Additive Light Field Displays:Realization of Augmented Reality with Holographic Optical Elements

Seungjae Lee Changwon Jang Seokil Moon Jaebum Cho Byoungho Lee∗

Seoul National University

Left-top view Right-bottom view

Front layer

Rear layer

Left-top view Right-bottom view

Front layer

Rear layer

Original light field

Original light field

HOE layers

Figure 1: See-through additive light field displays with holographic optical elements (HOEs). We propose a novel compressive light fielddisplay that uses HOE layers. Each layer diffuses a projection beam from a projector and functions as an additive layer. This prototypeconsists of two HOE layers, two projectors, and corresponding relaying optics. The images on the right demonstrate the display results ofour prototype, and its high levels of transparency, brightness, and image fidelity.

Abstract

We propose a see-through additive light field display as a novel typeof compressive light field display. We utilize holographic optical el-ements (HOEs) as transparent additive layers. The HOE layers arealmost free from diffraction unlike spatial light modulator layers,which makes this additive light field display more advantageouswhen modifying the number of layers, thickness, and pixel den-sity compared with conventional compressive displays. Meanwhile,the additive light field display maintains advantages of compressivelight field displays. The proposed additive light field display showsbright and full-color volumetric images in high definition. In addi-tion, users can view real-world scenes beyond the displays. Hence,we expect that our method can contribute to the realization of aug-mented reality. Here, we describe implementation of a prototypeadditive light field display with two additive layers, evaluate theperformance of transparent HOE layers, describe several results ofdisplay experiments, discuss the diffraction effect of spatial lightmodulators, and analyze the ability of the additive light field dis-play to express uncorrelated light fields.

Keywords: autostereoscopic 3D displays, holographic optical el-ements, transparent, light fields, additive layers

Concepts: •Computing methodologies→ Graphic systems andinterface; Computational photography; •Hardware→ Emergingtechnologies; Emerging optical and photonic technologies;

∗e-mail:byoungho@snu.ac.kr

1 Introduction

Augmented reality (AR) is a technology that integrates computer-generated information into a live view of a real-world broadcast.AR is regarded as one of the next-generation display technologiessince it can be used for various applications [Azuma 1997]. Forinstance, AR for entertainment or gaming applications can pro-vide fascinating experiences to interact with imaginary objects sur-rounded by real-world situations. In the medical field, AR can assistdoctors in surgery [State et al. 1996] by displaying information ofpatients such as heartbeat rate, blood pressure, and the location ofthe tumor. AR can be an effective tool for education [Kaufmannand Schmalstieg 2003] since students can learn math, chemistry, orgeometry with visualized structures. Furthermore, AR can supportthe military with a navigation system or assistance in perceiving thereal world.

With the current level of progress in computation speed and op-tical design skills, the realization of AR is no longer a daydreamthat is possible only in science fiction movies. However, there re-main some issues that should be solved or improved in order torealize more effectve and practical AR systems. First, introduc-ing 3-dimensional (3D) information of high-definition to users isa challenging topic. Stereoscopic 3D displays such as high-speedliquid crystal displays (LCDs) with shutter glasses could not suc-cessfully attract the public attention since consumers tend to feelantipathy when required to wear equipment for watching displayedimages. Autostereoscopic 3D displays suffer from display perfor-mances that are determined by viewing angle, image fidelity, anddepth of field. Second, implementing transparent displays for ARis another challenging issue. Manufacturing display panels withtransparent elements is one solution, but this can be difficult andexpensive. A more economical way to realize transparent displaysinvolves the use of beam-combiners in a projection system. Halfmirrors, wave guides, and holographic optical elements (HOEs) canbe utilized as the beam-combiners. However, additional optical el-ements make display systems more bulky.

Our aim is to construct a transparent display system that will pro-vide 3D information for AR. With inspiration from previous stud-

ies such as light field displays using multi-layers [Wetzstein et al.2011; Lanman et al. 2011] and transparent display using HOEs [Ol-wal et al. 2005; Hong et al. 2014], we introduce a novel type ofcompressive light field display with transparent HOE layers, calledthe additive light field display. The proposed display utilizes HOElayers as transparent projection screens, which diffuse images fromprojectors and generate independent 2D light fields. The generatedlight fields are merged into a single light field via addition, whichallows them to form 4D light fields. Therefore, this additive lightfield display can reconstruct 4D light fields, which can provide amotion-parallax according to the viewing position.

The additive light field display has distinct benefits. First, it is atransparent autostereoscopic 3D display that can be applied to AR.Second, other compressive displays employ a stack of LCDs thatinvolves moire and results in a loss of brightness, but the additivelight field display uses a stack of HOE layers and is relatively freefrom these problems. Third, the additive light field display is flexi-ble to allow increases in pixel density, while the other compressivedisplays suffer from diffraction caused by spatial light modulators.In the end, this system has obvious merits for several applicationssuch as head-mounted displays, for which time multiplexing is notessential [Huang et al. 2015].

The contributions of this study are as follows.

• We introduce an additive light field display for use as a trans-parent 3D display for AR.

• Using HOEs, we implement and evaluate transparent projec-tion screens for the multi-layered displays.

• We describe the design and implementation of a prototype ofthe additive light field display.

• We analyze the diffraction effect of spatial light modulatorlayers, evaluate the validity of ray approximation, and sug-gest a modified projection matrix that includes the diffractioneffect.

• We use a statistical approach to analyze the ability of the pro-posed additive light field display to compress uncorrelatedlight fields.

