Reducing speckle artifacts in digital holography through...

S P E C I A L I S S U E

Reducing speckle artifacts in digital holography throughprogrammable filtration

Yongjun Lim1 | Jae-Hyeung Park2 | Joonku Hahn3 | Hayan Kim1 | Keehoon Hong1 |

Jinwoong Kim1

1Broadcasting and Media ResearchLaboratory Electronics andTelecommunications Research InstituteDaejeon Rep of Korea2Department of Information andCommunication Engineering InhaUniversity Incheon Rep of Korea3School of Electronics EngineeringKyungpook National University DaeguRep of Korea

CorrespondenceYongjun Lim Broadcasting and MediaResearch Laboratory Electronics andTelecommunications Research InstituteDaejeon Rep of KoreaEmail yongjunetrirekrandJae-Hyeung Park Department ofInformation and CommunicationEngineering Inha University IncheonRep of KoreaEmail jhparkinhaackr

Funding InformationThis research was supported byGigaKOREA project (GK18D0100Development of TelecommunicationsTerminal with Digital Holographic Table-top Display)

We propose a speckle reduction technique in electronic holographic display sys-

tems where digital micro‐mirror array devices are used as spatial light modula-

tors By adopting a programmable filtration in a general 4‐f optic configuration it

is shown that the signal spectrum components in the frequency domain of a view-

ing‐window‐based holographic display system can be selectively filtered Com-

pared to the widely utilized single‐sideband filtration techniques in electronic

holographic display systems our proposed programmable filtration can be utilized

to effectively reduce the speckles in the reconstruction of point‐cloud‐basedcomputer‐generated holograms Experimental results are presented to verify our

proposed concept

KEYWORD S

holographic display holography spatial filter speckle speckle reduction

1 | INTRODUCTION

Speckle is one of the most intrinsic properties of digitalholographic display systems exhibited when coherent lightsources such as lasers are applied in the play back processof computer‐generated holograms (CGHs) [1ndash3] Highlycorrelated wave fields of coherent light sources makeunwanted granular patterns that is speckle artifacts appearin general electronic holographic display systems which

degrade the image quality of the reconstructed hologramsTo reduce or remove speckle patterns various methodshave been proposed In fundamental approach incoherentor partially coherent light sources are utilized [45] How-ever the low power throughput and broad linewidth of thelight sources result in a relatively weak intensity and blur-ring of the reconstructed three‐dimensional holographicscenes Recently novel works have been proposed forsolving speckle artifacts in capturing objects with digital

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -This is an Open Access article distributed under the term of Korea Open Government License (KOGL) Type 4 Source Indication + Commercial Use Prohibition + ChangeProhibition (httpwwwkoglorkrinfolicenseTypeEndo)1225-6463$ copy 2019 ETRI

Received 7 October 2018 | Revised 11 December 2018 | Accepted 17 December 2018

DOI 104218etrij2018-0554

32 | wileyonlinelibrarycomjournaletrij ETRI Journal 201941(1)32ndash41

holographic schemes They can be classified into two cate-gories that is numerical approaches and optical techniques[6] Numerical approaches fundamentally refer to imageprocessing techniques and statistical analysis and theseschemes have shown good performance in holographicimage denoising [6] Uzan et al showed that a nonlocalmeans (NLM) filtering method can be applied to specklenoise reduction in digital holography [7] Bianco et aladopted an enhanced grouping algorithm and a sparsityenhancement filtering scheme using which they couldremove the noise factors including speckle artifacts [8]Leo et al proposed a technique utilizing the pixel locationof temporally sequential images to suppress speckle pat-terns [910] Memmolo et al provided an encoding tech-nique based on a combination of multiple holograms andthey proved that it could improve the image quality inoptically reconstructed holograms [11] Rivenson et alapplied a compressive sensing scheme in an incoherentholographic display system and showed that effectivedepth range as well as good image quality could beachieved [12] In contrast methods for reducing specklesfrom a given three‐dimensional (3D) object dataset havebeen reported lately A spatial interleaving technique thatsequentially displays spatially interleaved subsets of a 3Dscene was reported [1314] This technique however islimited only to point‐cloud‐based CGHs being not applica-ble to general CGHs Recently an angular spectrum inter-leaving technique for mesh‐based CGHs as well as forpoint‐cloud‐based CGHs was proposed [15] The mainconcept is to deliver only the spectral components associ-ated with a single plane carrier wave to the users eye at atime Consequently there is no interference between thedifferent spectral component sets associated with differentplane carrier waves and thus the speckle artifacts can beeffectively reduced The depth of the field broadeningcaused by presenting the spectral components associatedwith only a single plane carrier wave is reduced by pre-senting the spectral components associated with differentplane carrier waves sequentially in a time‐multiplexingmanner

In the implementation of digital holographic displayswith time‐multiplexing digital micro‐mirror array devices(DMDs) are usually used for their fast refresh rate Becausea DMD has a limited modulation property that is onlybinary amplitude modulation [16ndash18] single‐sideband(SSB) filtering is generally applied to allow an appropriatehologram spectrum in the frequency domain to passthrough [1920] while blocking the unwanted spectrumcaused by the binary modulation Nevertheless previouslyreported work on speckle reduction using angular spectruminterleaving [15] did not clarify the effective region for fil-tration in a digital holographic display system whereDMDs are used to display binary‐type holograms

