

45 III. Holographic synthesis and measurement in micrometer scale 3.1 Micro field synthesis by demagnification Demagnification of optical field by SLM in with telecentric lens TNLC with double slits convex lens CCD telecentric lens Collimated light source polarizers waveplates Specifications of system Telecentric lens: Edmund gold series 0.09x SLM: Epson device L3P06X (12um pixel pitch) CCD: KODAK MegaPlus ES1.0/MV (9um pixel pitch) Laser: Coherent Verdi V-5 (Nd:YAG 532nm) J. Hahn, Y. Lim, H. Kim, and B. Lee, J. of Holography and Speckle (accepted for publication) (Invited paper). 44/56

46 III. Holographic synthesis and measurement in micrometer scale 3.1 Micro field synthesis by demagnification Holographic measurement for micro optical field PZT BS Reference arm Negative lens Microscope Microscopy Telecentric lens SLM CCD BS x10 Signal arm Laser Half waveplate Specifications of system Telecentric lens: Edmund gold series 0.09x SLM: 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 PZT: Piezo system Jena XYZ-38 Expander BS Mirror Expander ND filter Shutter Polarizer Mirror 45/56

47 III. Holographic synthesis and measurement in micrometer scale 3.1 Micro field synthesis by demagnification Holographic measurement of micro optical field with SLM Negative lens CCD Microscopy PZT Telecentric lens Signal arm Expander Reference arm SLM Polarizer Expander 46/56

the amplitude modulation condition 104µ m 7.

48 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 104µ m 7.5µ m Focused signal wave Defocused signal wave Phase profile of defocused signal wave Numerically reconstructed wave 47/56

in the phase modulation condition Spherical lens with focal length 6.

49 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 Spherical lens with focal length 6.78mm Phase profile of signal wave Numerically reconstructed wave at 6.89mm 48/56

50 III. Holographic synthesis and measurement in micrometer scale 3.2 Holographic angular spectrum analyzer Holographic microscopy for analyzing angular spectrum High N.A. objective 49/56

51 III. Holographic synthesis and measurement in micrometer scale 3.2 Holographic angular spectrum analyzer Holographic microscopy for analyzing angular spectrum PZT CCD Pinhole Focal plane BS BS Expander Laser Reference arm Microscope Micro structure x100 Signal arm Shutter BS Specifications of system CCD: SONY XCD-SX90 (3.75um pixel pitch) Laser: Coherent Verdi V-5 (Nd:YAG 532nm) Pinhole: Newport 5um aperture Objective: MPlanFLN-BDP 100x N.A. 0.9 PZT: Piezo system Jena XYZ-38 Mirror Expander ND filter Mirror 50/56

52 III. Holographic synthesis and measurement in micrometer scale 3.2 Holographic angular spectrum analyzer Transmission characteristics of objectives MPLAN FLN-BDP 100x LMPLAN FLN-BD 100x LMPLAN FLN-BD 50x degree Transmittance (a.u.) Transmission profile of objective (MPLAN FLN-BDP 100x) for compensation Incident Incident angle (degree) angle Products Magnification N.A. W.D. ( mm ) Resolution ( µ m ) MPLAN FLN-BDP 100x LMPLAN FLN-BD 100x LMPLAN FLN-BD 50x /56

53 III. Holographic synthesis and measurement in micrometer scale 3.2 Holographic angular spectrum analyzer Holographic measurement of angular spectrum SEM images of pyramidal shape structure Bottom side = 47.5µ m Height = 3.4µ m Interferogram Phase profile 52/56

Hologram plane CCD Object plane Stop plane At this position,

54 III. Holographic synthesis and measurement in micrometer scale 3.2 Holographic angular spectrum analyzer Fresnel domain filter at stop plane Objective lens Microscope Imaging optics BS Hologram plane CCD Object plane Stop plane At this position, Fresnel domain filter is located Pinhole Undesirable diffraction from the optical stop Before filtering After filtering 53/56

55 III. Holographic synthesis and measurement in micrometer scale 3.2 Holographic angular spectrum analyzer Perspective views with local angular spectrums Original view Top view Right view Left view 54/56 Bottom view

56 Summary Technical relation of my researches in digital holography Holographic synthesis Optimization of SLM Holographic stereogram Micro field synthesis Adaptive optical systems Optical IFRFTA Holographic measurement Phase-shifting interferometry Holographic microscopy Adaptive beam shaping Angular spectrum analyzer 55/56

from the experiments under longitudinal vibrations Reconstructed image from the experiments under

57 Work in progress Phase-shifting interferometry with three CCDs CCD The effects of longitudinal and transversal displacement in interferograms Reference wave Object wave BS Mirror Reconstructed image from the experiments under longitudinal vibrations Reconstructed image from the experiments under transversal vibrations J. Hahn, H. Kim, E.-H. Kim, J. Park, and B. Lee, Proc. SPIE, 7056, pp , /56

Three-dimensional directional display and pickup

Three-dimensional directional display and pickup Joonku Hahn NCRCAPAS School of Electrical Engineering Seoul National University CONTENTS I. Introduction II. Three-dimensional directional display 2.1 Uniform