2 Related Work

Autostereoscopic 3D Displays Glasses-free 3D displays havereceived attention from academia and industry since the displaysystems require no special glasses, which are inconvenient. Sev-eral autostereoscopic displays [Lee 2013], such as integral imag-ing [Lippmann 1908] and holographic displays, have been studiedfor more than a century. Holographic displays reconstruct com-plex wavefronts with coherent light sources and spatial light mod-ulators (SLMs). Holographic displays have a wide depth of fieldand provide depth cues without vergence-accommodation conflict.However, when a spatial bandwidth product (SBP) is settled, holo-graphic displays trade window size for viewing angle and spatialresolution. Despite efforts to enhance SBP with temporal multi-plexing [Takaki and Okada 2009; Li et al. 2016] and spatial mul-tiplexing [Sasaki et al. 2014] methods, the SBP is still not suffi-cient for commercialization or practical use. On the other hand,integral imaging displays, categorized as light field displays, recon-struct light fields by using a lens-array. Each elemental lens guidesrays from the pixels within the aperture of the lens. Since the direc-tions of guided rays vary according to the locations of pixels, 4Dlight fields could be generated. However, integral imaging displaysinvolve a trade-off between spatial resolution and angular resolu-tion [Park et al. 2009b]. In order to enhance the performance ofintegral imaging displays, temporal multiplexing [Hong and Javidi2004], viewer tracking [Park et al. 2009a], and spatial multiplexing

[Takaki and Nago 2010] methods have been proposed.

Recently, as an enhancement of light field displays, compressivelight field displays were proposed. A compressive light field dis-play uses a multi-layered structure to reconstruct condensed lightfields. Since most of the light fields from real objects are corre-lated, it is feasible to compress and express a large number of lightfields with limited parameters. The condensed light fields can bederived from an optimization algorithm based on a multi-layeredstructure. High-rank 3D [Lanman et al. 2010], attenuation-based[Wetzstein et al. 2011], polarization field [Lanman et al. 2011], andtensor displays [Wetzstein et al. 2011] are typical panel-type com-pressive light field displays. There is a common weakness in thosedisplays that comes from the stacking of SLMs. In a practical sense,SLMs diffract transmitting rays since SLMs consist of periodic pix-elated structures. However, the optimization algorithms of the com-pressive light field displays are based on ray optics, which neglectsdiffraction. Hence, when the effect of diffraction is considerable,reconstructed light fields from implemented systems could be dif-ferent from the simulation results. The diffraction effect makes itdifficult to increase the number of SLM layers or to use an SLMwith a small pixel pitch. In contrast, the proposed additive lightfield display with HOE layers is relatively free from the diffractioneffect since the elements do not have a pixelated structure. Also,additive light field displays are transparent, which is a significantmerit among compressive light field displays.

Volumetric Displays with Multi-Focal Planes The additivelight field display is closely related to volumetric stereoscopic dis-plays with multi-focal planes. Akeley et al. [2004] and Narainet al. [2015] proposed a stereoscopic volumetric display with astack of additive layers (beam splitters or LCD panels with time-multiplexing). Switchable lenses are utilized [Liu et al. 2008; Loveet al. 2009] to image display panels at a few planes of differentdepths. The four methods provide focus cues of different depthswith additive multi-layered imaging planes. The principle is similarto the additive light field display, which also generates light fieldsby addition. However, volumetric displays with beam splitters orswitchable lenses trade spatial resolution or refresh rates to achievemulti-focal planes, respectively. In particular, the volumetric dis-plays with switchable lenses or LCD panels have limited applica-tions since the viewer position is fixed. On the other hand, additivelight field displays are autostereoscopic 3D displays with the po-tential to be applied to projection-type, head-mounted, or head-updisplays.

Holographic Optical Elements D. H. Close [1975] first intro-duced HOEs, which are volume holograms that transform an inci-dent wavefront to a predefined wavefront when the incident wave-front satisfies the Bragg condition. On the other hand, lights from areal-world scene may pass through HOEs without diffraction sincethe lights does not satisfy the Bragg condition. This property givesHOEs a distinct characteristic of optical transparency. HOEs havevarious applications that include polarization-selective optical ele-ments [Huang 1994], see-through lens arrays for integral imaging[Hong et al. 2014; Jang et al. 2016], transparent diffusive screensfor projection displays [Yeom et al. 2015], and beam-combinersfor head-mounted displays [Kasai et al. 2001]. In fact, transparentdiffusive screens and head-mounted displays are ready for commer-cialization by HoloPro1 and DigiLens2.

Augmented Reality AR has recently become one of the mostspotlighted technologies based on advances in optical engineeringand computer science. For instance, wearable AR displays such

1http://www.holopro.com2http://www.digilens.com

Diffuser

Photopolymer

Reference wave

Signal waveM

BS

M

DM

RGB lasers

DM DM

ESOL PH CL

A

ND

ES : Electric shutterOL : Objective lensPH : Pinhole

CL : Collimating lensBS : Beam splitterA : ApertureM : MirrorND : Neutral density filter

DM : Dichroic mirror

Figure 2: Recording process of DHOEs. This recording set up is divided into three parts: wavelength multiplexing, collimating, andrecording. Details of the recording part are described on the right-hand side.

as Google Glass3 and HoloLens4 have attracted considerable pub-lic attention. At the Retail Asia Expo 2015, Samsung introduced atransparent organic light-emitting diode (OLED) display that couldbe utilized as a panel-type device for AR. Hilliges et al. [2012]proposed a HoloDesk that enables users to interact with virtual im-ages in real time. Maimone et al. [2014] designed wide field ofview see-through glasses, which float virtual images on real-world.These devices provide 2D images or stereoscopic 3D images floatedonto a specific plane.

Researchers working in 3D display fields have also been attractedto AR. Several methods to implement see-through 3D displays havebeen proposed. For instance, lens arrays for integral imaging werereplaced by concave half mirror arrays [Hong et al. 2010] or byHOEs [Hong et al. 2014; Kim et al. 2015]. The concave half mir-ror arrays were implemented with index-matching oil, which givestransparency to conventional half mirror arrays. Takaki and Yam-aguchi [2015] designed relaying optics that allow observers to seebeyond a lens array. Waveguides were utilized for see-through in-tegral floating displays [Hong et al. 2012] and for head-mounted3D displays of projection-type [Javidi and Hua 2014]. All of thesemethods are based on the principles of integral imaging displays,which generate light fields by using a lens array.