In this paper we show that the binarization of the ampli-tude holograms in the numerical process of CGHs can induceunwanted spectral components in the frequency domain or ina spatial filter position In case of utilizing a single plane car-rier wave technique it is shown that the effective spectralzone in the filter domain should be much smaller than themaximum size allowed for usual SSB holography to blockthe unwanted spectral components caused by the binarymodulation To solve this problem we propose a pro-grammable dynamic filtration method to reduce the speckleartifacts using the angular spectrum interleaving technique indigital holographic display systems where a DMD is used asa spatial light modulator (SLM) To achieve dynamic filtra-tion in the spectrum domain another DMD is used in theFourier plane of a 4‐f optics Therefore in our proposedmethod two DMDs are used that is one as an SLM and theother as a programmable filter In the experiment we mea-sure the speckle contrast values in the conventional and pro-posed systems for quantitative comparison

2 | FUNDAMENTAL CONCEPTS

In this section we briefly describe a single‐carrier‐wavetechnique for reducing the speckle distribution in point‐cloud‐based CGHs of viewing‐window‐based hologramsConsidering the use of DMDs as SLMs a general filteringmethod adopting an SSB in the reconstruction of ampli-tude‐type holograms and the unwanted signals given bytheir binarization are described After describing the bina-rization of amplitude‐type holograms the unwanted signalintervention in the SSB is provided

21 | Angular spectrum interleavingtechnique for reducing speckle artifacts inpoint‐cloud‐based CGHs

The fundamental concept of the angular spectrum interleav-ing technique reported in [15] was to deliver the angularspectrum associated with only a single plane carrier wave tothe users eye at a time In [15] it was demonstrated withmesh‐based CGHs using a simple holographic display set‐up This technique can be readily modified to be applied topoint‐cloud‐based CGHs for viewing window‐type holo-graphic displays In the viewing window‐type holographicdisplays a point‐cloud‐based CGH is synthesized by [21]

Uethx yTHORN frac14 summam expethjθmTHORNexp j 2πλ rm rm

(1)

where am and θm are the amplitude and phase respectivelyof the object point located at (xm ym zm) and λ is thewavelength rm in (1) is given by

LIM ET AL | 33

rm frac14ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixmi xeth THORN2 thorn ymi yeth THORN2 thorn z2mi

q (2)

where (xmi ymi zmi) is related to the displayed object pointlocation (xm ym zm) in the viewing window‐type holo-graphic display using a converging lens of focal length fby

zmi frac14 fzmf zm

xmi frac14 fxmf zm

ymi frac14 fymf zm

(3)

In usual point‐cloud‐based CGHs phase θm of the objectpoint is given by a random value In the angular spectruminterleaving technique however phase θm of the object pointis given for a plane carrier wave having spatial frequencypair (νxo νyo) by

θm frac14 2π νxoxmi thorn νyoymi thorn zmi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1λ2

ν2xo ν2yo

r (4)

Equation (4) structures the phase distribution on the dis-played 3D object surfaces according to the single planecarrier wave of spatial frequency pair (νxo νyo) Thereforein the Fourier plane of the hologram the spectrum ofhologram U(x y) is centered around plane carrier wavespatial frequency pair (νxo νyo) with a width given by thebandwidth of the 3D object itself Because the spectrumis associated only with a single plane carrier wave thereis no interference between the different plane carrier wavecomponents and thus the speckle artifact is removed atthe expense of the enlarged depth of field of the recon-struction In the angular spectrum interleaving techniquemultiple holograms are synthesized with different spatialfrequency pairs of the plane carrier waves Moreover theyare presented sequentially such that the temporal accumu-lation of the spectrum fills the entire spectral area sup-ported by the pixel pitch of the SLM giving speckle‐freeand narrow‐depth‐of‐field 3D holographic images

22 | Multiple spectral components caused bybinary amplitude modulation of DMD

As described in section 21 for a speckle‐free reconstructionusing the angular spectrum interleaving technique the spec-tral components associated only with a single plane carrierwave should exist in each frame of the time‐multiplexingHowever the amplitude binary modulation property of theDMD generates multiple harmonics in each frame dissatisfy-ing this requirement Let us denote the amplitude and phaseof ideal complex field hologram U(x y) in (1) as A(x y) andϕ(x y) respectively such that U(x y) = A(x y)exp[jϕ(x y)]Ideal complex field U(x y) is encoded into a real‐valued pat-tern by adding its complex conjugate based on the SSBencoding technique and then it is binarized by

bethx yTHORN frac14 B Uethx yTHORN thorn Uethx yTHORNfrac12 frac14 B 2Aethx yTHORN cosϕethx yTHORNfrac12

frac14 1 if cosϕethx yTHORNgt0

0 otherwise

(5)

where B[] represents a binarization operator This binarypattern b(x y) is loaded to the DMDThe multiple har-monics in the spectrum of binary pattern b(x y) is readilyunderstood by expanding it using a Fourier series withrespect to phase ϕ(x y) From the last line of (5) it isevident that b(x y) is a periodic function of ϕ(x y) withfundamental period 2π Then b(x y) can be written as

bethx yTHORN frac14 sum1

nfrac141Cn exp jnϕethx yTHORNfrac12 (6)

with Fourier coefficient Cn given by

Cnfrac14 12π

Z π

πbethϕTHORNexp jnϕfrac12 dϕfrac14 1

2π

Z π=2

π=2exp jnϕfrac12 dϕ (7)

where b(x y) is denoted by b(ϕ) to stress that it depends onϕ by (5) After some manipulations (6) and (7) reduce to

bethx yTHORN frac14 12thorn 2πsum1

nfrac141

1eth THORNnthorn1

2n 1ejeth2n1THORNϕethxyTHORN thorn ejeth2n1THORNϕethxyTHORNn o

(8)

Equation (8) indicates that binarized pattern b(x y) containsnot only the desired term that is exp[jϕ(x y)] but alsodirect current (DC) term 12 conjugate exp[ndashjϕ(x y)] andmany other harmonics exp[plusmnj(2n ndash 1)ϕ(x y)] (wheren = 2 3 4 hellip) Therefore even though ideal complexfield hologram U(x y) is synthesized with a single planecarrier wave such that its spectrum is concentrated aroundsingle carrier wave spatial frequency pair (νxo νyo) bina-rized amplitude pattern b(x y) has multiple spectral compo-nents centered at ((2n ndash 1)νxo (2n ndash 1)νyo) (where n =plusmn1 plusmn2 plusmn3 hellip) and (0 0) With a viewing window‐typeholographic display with a 4‐f optics filter plane of focallength f1 as shown in Figure 1A the spectra of ideal com-plex field U(x y) and binarized pattern b(x y) for a singleplane carrier wave are illustrated in Figures 1B C respec-tively Here the pixel pitch of the DMD is denoted byp As shown in Figure 1C inside the usual filtration area(ie aperture area) of the SSB technique the binary modu-lation generates multiple harmonics which interfere witheach other in the reconstruction generating speckle artifactseven in the single plane carrier wave case

3 | PROPOSED METHOD

31 | Working principles

As is described in the previous section an unwanted spec-trum is generated in the process of binary modulation and

34 | LIM ET AL

this can be added in the filtering zone of conventional SSBAs a consequence a single carrier wave spectrum can beaffected by the intrusion of unwanted signal componentsand so the speckle artifacts can be increased than expectedHere we describe a novel filtration scheme to reduce speckleartifacts in an effective way The fundamental concept forour novel filtration technique is presented in Figure 2

As is presented in Figure 2 the filter size of the con-ventional SSB is larger than that of the single carrier wavesets when the speckle artifacts are required to be reduced

In addition mixing of the different spectral components ofthe single carrier wave sets or enabling temporal multiplex-ing of several spectral components simultaneously needs tobe achieved Therefore it is desirable to implement passingthrough the necessary region dynamically and synchronizethe filter region with which the CGH images are displayedon the SLM DMD As is described in a previous work itis enough to mix four holograms with different carrierwave sets to provide wide viewing angles and narrowdepths of fields [15] As a consequence an effectivemethod for filtering signal components is required for thespeckle reduction techniques adopting single carrier wavesets In other words the first order in (8) should be filteredin accordance with the CGH displayed on the SLM DMDand four other different sets should be temporally multi-plexed simultaneously To achieve those concepts it is nec-essary to use a dynamically controllable device and weplace another DMD in the filter position

32 | Implementation of a programmablefilter

To implement a programmable filtration technique we useanother DMD as a dynamic filter or a programmable filterIn particular in Figure 3 DMD 1 is used to display thepoint‐cloud‐based CGHs whereas DMD 2 is placed at theback focal plane of lens 1 and applied to reflect a propersignal spectrum according to DMD 1 Lens 2 is the secondlens in the 4‐f optics configuration and lens 3 is a fieldlens in the viewing‐window‐based holographic display sys-tem [2223] A charge coupled device (CCD) captures thereconstructed holograms and the captured images areutilized to estimate the speckle patterns

f1 f1 f1 f1

DMD plane(SLM)

Filter plane(Fourier domain of SLM)

Viewing windowplane

f2

Re-imagedSLM plane

Lens 1 Lens 2 Lens 3

z

y0 y1 y2 y3

x0 x1 x2 x3

x1

y1

(f1λνxo f1λνyo)

Bandwidth of 3D object

Filter plane

Filtration area for single sidebandf1λ p

f1λ 2p

x1

y1

Filter plane

(f1λνxo f1λνyo)

(3f1λνxo3f1λνyo)


(00)

(-f1λνxo -f1λνyo)

(-3f1λνxo -3f1λνyo)

(B)

y0

(A)

(C)

y1 y2 y3

x0 x1 x2 x3

f1

(f1λνxo f1λνyo)

f1 f1 f1 f2

(f1λνxo f1λνyo)

(3f1λνxo 3f1λνyo)

(ndashf1λνxo ndashf1λνyo)

(ndash3f1λνxo ndash3f1λνyo)


FIGURE 1 (A) is the fundamental configuration for electronicdisplay systems adopting viewing window and 4‐f optics (B) showsthe spectrum of ideal complex field U(x y) associated with a singleplane carrier wave of spatial frequency pair (νxo νyo) in the filterplane of the 4‐f optics and (C) shows the spectrum of binarizedamplitude pattern b(x y) in the same plane

x1

y1

Filter plane

x1

y1

Filter plane

Dynamic filter

Time multiplexing with dynamic filtration

Dynamic filter

( f1λνxo f1λνyo)

( f1λνx1 f1λνy1)

FIGURE 2 The proposed method for excluding falsecomponents and for enabling programmable filtration is described

LIM ET AL | 35

To use a DMD as a programmable dynamic filter wedescribe the procedure for launching the filtering region onthe filter DMD as is presented in Figure 4 CGHs are gener-ally given by the 3D object data and the inverse Fouriertransform of the CGHs can generate the spectral componentsat the filter plane in the first step Then the signal spectrumregion for the holograms can be found numerically in thesecond step and the masking of other regions except for thesignal spectrum occurs in the third step As the coordinate inthe numerical process does not match the real coordinate offilter DMD 2 coordinate transformation should be per-formed in the last step Finally the images for the filterregion are displayed on DMD 2

4 | EXPERIMENTAL VERIFICATION

41 | Experimental set‐up and preparation

In Figure 5A the schematic of the experimental set‐up ispresented and its image is shown in Figure 5B