Our work demonstrates how compressive light field displays canbe extended to AR applications. For the present study, we imple-mented HOEs, which only diffuse incident light from a specific di-rection. The optical property of angular selectivity makes it possi-ble to design see-through multi-layered displays (additive light fielddisplays). Transparent multi-layered displays present new possi-bilities in this field, because they convey high transparency whilemaintaining image fidelity. Also, the proposed system can impartmotion parallax to observers. We expect that the additive light fielddisplay can be modified for use with a head-mounted display.

3 Additive Light Field Displays

This section describes the principles of additive light field displays.First, we introduce diffuser HOEs (DHOEs) for see-through pro-jection screens. Descriptions of the recording and reconstructionprocesses for DHOEs are presented. Second, we describe how light

3http://www.google.com/glass4http://www.microsoft.com/microsoft-hololens/en-us

fields from DHOE layers are merged into a single light field by ad-dition. The light fields from the layers do not interfere with eachother since the illumination sources are incoherent. Third, we de-scribe how an additive light field display expresses an optimizedlight field with a non-negative least squares method. We concludeby solving an optimization problem and presenting simulation re-sults.

3.1 Diffuser Holographic Optical Elements

3.1.1 Recording Process

Figure 2 shows the recording scheme of DHOEs. Three coherentlight sources are used for the full-color expressions of red, green,and blue. Neutral density filters are placed in front of the threelight sources in order to modulate power densities, which affect thediffraction efficiency of each color in the reconstruction process.The three laser beams are merged into a single laser beam usingdichromatic mirrors. The exposure time of the single laser beam iscontrolled by an electric shutter. Then, the laser beam is convertedto the collimated plane wave using a spatial filter and a collimatinglens. The laser beam is divided into signal and reference waves us-ing a beam splitter. Mirrors guide the signal and reference wavesto the holographic material. The signal wave passes a diffuser be-fore it is introduced to the holographic material, while the referencewave is introduced directly to the holographic material.

Details of the recording are described on the right side of Fig. 2.The signal wave is converted to a scattered wave from the colli-mated plane wave via passage through the diffuser. The referencewave is introduced on the holographic material from the oppositeside. Since the signal and reference waves are coherent, the twowaves create an interference pattern on the holographic material.The interference pattern is recorded in the holographic material asa form of volume grating via refractive index modulation. Utiliz-ing photopolymers that have definite optical transparency as holo-graphic materials, we fabricate transparent projection screens. Thedetails of the principles for the recording of the HOEs are presentedin Supplementary Appendix A.

3.1.2 Reconstruction Process

In the reconstruction process, the DHOE converts an incident wave-front to that of a signal wave (diffusing wave) when the Bragg con-

dition is satisfied. The Bragg condition is satisfied if a probe waveis projected on the DHOE with a wavefront identical to the refer-ence wave of the recording process. The details of the principles ofthe Bragg condition are described in Supplementary Appendix A.In the Bragg condition, the wavefront of the probe wave is scatteredby diffraction since a diffusing wavefront is recorded as the signalwave. The scattered wave is referred to as a reconstructed wavewhose wavefront is identical to the signal wave. The amplitude ofthe probe wave, which corresponds to the projected image informa-tion, is preserved after diffraction. Thus, the image is displayed onthe DHOE plane, which means the DHOE functions as a projectionscreen under the Bragg condition.

R

G

BCollimating optics

RelayOptics

Real object

DHOE

(b)(a)

(a)

PH

(b1) (b2)

DHOE

DHOE

Figure 3: The reconstruction process of DHOEs as illustrated witha 1-layer DHOE system. The reconstruction system consists of col-limating and screen parts. Details of the collimating optics (a) andDHOE screen (b) are described. (b1) and (b2) indicate the angularselectivity and transparency of the DHOE screen, respectively.

The reconstruction system using beam projectors with a DHOElayer is shown in Fig. 3. First, white illumination from a back-light source is divided into three primary colored beams (red, green,and blue) using dichroic mirrors. Each colored beam is modulatedby a separate LCD panel. Then, a dichroic prism recombines andguides the three colored beams into relay optics. The combinedbeam passes through collimating optics, which convert the beamto a collimated plane wave. The function of the collimating opticsalso includes noise filtering and beam expanding. Finally, the col-limated plane beam is introduced to the DHOE in an appropriateangle and is diffused at the DHOE plane. The displayed images areupdated by the beam projector in a manner of conventional beamprojection systems.

If a probe wave, which does not satisfy the Bragg condition, is in-troduced to the DHOE, the probe wave passes through the DHOEwithout diffraction, as illustrated in Fig. 3(b1). Figure 3(b2) de-scribes a real-world scene passing through the DHOE withoutdiffraction, since the Bragg condition is not satisfied. This propertyallows us to apply the DHOE as a transparent projection screen.The DHOE shows transmittance that is superior to half mirrors,which partially transmit and reflect a real-world scene. In addition,we are able to design the probe wave to diffuse at a desired depthby using multi-layer DHOEs. If each DHOE is designed to havea different angular selectivity, the incident angle of a probe wavedetermines the DHOE layer that diffuses the probe wave.