In the experimental set‐up a 532 nm laser (SambaTMCobolt Corp) the maximum optical power of which is100 mW is used as a coherent light source and twoDMDs having 1024 (horizontal) times 768 (vertical) pixels

are applied One is used as an SLM to display the binary‐type CGHs and the other is used as a programmable filterThe pixel size of both the DMDs is 1368 μm and themaximum operating speed is approximately 22 kHz (V‐7000 Vialux GmbH) The focal length of lens 1 and lens2 is 150 mm whereas that of lens 4 and lens 5 is180 mm To illuminate DMD 1 which is used as theSLM a collimator and transmission‐type total internalreflection (TIR) prism are placed in front of it whereas areflection‐type TIR is placed in front of DMD 2 used asthe programmable dynamic filter The specific descriptionof the two different TIR prisms for illuminating DMDscan be found in [2425] Lens 1 is a Fourier lens and itconverts the optical field emanating from DMD 1 into spa-tial frequency components and DMD 2 is placed in theFourier plane generated by lens 1 and DMD 1 DMD 2 islaunched at a six‐axis stage with three axes for translationand three axes for roll pitch and yaw to align DMD 2 asfine as possible One beam splitter denoted by BS 1 inFigure 5 separates the beam path into two paths Onepasses through lens 2 and lens 3 and it reaches the CCDand the other passes through lens 4 and lens 5 The CCD(Grasshopper 3 Point Grey Corp) has a pixel number of4240 (horizontal) times 2848 (vertical) and pixel pitch of345 μm and it captures images of the reconstructed holo-grams In capturing the hologram images no lens is placedin front of the CCD that is objective measurement forspeckle is applied Lens 4 and lens 5 constituting another

DMD 1

DMD 2

Lens 1Lens 2

Lens 3

CCD

f1

f1

f1

f1

(Programmable filter)

(SLM)

FIGURE 3 The scheme for the proposed filtration method inviewing‐window‐based holographic display systems

1 Perform inverse Fourier transform

2 Find a region for spectrumin the filter plane

4 Match the numerical coordinate with the real position of DMD2

3 Mask other regions

Three-dimensionalobject data

CGH

5 Display the signal spectrum region on DMD 2

FIGURE 4 Shows the flowchart for generating a filtering regionon the DMD used as a programmable filter

DSLR

Lens 1

Lens 2

Lens 3CCD

LENS 5

LENS 4DMD 2

DMD 1

BS 1Collimator

Lens 1

Lens 2

Lens 3 CCD

LENS 5

LENS 4

DMD 2

DMD 1

BS 1

Collimator

Laser(532 nm)

Fiber combiner

(A)

(B)

camera

6-axisstage

6-axisstage

DSLR camera

FIGURE 5 (A) is the schematic of the experimental set‐up and(B) is the corresponding real picture

36 | LIM ET AL

4‐f optics are inserted to ensure DMD 2 identifies the fil-ter position conveniently The captured images of the filterplane DMD 2 by a DSLR camera (5D MARK III CanonCorp) are presented in Figures 6B C Figure 6A showsthe conventional SSB filter where half the region of theSSB is implemented for the experiment The implementedSSB filter on DMD 2 is shown in Figure 6B andthe implemented region for the single carrier wave tech-nique on DMD 2 is shown in Figure 6C In Figures 6AB the size of the filter region for the SSB is given by(f1λ2p) times (f1λ2p) where f1 = 150 mm λ = 532 nm andp = 1368 μm The corresponding pixel numbers displayedon DMD 2 are 214 times 214 In the experiment for the pro-grammable filtration the actual position is changed accord-ing to the single carrier wave sets Consequently the filterregion shown in Figure 6C can be varied and synchronizedwith the image displayed on the SLM DMD The filterregion shown in Figure 6C is given by following the pro-cess presented in Figure 4 and the estimated pixel num-bers are 70 (horizontal) times 70 (vertical)

To verify the effectiveness of the proposed pro-grammable filter in terms of the speckle artifact reductionthe speckle contrast value is used to quantify the measuredspeckles [2627] The speckle contrast is given by

SC frac14 σ

Ih i (9)

where hIi and σ represent mean values of the intensity andstandard deviation of the captured images respectively Wedesign the test pattern for measuring the speckle distributionand the test image pattern referring to the conventionalUSAF 1951 is shown in Figure 7 the center of which iscomposed of the rectangular region for the calculation ofspeckle contrast values The entire size of the test image is1024 times 768 pixels and that of the square at the center is150 times 150 pixels

In Figure 8 the CGH images of the four different setsgiven by the single carrier wave technique for point‐cloud‐based holograms are presented Figures 8A C E and G arethe CGHs of the four different single carrier wave sets andthey are to be displayed on DMD 1 (SLM) The

corresponding filter images given by referring to the proce-dure presented in Figure 4 are respectively shown in Fig-ures 8B D F and H and these are to be uploaded on DMD2 (programmable filter)

In Figures 8B D F and H the positions on the DMDsare 40 pixels away from one another horizontally and verti-cally because they have different carrier wave sets

42 | Experimental results

In this subsection experimental results to verify the pro-posed concept are presented First we conduct three typesof experiments depending on the filtering condition One isbased on the conventional method which implies that theconventional SSB is placed in the filter plane and adoptsthe SSB filter shown in Figure 6A Another is to adoptSSB on DMD 2 as shown in Figure 6B the case of whichis to include the false spectral components in the SSBregion while using DMD 2 in the filter plane In these twoexperiments half of the SSB along the horizontal directionis applied The other experiment is the programmable filtertest on DMD 2 as presented in Figure 6C which is themain experiment for our proposed concept Results forthese three types of experiments are displayed in Figure 9To compare the results easily they are listed and groupedin three columns Four images Figures 9A D G and J inthe left column of Figure 9 denoted by conventional SSBshow the reconstructed holograms of the conventional SSB

(A) (B) (C)

FIGURE 6 (A) is the image of a conventional SSB filter the center of which is applied as the filtering area (B) is the captured image of aprogrammed SSB filter on DMD 2 and (C) is the captured image of a programmed filter image for a single carrier wave technique on DMD 2