3.2 Additive Light Fields

3.2.1 Incoherent Addition of Light Fields

Figure 4 describes how the additive light field displays work withmulti-layer DHOEs. Each DHOE is fabricated via the recording

process described in Section 3.1.1. In the recording processes ofDHOEs 1 and 2, the incident angles of the reference waves are θ1and θ2, respectively. In the reconstruction process, probe waves 1and 2 are incident on the 2-layer DHOEs with different angles. Theincident angles of probe waves 1 and 2 are θ1 and θ2, which areidentical to reference waves 1 and 2, respectively. Since DHOEs1 and 2 have different angular selectivity broadbands, probe wave2 is diffracted by DHOE 2 while it passes through the DHOE 1.On the other hand, probe wave 2 is scattered only by DHOE 1.Consequently, DHOEs 1 and 2 function as rear and front projec-tion screens, respectively, for compressive displays. However, inpractical application, probe waves 1 and 2 are weakly diffracted byDHOEs 2 and 1, respectively, which is referred to as a ghost effect.The reconstructed waves from the DHOE layers are merged intoa single wave. Since the waves are from incoherent illuminationsources, it can be described using the following equation:

Itotal = I1 + I2, (1)

where Itotal is the intensity distribution of the merged wave, andI1 and I2 are the intensity distributions of the reconstructed wavesfrom DHOEs 1 and 2, respectively.

Probe wave 1Probe wave 2

𝒛𝒛 = 𝒉𝒉𝟐𝟐

𝒛𝒛 = 𝒉𝒉𝟏𝟏

𝒛𝒛 = 𝟎𝟎

Probe wave 2Probe wave 1

Merged wave

: transmission

: scattering

1θ

2θ

DHOE 2

DHOE 1

𝑰𝑰𝟐𝟐

𝑰𝑰𝟏𝟏

𝑰𝑰𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕

Figure 4: The principle of the additive light field display is illus-trated with a stack of two DHOE layers. Each layer generates in-dependent additive light fields, which are merged into a single lightfield.

3.2.2 Parameterization for Additive Light Fields

In 4D light fields, rays in 3D space are parameterized by a pairof points on two parallel planes. A light field L(Px, Py, Qx, Qy)which passes through two points, P and Q, which are locatedon the DHOE 1 and DHOE 2 planes, respectively. If the probewaves 1 and 2 are projected on the 2-layer DHOEs, a couple ofthe rays corresponding to the light field L(Px, Py, Qx, Qy) are re-constructed independently at points P and Q. Thus, the light fieldL(Px, Py, Qx, Qy) is given using the following equation:

L(Px, Py, Qx, Qy) = I1(Px, Py) + I2(Qx, Qy), (2)

where I1 and I2 are intensity distributions of the diffused imagesfrom DHOEs 1 and 2, respectively. When more than two DHOElayers are stacked for an additive light field display, it is morestraightforward to parameterize light fields with a point on the xyplane and two angles. The two angles θx and θy are defined asfollows:

θx = tan−1 rxrz, θy = tan−1 ry

rz, |θx| , |θy| ≤ θd (3)

where ~r = (rx, ry, rz) denotes a direction vector of a ray, andθd is the diffusing angle of the DHOE layers. The 4D light field,

which is generated from the n-layer of the DHOEs, is given usingthe following equation:

L(x, y, θx, θy) =

n∑i=1

Ii(x+ hi tan θx, y + hi tan θy), (4)

where Ii is the intensity distribution of the diffused image fromthe i-th DHOE layer, and hi indicates the depth of the i-th DHOEplane, as described in Fig. 4. Equation (4) is based on the assump-tion that the scattering profile of the recorded diffuser is uniform.

3.3 Non-Negative Least Squares Problem

1( , )L x θ

1x

mx

1x

mx

( , )nL x θ

1 1( , )L x θ

11 11( : column number)a i b i iδ δ+

( , )m nL x θ

1( )I x

1x

mx

1x

mx

2 ( )I x

( : column number)mn mna i b i iδ δ+

Figure 5: A method that can be used to express the least squaresproblem by matrices is illustrated with 2D light fields and a coupleof 1D additive layers. The column vectors of the target light fieldsand parameters are described on the left and right-hand sides, re-spectively. Each row of the projection matrix is determined by thespecifications of target light fields and by the structure of the layers.

For the additive light field display, we are compelled to solve thefollowing problem:

min‖Lt(x, y, θx, θy)− L(x, y, θx, θy)‖, (5)

where Lt(x, y, θx, θy) is the target light field, which is desired tobe emitted from the additive light field display. If the parametersfor the light field are assumed to be discrete, the light field couldbe represented as a 4D matrix. The matrix can be reshaped to acolumn vector Lt with M elements, as shown in Fig. 5. The inten-sity distributions from the n-layer DHOEs are also represented as acolumn vector I with N elements. We define the projection matrixP as a binary matrix with N columns and M rows. When the pro-jection matrix is multiplied by the column vector I , the elements ofthe column vector I are selectively summed for each row. Thus, theprojection matrix can be designed to satisfy the following equation,which corresponds to Eq. (4):

Li =

N∑j=1

PijIj , (6)

where Li denotes the additive light field L(i;x, y, θx, θy), and P isthe projection matrix. Consequently, Eq. (5) can be rewritten withthe column vectors and matrix as follows:

min‖Lt − PI‖. (7)

Finding an optimized solution for Eq. (7) is to solve linear the leastsquares problem. However, there is a constraint whereby the ele-ments of the column vector I should be positive since the intensityof illumination cannot be less than zero. Hence, a non-negativeleast squares problem is encountered. The trust region algorithm[Coleman and Li 1996] is applied to solve the problem. Figure 6demonstrates the simulation results of the introduced algorithm.

4 Implementation

In this section, we describe the implementation process of the ad-ditive light field display prototype. First, a description is presentedfor the recording process of the DHOEs. Second, a reconstructionsystem for additive light fields is demonstrated. Detailed config-urations of recording and reconstruction systems are described inSupplementary Appendix B. In the last of this section, we intro-duce the software that is used for the prototype.