Region forspeckle contrastestimation

FIGURE 7 The test pattern for speckle estimation is described

LIM ET AL | 37

experiments Four images Figures 9B E H and K in themiddle column of Figure 9 denoted by SSB on DMD 2present the results for the SSB filter on DMD 2 Fourimages Figures 9C F I and l in the right column of Fig-ure 9 denoted by programmable filter present the experi-mental results for the proposed concept

In Figure 9 the estimated speckle contrast values areinserted in the upper region of each image The capturedimages in the experiments are horizontally flipped becauseof the reflection‐type TIR prism for illuminating DMD 2

Second the temporal multiplexing experiments for fourdifferent carrier wave CGHs were performed where theresults were given by temporally multiplexing the CGHsshown in Figures 8A C E and G For the conventionalSSB experiment only DMD 1 is activated where the filterpresented in Figure 6A is used

The captured hologram image for the conventional SSBexperiment is shown in Figure 10A The estimated speckle

distribution for the inset square region is presented in Fig-ure 10B and its speckle contrast value is 347 Theexperimental result with the SSB on DMD 2 is presentedin Figure 10C The corresponding speckle contrast value is305 the speckle distribution of which is presented inFigure 10D The result for the programmable filter experi-ment is presented in Figure 10E The speckle contrastvalue is 202 and the speckle distribution is shown inFigure 10F In these temporal‐multiplexing experimentsthe repetition rate of both the DMDs is set as 3600 Hzand they are synchronized for the programmable filterexperiments In synchronizing and displaying the CGHs onDMD 1 and DMD 2 commercial software LabVIEW wasapplied

Regarding the resolution confirmation of the proposedmethod we perform an additional experiment In Fig-ures 11A B the third group in the USAF image isenlarged and shown in the left side of the correspondingholograms In both the magnified images horizontal andvertical bars less than the third element in the third groupbecome indistinguishable Thus by comparing the resolu-tion image of the program filter with that of the SSB filter

(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)

FIGURE 9 (A) (B) and (C) are the reconstructed hologramimages of the CGH in Fig 8(A) (D) (E) and (F) are thereconstructed hologram images of the CGH in Figure 8(C) (G) (H)and (I) are the reconstructed hologram images of the CGH inFigure 8(E) (J) (K) and (L) are the reconstructed hologram imagesof the CGH in Figure 8(G)

(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)

FIGURE 8 (A) (C) (E) and (G) are the CGHs of the testpatterns of the four different sets of the single carrier wave techniquewhich are to be uploaded on DMD 1 (SLM) (B) (D) (F) and (H)are the corresponding images for the programmed filter region to bedisplayed on DMD 2

38 | LIM ET AL

on DMD 2 it is observed that the use of the programmedfilter does not cause resolution to be lowered

5 | DISCUSSION

As is seen from the experimental results in Figures 9 and10 the programmable filter achieved by the use of a DMDeffectively reduces the speckle artifacts The speckle con-trast values for the programmable filter case are smallerthan those for the conventional SSB methods as shown inFigure 9 In the temporal multiplexing experiments thespeckle contrast value for the programmable filter is thelowest of all the experiments Another characteristicapproach is to synchronize the SLM DMD with the

programmable filter DMD dynamically which has not beenshown in previous works regarding speckle reduction tech-niques as well as filtering methods for binary‐type holo-grams This feature would be particularly useful if ourproposed method was to be applied in other holographicresearch such as synthetic aperture holograms wheredynamic filters can be applied However owing to the rela-tively small pixel pitch of DMD 2 compared to that of thespectrum region of the single carrier wave hologramsreplicas of hologram signals are observed in Figures 9 and10 where DMD 2 is implemented as a programmabledynamic filter This is caused by the periodic pixel pitch ofDMD 2 placed in the filter plane To remove this the pixelsize should be increased to the size of the signal spectrumAlthough we used a DMD as a filter fast‐activating

SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)

FIGURE 10 (A) (C) and (E) are thetemporally multiplexed results for the fourdifferent single carrier wave sets presentedin Figure 8 (A) (C) (E) and (G) Theircorresponding speckle distributions arerespectively shown in (B) (D) and (F)with the calculated speckle contrast values

LIM ET AL | 39

mirrors with a large diameter equal to the spectrum spotsize of the single carrier waves can be applied to solve thisproblem In addition a horizontal shrinkage is observed inthe captured hologram images when the DMDs are used asa spatial filter This is caused by the misalignment ofDMD 2 although we tried to adjust it as possible as wecan Thus the image is horizontally distorted Although therefresh rate of the DMDs in the temporal multiplexingexperiments was 3600 Hz for convenience it could bedynamically altered in other applications

6 | SUMMARY AND CONCLUSION

Previously reported works gave a good description for reduc-ing the speckle artifacts in binary‐type holographic displaysystems However the conventional approaches did notprovide delicate considerations in the filtering technique Ourproposed concept features how to effectively filter the

unwanted signal spectra to recover hologram images withreduced speckle artifacts In addition to estimate the speck-les we designed a test image pattern and quantified themwith speckle contrast values Thus it has been provedthat our proposed programmable filter can effectively reducespeckle artifacts compared to the conventional filteringtechnique

ORCID

Yongjun Lim httpsorcidorg0000-0003-3285-0651

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2 J Hong et al Three‐dimensional display technologies of recentinterest Principles status and issues Appl Opt 50 (2011) no34 H87ndashH115

3 L Onural F Yaras and H Kang Digital holographic three‐dimensional video display Proc IEEE 99 (2011) no 4 576ndash589

4 F Yaraş H Kang and L Onural Real‐time phase‐only colorholographic video display system using LED illumination ApplOpt 48 (2009) no 34 H48ndashH53