4.1 Recording System

To record a full-color DHOE, we apply a wavelength multiplexingmethod [Coufal et al. 2000]. Three different lasers are used forthe coherent illumination sources with three colors: red (CoboltFlamenco, 660 nm), green (Coherent Verdi, 532 nm), and blue(Spectra-Physics Excelsior, 473 nm). Photopolymers (HX film)provided from Covestro AG are utilized as the holographic mate-rial. The diffuser is a holographic diffuser from Edmund with adiffusing angle of 10◦. The signal wave passes through the diffuserand is introduced to the photopolymer in the normal direction. Thereference wave is guided by two mirrors and introduced to the pho-topolymer. The incident angles of the reference waves for recordingDHOEs 1 and 2 are 45◦ and 60◦, respectively. The different inci-dent angles are set in order to reduce the ghost effect. The exposedenergies of the red, green, and blue lasers are 36 mJ/cm2, 10.92mJ/cm2, and 32.4 mJ/cm2, respectively. Table 1 describes the spec-ifications of the recording process for the DHOEs.

4.2 Reconstruction System

For the additive light field display, we use PT-AE1000E beam pro-jectors that support a 1920×1080 spatial resolution with scanningfrequencies 30-70 kHz and 50-87 Hz for horizontal and verticaldirections, respectively. The relay optics are replaced by invertedprojection lenses in the beam projectors. Two 0.16×silver seriestele-centric lenses from Edmund function are used as the collimat-ing and noise filtering optics. The projection beam-size, which isdetermined by the tele-centric lens, is 48×27 mm2. The collimatedprojection beams are guided to the DHOEs by mirrors as probewaves. The probe waves 1 and 2 are introduced to the DHOEsat angles of 45◦ and 60◦, respectively. The DHOE screen has acircular form with a diameter of 37 mm. The prototype of the ad-ditive light field display has a viewing window of 30×22.5 mm2

with 692×900 pixels that provide 595 dpi under ideal conditions.In practical, the dpi is 406, which reflects a decline of 32% causedby the optical blur of the collimating system. The gap between theDHOE layers is set at 6 or 10 mm. The gaps show the flexibilityof the system design, which is achieved with low diffraction of theDHOE layers. The 10 mm thickness system (prototype A) showsan additive light field display that is free from the diffraction effect.For the system with a 10 mm thickness, the viewing angle is setto 3◦ while the field of view for the target light fields is rescaledto 10◦ in order to demonstrate a more defined parallax view. Onthe other hand, the 6 mm thickness system (prototype B) generatesactual-size virtual 3D images with a viewing angle of 10◦.

Figure 7 shows photographs of the additive light field display proto-type. We used various 3D images in order to exhibit the versatilityof the additive light field display. The first is a 3D image of a statueof Mercury with minute details. In that result, minute details suchas the folds of clothing or locks of hair are expressed. The secondis a 3D image of two pair of dice with different colors and depths.Full-color and occlusion effect between the dice can be observed.The third includes 3D images of a toy plane, tropical fish, and a Chi-nese dragon, which confirms the generality for types of 3D images.

5 layersTarget light fields 2 layers 3 layers

9th

view

41st

view

Addi

tive

light

fiel

d di

spla

yOptimized additive layers

2 layers 3 layers

5 layers

2 la

yers

3 la

yers

5 la

yers

9th

41st

Figure 6: Simulation results are described for the additive light field displays with two, three, and five layers. Corresponding optimizedimages of the additive layers are shown in the bottom row. According to an increase in the number of layers, image fidelity improves as shownin the enlargements of the reconstructed images.

In addition, small real objects (house, dice, cars, lady, and tree) areplaced behind the DHOE layers. The real objects can clearly beobserved, which proves that the system has see-through properties.

Table 1: Specifications for recording the DHOE layers 1 and 2.

DHOE1 45◦

DHOE2 60◦Incident angleof reference

wave

473 nm 32.4 mJ/cm2

532 nm 10.92 mJ/cm2

660 nm 36 mJ/cm2

Exposedenergy forfull-color

Diffusing angle 10◦Referencediffuser

4.3 Software

The target light fields used for the additive light field display arerendered using POV-Ray. The target light fields consist of 7×7views, which capture parallax images of 3D scenes within a fieldof view of 10◦. The spatial resolution of each parallax image is512×384. We apply an additional focal blur effect on some of thetarget light fields by using an inner function of POV-Ray.

We employ a Matlab LSQLIN solver to determine optimized solu-tions for the non-negative least squares problems described in Eq.(7). The solver is based on a trust region method [Coleman andLi 1996]. We use a 2.8 GHz 64-bit Intel Xeon E5-2680 worksta-tion with 256GB of RAM to solve the least squares problems. Theoptimization requires approximately 6 minutes using 20 iterations.

Alignment of the 2-layer images on the DHOEs is performed usingan image move program, which is designed in a Microsoft Founda-tion Class. The image move program is employed for the resizing,moving, and rotating of the projected images.

5 Evaluation

In this section, the prototype of the additive light field display isevaluated. First, we discuss the valuation of the DHOE layers assee-through projection screens. Diffraction efficiency and transmit-tance of the DHOE layers are demonstrated. Second, we assess thedisplay performances of the additive light field display. The peaksignal-to-noise ratios (PSNRs) of the additive light field display,the attenuation-based display, and the polarization field display aredemonstrated and compared via simulation.

5.1 Diffraction Efficiency and Transmittance

The diffraction efficiency of the DHOE is defined as the ratio ofthe reconstructed wave intensity to the probe wave intensity. Thus,the diffraction efficiency is an important factor in determining thebrightness and energy efficiency of the additive light field display.To measure the diffraction efficiency, a probe wave is guided to theDHOE with a proper incident angle, and then a reconstructed waveis generated, as described in Section 3.1.2. In order to measure thereconstructed wave intensity, an optical power meter is placed infront of the DHOE. The diffraction efficiencies for the red, blue,and color illuminations are measured with the corresponding wave-lengths of the probe waves. The results of the experiment are shownin Table 2.

The transmittance of the DHOE is defined as the ratio of the trans-mitted wave intensity to the incident wave intensity. High transmit-tance is essential to provide a bright real-world scene or to stackmultiple DHOE layers. In order to measure the transmittance ofnatural illumination sources, we use a white light source and anoptical spectrometer. The transmittance of DHOE layer 1 accord-ing to the wavelength is demonstrated in Fig. 8. There are threedips of transmittance since the recorded gratings of the three colorsaffect the transmittance. The average transmittance of the DHOElayer is 0.91, which is high enough to be seen beyond the displaysystem. Figure 9 demonstrates the high degree of transparency ofthe DHOE layers. The SIGGRAPH logo is projected on the front

25th view 9th view 41st view 9th view 41st view

Front layer

Rear layer

Front layer

Rear layer

Front layer

Rear layer

Front layer

Rear layer

Front layer

Rear layer

Original light field Original light field

Original light field Original light field

Original light field Original light field

Original light field Original light field

Original light field Original light field

Prototype A

Prototype A

Prototype B

Prototype B

Prototype A

House (real object)

Cars (real object)

Dice (real object)

Woman (real object)

Tree & Crane (real object)

Figure 7: These photographs of the prototype additive light field display show several reconstructed light field images from the two differentsystems. The first three images (Mercury, toy plane, and dices) are the results of the additive light field display with a 10 mm gap (prototypeA). The other two images (tropical fish and Chinese dragon) are the results of the additive light field displays with a 6 mm thickness (prototypeB). The original light fields, additive layer images, and detailed parallax views are illustrated with the enlargements of the results. Additionalresults and sources of the 3D images are included in Supplementary Appendix C.

DHOE layer. A car, a house, and a lovely couple are real objectsbehind the additive light field display.

Table 2: Diffraction efficiency of the DHOE layer 1.

Incident angle of the probe wave 45◦

473 nm 11.1 %

532 nm 5.8 %Diffraction

efficiency660 nm 23.3 %

The DHOE layer prototype shows a different diffraction efficiencyaccording to the three wavelengths since the exposed power of eachlaser is different in the recording process, as described in Section4.1. Since uniform diffraction efficiency does not guarantee opti-mized color reproducibility, we manually balanced the diffractionefficiency ratio between each color. However, color artifacts arestill observed in the prototype. A rigorous optimization process forthe diffraction efficiency ratio is essential to performing an accu-rate full-color expression. Based on the colorimetry, the optimizeddiffraction efficiency ratio of the DHOE layer could be determinedby the spectral density of the illumination that is utilized as probewaves.

(471, 0.76) (532, 0.81)

(654, 0.69)

Wavelength (nm)

Tran

smitt

ance

0.6

0.8

1

0.4

0.2

0400 500 600 700 800

Figure 8: Transmittance of the DHOE layer 1 is demonstrated.There are three dips, (471, 0.76), (532, 0.81), and (654, 0.69),which correspond to the recorded wavelengths.

5.2 PSNR of Additive Light Field Displays

The three methods for compressive displays show different displayperformances according to utilized algorithms as shown in Fig. 10.We compute the PSNRs in order to assess display performances.The PSNRs are estimated according to the differences between thetarget light fields and the reconstructed light fields. In the sim-ulation, we neglect other technical issues such as the attenuationof brightness by a stack of layers. Figure 10 describes the aver-age PSNRs for the five target light fields. The green, orange, andblue lines correspond to the additive light field display, attenuation-based display, and polarization field display, respectively. Thesolid, dotted, and broken lines indicate PSNRs of reconstructedlight fields derived by trust region [Coleman and Li 1996; Wet-zstein et al. 2011], simultaneous algebraic reconstruction technique(SART) [Andersen and Kak 1984; Lanman et al. 2011], and factor-ization algorithm [Lee and Seung 1999; Hirsch et al. 2014], respec-tively. According to the simulation results, the additive light field

Figure 9: Transparency of the stacks of DHOE layers 1 and 2 isdemonstrated by a photograph. Real objects are clearly observedbeyond the DHOE layers.

22

24

26

28

30

1 3 5 7 9 113 5 117 9

24

26

28

30

PSN

R (d

B)

Number of layers

Additive layers

Attenuation layers

Polarization layers

Trust region

SART

Factorization

221

Figure 10: Average PSNRs of the three compressive displays areestimated with 5 target light fields, which correspond to Fig. 7. Forcomparison, Trust-region, SART, and factorization algorithms areused to compute the PSNRs. The resolutions of the target light fieldsare 512×384 with an angular resolution of 7×7 within a range of[-5,5]. The thickness of the system is 6 mm while the screen size is30×22.5 mm2.

display shows an intermediate display performance from among thethree compressive display methods. When the trust region or SARTalgorithm is utilized, the additive light field display surpasses theattenuation-based display. In the attenuation-based display, a haloeffect appeared since the logarithm transformation amplifies errors.The halo effect is diminished when a factorization algorithm is ap-plied that does not include the logarithm transformation. In thatcase, the attenuation-based display shows a performance that issimilar to that of the additive light field and polarization field dis-plays.

6 Analysis

In this section, we describe two issues of compressive displays.First, the validity of ray approximation for compressive displaysis analyzed with wave optics. Since the SLM consists of pixelatedstructures, the diffraction effect could be considerable under spe-cific conditions. When the diffraction effect could not be neglected,a method to include the diffraction effect in the optimization algo-rithm is described. Second, the inability to express uncorrelated

target light fields is analyzed using a statistical method. The analyt-ical estimation is confined to the additive light field display.

6.1 Validity of Ray Approximation

When a plane wave passes through a rectangular aperture, the waveis diffracted. In the Fraunhofer approximation, the diffraction effectis described as follows [Saleh et al. 2007].