5 T S McKechnie Speckle reduction in laser speckle and related phe-nomena J C Dainty ed Springer-Verlag BerlinHeidelberg 1975

6 V Bianco et al Strategies for reducing speckle noise in digitalholography Light Sci Appl 7 (2018) no 1 481ndash4816

7 V Bianco et al Quasi noise‐free digital holography Light SciAppl 5 (2016) no 9 e161421ndashe1614212

8 A Uzan Y Rivenson and A Stern Speckle denoising in digitalholography by nonlocal means filtering Appl Opt 52 (2013)A195ndashA200

9 M Leo et al Automatic digital hologram denoising by spa-tiotemporal analysis of pixel‐wise statistics J Display Technol 9(2013) no 11 904ndash909

10 M Leo et al Multilevel bidimensional empirical mode decompo-sition A new speckle reduction method in digital holographyOpt Eng 53 (2014) no 11 1123141ndash11231410

11 P Memmolo et al Encoding multiple holograms for speckle‐noise reduction in optical display Opt Express 22 (2014) no21 25768ndash25775

12 Y Rivenson A Stern and J Rosen Compressive multiple view projec-tion incoherent holography Opt Express 19 (2011) no 7 6109ndash6118

13 Y Takaki and M Yokouchi Speckle‐free and grayscale holo-gram reconstruction using time‐multiplexing technique OptExpress 19 (2011) no 8 7567ndash7579

14 T Kurihara and Y Takaki Speckle‐free shaded 3D images pro-duced by computer‐generated holography Opt Express 21(2013) no 4 4044ndash4054

15 S -B Ko and J -H Park Speckle reduction using angular spec-trum interleaving for triangular mesh‐based computer‐generatedhologram Opt Express 25 (2017) no 24 29788ndash29797

16 T M Kreis P Aswendt and R Hoefling Hologram reconstructionusing a digital micromirror device Opt Eng 40 (2001) no 6 926ndash933

17 J -Y Son et al Holographic display based on a spatial DMDarray Opt Lett 38 (2013) no 16 3173ndash3176

(A)

(B)

SC = 297

SC = 193

FIGURE 11 (A) is the captured image with an enlarged viewgiven by the SSB on DMD 2 and (B) is the captured image with anenlarged view given by the programmed filter on DMD 2

40 | LIM ET AL

18 T Inoue and Y Takaki Table screen 360‐degree holographicdisplay using circular viewing‐zone scanning Opt Express 23(2015) no 5 6533ndash6542

19 O Bryngdahl and A Lohmann Single‐sideband holography JOpt Soc Am 58 (1968) no 5 620ndash624

20 Y Takaki and Y Tanemoto Band‐limited zone plates for single‐sideband holography Appl Opt 48 (2009) no 34 H64ndashH70

21 J -H Park Recent progresses in computer generated holographyfor three‐dimensional scene J Inform Display 18 (2017) no 11ndash12

22 Y Lim et al 360‐degree tabletop electronic holographic displayOpt Express 24 (2016) no 22 24999ndash25009

23 M Kim et al Expanded exit‐pupil holographic head‐mounteddisplay with high‐speed digital micromirror device ETRI J 40(2018) no 5 366ndash375

24 C-M Chang and H-P D Shieh Design of illumination and pro-jection optics for projectors with single digital micromirrordevices Appl Opt 39 (2000) no 22 3202ndash3208

25 J-W Pan et al Portable digital micromirror device projectorusing a prism Appl Opt 46 (2007) no 22 5097ndash5102

26 J W Goodman Some fundamental properties of speckle J OptSoc Am 66 (1976) no 11 1145ndash1150

27 DA Boas and A K Dunn Laser Speckle Contrast Imaging inBiomedical Optics J Biomed Opt 15 (2010) no 1 0111091ndash01110912

AUTHOR BIOGRAPHIES

Yongjun Lim received his PhDdegree from Seoul NationalUniversity Korea in 2010From 2011 to 2014 he workedfor Samsung Electronics as asenior engineer Since 2014 hehas been working for ETRI

Daejeon Rep of Korea where he is now a seniorresearcher His research interests include electronicholographic display systems holographic micro-scopy optical lithography non‐diffracting beamssurface plasmons diffractive optics and near‐fieldoptics

Jae-Hyeung Park received hisBS MS and PhD degrees fromSeoul National UniversityKorea in 2000 2002 and 2005respectively From 2005 to2007 he worked for SamsungElectronics as a senior engineer

In 2007 he joined the faculty member of ChungbukNational University Korea Since 2013 he has beenwith Inha University where he is now a full profes-sor of the department of information and communi-cation engineering His research interests include

light field and holographic information processingand display techniques

Joonku Hahn received his PhDdegree in 2009 from School ofElectrical Engineering SeoulNational University SeoulKorea In 2011 he joined thefaculty of school of electronicsengineering Kyungpook

National University Daegu Rep of Korea and he isnow an associate professor His main interests are 3Ddisplay and digital holography applications

Hayan Kim received her BS andMS degrees in optical engineer-ing from the School of Electron-ics and Information EngineeringSejong University Seoul Rep ofKorea in 2014 and 2016 Since2016 she has been with the Elec-

tronics and Telecommunications Research InstituteDaejeon Rep of Korea where she is now a researcherHer main research interests include digital holographyand holographic display system

Keehoon Hong received his BSdegree in Electrical and Elec-tronic Engineering from YonseiUniversity Seoul Korea in2008 and his PhD degree inElectrical Engineering andComputer Science from Seoul

National University Seoul Korea in 2014 He iscurrently working as a Senior Researcher for Elec-tronics and Telecommunications Research InstituteDaejeon Rep of Korea His research interestsinclude autostereoscopic display digital holographicdisplay and holographic optical elements

Jinwoong Kim received his BSand MS degrees in electronicsengineering from SeoulNational University Seoul Repof Korea in 1981 and 1983respectively He received hisPhD degree in electrical engi-

neering from Texas AampM University College Sta-tion TX USA in 1993 He has been working forETRI Daejeon Rep of Korea since 1983 leadingmany projects in the telecommunications and digitalbroadcasting areas

LIM ET AL | 41

holographic schemes They can be classified into two cate-gories that is numerical approaches and optical techniques[6] Numerical approaches fundamentally refer to imageprocessing techniques and statistical analysis and theseschemes have shown good performance in holographicimage denoising [6] Uzan et al showed that a nonlocalmeans (NLM) filtering method can be applied to specklenoise reduction in digital holography [7] Bianco et aladopted an enhanced grouping algorithm and a sparsityenhancement filtering scheme using which they couldremove the noise factors including speckle artifacts [8]Leo et al proposed a technique utilizing the pixel locationof temporally sequential images to suppress speckle pat-terns [910] Memmolo et al provided an encoding tech-nique based on a combination of multiple holograms andthey proved that it could improve the image quality inoptically reconstructed holograms [11] Rivenson et alapplied a compressive sensing scheme in an incoherentholographic display system and showed that effectivedepth range as well as good image quality could beachieved [12] In contrast methods for reducing specklesfrom a given three‐dimensional (3D) object dataset havebeen reported lately A spatial interleaving technique thatsequentially displays spatially interleaved subsets of a 3Dscene was reported [1314] This technique however islimited only to point‐cloud‐based CGHs being not applica-ble to general CGHs Recently an angular spectrum inter-leaving technique for mesh‐based CGHs as well as forpoint‐cloud‐based CGHs was proposed [15] The mainconcept is to deliver only the spectral components associ-ated with a single plane carrier wave to the users eye at atime Consequently there is no interference between thedifferent spectral component sets associated with differentplane carrier waves and thus the speckle artifacts can beeffectively reduced The depth of the field broadeningcaused by presenting the spectral components associatedwith only a single plane carrier wave is reduced by pre-senting the spectral components associated with differentplane carrier waves sequentially in a time‐multiplexingmanner

In the implementation of digital holographic displayswith time‐multiplexing digital micro‐mirror array devices(DMDs) are usually used for their fast refresh rate Becausea DMD has a limited modulation property that is onlybinary amplitude modulation [16ndash18] single‐sideband(SSB) filtering is generally applied to allow an appropriatehologram spectrum in the frequency domain to passthrough [1920] while blocking the unwanted spectrumcaused by the binary modulation Nevertheless previouslyreported work on speckle reduction using angular spectruminterleaving [15] did not clarify the effective region for fil-tration in a digital holographic display system whereDMDs are used to display binary‐type holograms

In this paper we show that the binarization of the ampli-tude holograms in the numerical process of CGHs can induceunwanted spectral components in the frequency domain or ina spatial filter position In case of utilizing a single plane car-rier wave technique it is shown that the effective spectralzone in the filter domain should be much smaller than themaximum size allowed for usual SSB holography to blockthe unwanted spectral components caused by the binarymodulation To solve this problem we propose a pro-grammable dynamic filtration method to reduce the speckleartifacts using the angular spectrum interleaving technique indigital holographic display systems where a DMD is used asa spatial light modulator (SLM) To achieve dynamic filtra-tion in the spectrum domain another DMD is used in theFourier plane of a 4‐f optics Therefore in our proposedmethod two DMDs are used that is one as an SLM and theother as a programmable filter In the experiment we mea-sure the speckle contrast values in the conventional and pro-posed systems for quantitative comparison

2 | FUNDAMENTAL CONCEPTS

In this section we briefly describe a single‐carrier‐wavetechnique for reducing the speckle distribution in point‐cloud‐based CGHs of viewing‐window‐based hologramsConsidering the use of DMDs as SLMs a general filteringmethod adopting an SSB in the reconstruction of ampli-tude‐type holograms and the unwanted signals given bytheir binarization are described After describing the bina-rization of amplitude‐type holograms the unwanted signalintervention in the SSB is provided

21 | Angular spectrum interleavingtechnique for reducing speckle artifacts inpoint‐cloud‐based CGHs

The fundamental concept of the angular spectrum interleav-ing technique reported in [15] was to deliver the angularspectrum associated with only a single plane carrier wave tothe users eye at a time In [15] it was demonstrated withmesh‐based CGHs using a simple holographic display set‐up This technique can be readily modified to be applied topoint‐cloud‐based CGHs for viewing window‐type holo-graphic displays In the viewing window‐type holographicdisplays a point‐cloud‐based CGH is synthesized by [21]

Uethx yTHORN frac14 summam expethjθmTHORNexp j 2πλ rm rm

(1)

where am and θm are the amplitude and phase respectivelyof the object point located at (xm ym zm) and λ is thewavelength rm in (1) is given by

LIM ET AL | 33


q (2)


zmi frac14 fzmf zm

xmi frac14 fxmf zm

ymi frac14 fymf zm

(3)




ν2xo ν2yo

r (4)






0 otherwise

(5)





Cnfrac14 12π

Z π


2π

Z π=2




nfrac141

1eth THORNnthorn1


(8)


3 | PROPOSED METHOD



34 | LIM ET AL






f1 f1 f1 f1

DMD plane(SLM)


Viewing windowplane

f2

Re-imagedSLM plane


z

y0 y1 y2 y3

x0 x1 x2 x3

x1

y1

(f1λνxo f1λνyo)


Filter plane


f1λ 2p

x1

y1

Filter plane

(f1λνxo f1λνyo)



(00)



(B)

y0

(A)