Ii(u, v) = Igsinc2(wxu

λd)sinc2(

wyv

λd), (8)

where the rectangular aperture is placed at the origin point (0, 0);Ii(u, v) is the intensity of the diffracted wave at (u, v, d); Ig is theintensity of the incident plane wave; wx and wy are the width andheight of the rectangular aperture, respectively; and, λ and d are thewavelength and propagation distance of the wave, respectively. If dis sufficiently large compared with u or v, Eq. (8) can be approxi-mated as follows:

Ii(θx, θy) ≈ Igsinc2(wxu

λθx)sinc

2(wyv

λθy), (9)

where θx and θy are tan−1(u/d) and tan−1(v/d), respectively.

Since the SLM consists of pixelated rectangular apertures, each in-cident wave is diffracted at each pixel, as described above. Thisdiffraction effect, which is not considered in the optimization, coulddegrade the image fidelity of compressive displays. For instance,the diffraction effect in compressive displays with 2-layer SLMsis analyzed as follows. First, a local plane wave from a pixelP (xp, yp) of the rear SLM is considered, which is approximatedto a ray L(xp, yp, θx, θy) in a 4D light field. When the localplane wave passes through a pixel Q(xq, yq) of the front SLM, thewave is diffracted by the rectangular aperture of the pixel Q. Thediffracted wave is divided into local plane waves, which can be ap-proximated to a set of rays. Each ray passes the pixelQwith alteredpropagation angles θ′x and θ′y . Tracing back the optical path of therays, the rays are parameterized in a 4D light field domain.

x′p = xq −4h tan θ′x = xp +4h(tan θx − tan θ′x), (10)

y′p = yq −4h tan θ′y = yp +4h(tan θy − tan θ′y), (11)

where 4h is the gap between SLM layers, and x′p and y′p are the4D light field parameters of rays Ld(x′p, y′p, θ′x, θ′y). According toEq. (9), the intensity of each ray is given as follows:

I(Ld; θ′x, θ′y) ≈ Igsinc2(

wxλ

(θ′x − θx))sinc2(wyλ

(θ′y − θy)).(12)

If we assume that rays with intensities of less than 0.25Ig could beneglected, the set of rays covers an ellipse on the rear SLM plane.The major or minor axis of the ellipse is given by the followingequation:

a = maxθ′x|x′p − xp| ≈ 4hmax

θ′x|θ′x − θx| = 4h

λ

wxc0.5, (13)

b = maxθ′y|y′p − yp| ≈ 4hmax

θ′y|θ′y − θy| = 4h

λ

wyc0.5, (14)

where either a or b is the major or minor axis of the ellipse, and c0.5is a constant which is sinc−1(0.5). Since approximation for theoptimization is valid when each axis is smaller than a pixel pitch,the validity condition is described as follows.

vx = | awx| ≈ |4hc0.5λ

w2x

| < 1, (15)

vy = | bwy| ≈ |4hc0.5λ

w2y

| < 1, (16)

where vx and vy are validity coefficients. Consequently, if a pixelpitch is much smaller than the distance to the panel, the ray approx-imation could fail, as described in Fig. 11.

1

10

100

1000

0 200 400 600 800 1000 1200

Dot per inch (DPI)

Thic

knes

s (m

m)

MobileDesktopAdditive light field displays

Content-adaptive parallax barrier

Attenuation-based display

Polarization field display

103

102

101

100

0 200 400 600 800 1000

Prototype 1

Prototype 2

Vertical DPI

Figure 11: A validity curve for the ray approximation is described.The wavelength of illumination is set to 660 nm, to show the largestdiffraction. Ray approximation is not guaranteed in an LCD lay-ered structure with our prototype specifications (vertical dpi), whileit has validity in the other previous prototypes. In order to achievea high dpi with conventional display panels (e.g. LCD layers), thediffraction effect should be considered.

This problem could be alleviated if the diffraction effect is includedin the projection matrices. An example would be a more specificsystem, with valid coefficients, vx and vy , of 2. In this case, theadjacent 25 pixels could generate the same light fields with differentintensities. Thus, the modified light field expression is given usingthe following equation:

Lp =

2∑j=−2

2∑i=−2

kijt1(xp + iwx, yp + jwy)t2(xq, yq), (17)

whereLp indicates a rayL(xp, yp, θx, θy); kij is the intensity coef-ficient derived from Eq. (12); and, t1(x, y) and t2(x, y) denote thespatially varying transmittance functions of the rear and front SLMlayers, respectively. Based on Eq. (17), we could revise the pro-jection matrix for the rear layer. The simulation results are shownin Fig. 12, verifying the analysis of the diffraction effect. However,the optimization time is sacrificed since the number of non-zero el-ements of the projection matrix is increased approximately 25-fold.

6.2 Uncorrelated Target Light Fields

The additive light field display is limited in its generation of un-correlated target light fields. The attenuation-based display has asolution to utilize a front layer as a parallax barrier or pinhole ar-ray, but the additive light field and polarization field displays do nothave an efficient solution. This problem was described in examplesfrom Lanman et al. [2011]. In the present study, we approach theproblem with a statistical method, which enables a more quantita-tive analysis. First, we assume that uncorrelated target light fieldsconsist of independent and identically distributed random variables.We compute expected values of mean squared errors (MSE) with arandom target light fields. The constraints of the least squares prob-lems are neglected in order to determine analytic solutions. Without

Without diffraction

With diffraction

Compensation

Without diffraction

With diffraction Enlargement

Layers

Figure 12: Diffraction effect when the validity constants are 2. The2D (eye chart) and 3D images are blurred when diffraction is con-sidered. When a compensated projection matrix is applied, as de-scribed in Eq. (17), the reconstructed images are improved.

the constraints, the solutions are given by the following equation:

min‖y − Px‖, (18)

x? = PP+y, (19)

where x and y indicate parameters and a target light field, respec-tively; x? is the solution of the least squares problem; and P+ isthe pseudoinverse of the projection matrix P. Thus, errors in thesolution are given by the following equation:

error = (I− PP+)y = Cn×ny, (20)

where I is an n × n unit matrix, and C is an n × n matrix definedas C = I − PP+. Using Eq. (20), we derive the expected value ofMSE, as follows:

E [MSE] =1

nE

[n∑i=1

(

n∑j=1

Cijyj)2

]=

1

n

n∑i=1

(µ2i + σ2

i ), (21)

where σi = σ(y)(∑nj=1 C

2ij)

12 and µi = E(y)

∑nj=1 Cij . The

details of the derivations are described in Supplementary AppendixD.