(C)

y1 y2 y3

x0 x1 x2 x3

f1

(f1λνxo f1λνyo)

f1 f1 f1 f2

(f1λνxo f1λνyo)






x1

y1

Filter plane

x1

y1

Filter plane

Dynamic filter


Dynamic filter




LIM ET AL | 35







DMD 1

DMD 2

Lens 1Lens 2

Lens 3

CCD

f1

f1

f1

f1


(SLM)







CGH



DSLR

Lens 1

Lens 2

Lens 3CCD

LENS 5

LENS 4DMD 2

DMD 1

BS 1Collimator

Lens 1

Lens 2

Lens 3 CCD

LENS 5

LENS 4

DMD 2

DMD 1

BS 1

Collimator

Laser(532 nm)

Fiber combiner

(A)

(B)

camera

6-axisstage

6-axisstage

DSLR camera


36 | LIM ET AL



SC frac14 σ

Ih i (9)







(A) (B) (C)




LIM ET AL | 37







(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)


(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)


38 | LIM ET AL


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41


q (2)


zmi frac14 fzmf zm

xmi frac14 fxmf zm

ymi frac14 fymf zm

(3)




ν2xo ν2yo

r (4)






0 otherwise

(5)





Cnfrac14 12π

Z π


2π

Z π=2




nfrac141

1eth THORNnthorn1


(8)


3 | PROPOSED METHOD



34 | LIM ET AL






f1 f1 f1 f1

DMD plane(SLM)


Viewing windowplane

f2

Re-imagedSLM plane


z

y0 y1 y2 y3

x0 x1 x2 x3

x1

y1

(f1λνxo f1λνyo)


Filter plane


f1λ 2p

x1

y1

Filter plane

(f1λνxo f1λνyo)



(00)



(B)

y0

(A)

(C)

y1 y2 y3

x0 x1 x2 x3

f1

(f1λνxo f1λνyo)

f1 f1 f1 f2

(f1λνxo f1λνyo)






x1

y1

Filter plane

x1

y1

Filter plane

Dynamic filter


Dynamic filter




LIM ET AL | 35







DMD 1

DMD 2

Lens 1Lens 2

Lens 3

CCD

f1

f1

f1

f1


(SLM)







CGH



DSLR

Lens 1

Lens 2

Lens 3CCD

LENS 5

LENS 4DMD 2

DMD 1

BS 1Collimator

Lens 1

Lens 2

Lens 3 CCD

LENS 5

LENS 4

DMD 2

DMD 1

BS 1

Collimator

Laser(532 nm)

Fiber combiner

(A)

(B)

camera

6-axisstage

6-axisstage

DSLR camera


36 | LIM ET AL



SC frac14 σ

Ih i (9)







(A) (B) (C)




LIM ET AL | 37







(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)


(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)


38 | LIM ET AL


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41






f1 f1 f1 f1

DMD plane(SLM)


Viewing windowplane

f2

Re-imagedSLM plane


z

y0 y1 y2 y3

x0 x1 x2 x3

x1

y1

(f1λνxo f1λνyo)


Filter plane


f1λ 2p

x1

y1

Filter plane

(f1λνxo f1λνyo)



(00)



(B)

y0

(A)

(C)

y1 y2 y3

x0 x1 x2 x3

f1

(f1λνxo f1λνyo)

f1 f1 f1 f2

(f1λνxo f1λνyo)






x1

y1

Filter plane

x1

y1

Filter plane

Dynamic filter


Dynamic filter




LIM ET AL | 35







DMD 1

DMD 2

Lens 1Lens 2

Lens 3

CCD

f1

f1

f1

f1


(SLM)







CGH



DSLR

Lens 1

Lens 2

Lens 3CCD

LENS 5

LENS 4DMD 2

DMD 1

BS 1Collimator

Lens 1

Lens 2

Lens 3 CCD

LENS 5

LENS 4

DMD 2

DMD 1

BS 1

Collimator

Laser(532 nm)

Fiber combiner

(A)

(B)

camera

6-axisstage

6-axisstage

DSLR camera


36 | LIM ET AL



SC frac14 σ

Ih i (9)







(A) (B) (C)




LIM ET AL | 37







(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)


(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)


38 | LIM ET AL


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41







DMD 1

DMD 2

Lens 1Lens 2

Lens 3

CCD

f1

f1

f1

f1


(SLM)







CGH



DSLR

Lens 1

Lens 2

Lens 3CCD

LENS 5

LENS 4DMD 2

DMD 1

BS 1Collimator

Lens 1

Lens 2

Lens 3 CCD

LENS 5

LENS 4

DMD 2

DMD 1

BS 1

Collimator

Laser(532 nm)

Fiber combiner

(A)

(B)

camera

6-axisstage

6-axisstage

DSLR camera


36 | LIM ET AL



SC frac14 σ

Ih i (9)







(A) (B) (C)




LIM ET AL | 37







(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)


(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)


38 | LIM ET AL


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41



SC frac14 σ

Ih i (9)







(A) (B) (C)




LIM ET AL | 37







(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)


(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)


38 | LIM ET AL


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41







(A)

(D)

(G)

(J)

(B)

(E)

(H)

(K)

(C)

(F)

(I)

(L)


(A)

(C)

(E)

(G)

(B)

(D)

(F)

(H)


38 | LIM ET AL


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41


5 | DISCUSSION



SC = 347

SC = 305

SC = 202

(B)(A)

(D)(C)

(F)(E)


LIM ET AL | 39





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41





ORCID


REFERENCES


















(A)

(B)

SC = 297

SC = 193


40 | LIM ET AL











AUTHOR BIOGRAPHIES














LIM ET AL | 41











AUTHOR BIOGRAPHIES














LIM ET AL | 41

Reducing speckle artifacts in digital holography through...

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