According to Eq. (21), the expected value of the MSE for the ad-ditive light field display is estimated, and is shown in Fig. 13. Thedetails of the specifications that are used to design the projectionmatrix are described as follows. We consider a 1D k-layered struc-ture that generates 2D light fields. The random distribution of thetarget light field is assumed to be a uniform distribution within [0,1]. The layer distance is given by h = D/k where D is the thick-ness of the light field display. The spatial resolutions of each layerand the target light fields are rs, and the angular resolution of thetarget light fields is ra. The compression ratio is utilized as a ma-nipulated variable, and is defined as follows:

Cr =rsrarsk

=rak. (22)

The blue line and orange dots in Fig. 13 indicate the expected andsampled PSNRs of the additive light field display according to thecompression ratio. The sampled PSNRs are average values, whichare derived by the trust-region algorithm with constraints from 30sets of uncorrelated target light fields.

10

12

14

16

18

20

0 2 4 6 8 10 12

Average PSNR with constraints

Compression ratio

PSN

R (d

B) Expected value of PSNR without constraints

10

16

18

20

12

14

0 2 4 6 8 10 12

Figure 13: Expected values of the MSE of the additive light fielddisplay without constraints are described. Logarithms of the ex-pected values are utilized as expected PSNRs. For comparison, theaverage PSNRs derived via iteration algorithm with constraints arealso estimated from 30 sets of uncorrelated target light fields.

7 Discussion

7.1 Benefits and Limitations

Multi-layered Displays for AR The additive light field displayis a novel type of compressive light field display that is based on ad-dition rather than on either multiplication or rotating polarization.DHOEs are utilized as transparent projection screens for additivelight field displays. Thus, an additive light field display has the po-tential to be applied to AR. The multi-layered structure of DHOEshas several merits for compressive displays. Issues such as diffrac-tion, brightness, color-channel cross talk, and moire, which appearin the use of stacked LCDs, are significantly improved with multi-layer DHOEs. Hence, the additive light field display with DHOEscould be an effective method to realize compressive displays withhigh a dpi.

In the present study, we implement a prototype of the additive lightfield display. High fidelity in reconstructed light fields is demon-strated in the display results. Full-color expression is realized withfull-color DHOE layers. The pixel density of the additive light fielddisplay prototype is estimated at 406 dpi, which is about 5 timeshigher than moderate LCD panels. The average transparency ofeach DHOE layer is about 90%, which is superior to other beamcombiners such as beam splitters and waveguides. The additivelight field display shows a display performance that is similar tothat of the polarization field and the attenuation-based displays. Weanalyze the diffraction effect of a stack of SLM layers as well asthe validity of the ray approximation for compressive displays. Ac-cording to the analysis, the ray approximation is valid only for theadditive light field display in instances where a high pixel densityis essential.

Ghost Effect The experimental results of the prototype show aghost effect, which degrades the image fidelity. A ghost effect oc-curs due to an undesired diffraction of probe waves (Bragg mis-matched reconstruction [Lee et al. 2016]). For instance, the frontDHOE layer weakly diffracts a probe wave that is intended to bediffracted only by the rear DHOE layer. In addition, a probe wavereflected by the rear DHOE layer could also be diffracted by thefront layer. A detailed analysis of the ghost effect is included inSupplementary Appendix E. In order to alleviate the ghost effect,we establish angular spacing between the incident angles of theprobe waves. There are some methods that can be employed forfurther improvement. First, we can utilize anti-reflection glasses,or we could block the optical paths of reflected light with half-waveplates and polarizers. Second, it is also possible to use thicker pho-topolymers for recording DHOEs, which have a higher degree ofangular selectivity.

Optical Blur Since the collimating system of the prototype in-volves a chromatic aberration, color dispersion is observed in thedisplay results. The color dispersion blurs the effective pixel pitch,leading to a degradation of the spatial resolution. Meanwhile, theimaged pixels are so small that the projection beam has a narrowdepth of focus, which could be responsible for the blurred images.These artifacts, which we call optical blur, are demonstrated in Sup-plementary Appendix E. Because of the optical blur, the dpi of aprojected image can decline from 595 to 406. The optical blur couldbe alleviated through several engineering efforts. First, free-formwaveguides can function as collimating optics and compensatorsfor chromatic dispersion. Second, laser projectors can replace beamprojectors for extending the depth of focus.

More than 2 DHOE Layers In this paper, we utilize a 1D an-gular selectivity of the DHOE layer. Nonetheless, the DHOE layerhas a 2D angular selectivity. Thus, we could design a 4-layer sys-tem with projections from left, right, top, and bottom. However, theimplementation of a prototype with 3 or more DHOE layers wouldinvolve more engineering issues. A display system for each layerwould be too bulky to allow an increase in the number of layers.Optimizing the system size should precede an increase in the num-ber of layers. Applying free-form waveguides and pico-projectorscould simplify the system. Also, we could utilize a diverging wavefor the reference wave in the recording process. The projectionbeams could then function as probe waves without collimating op-tics in the reconstruction process. Another engineering issue of theprototype is a small display window, which would attenuate the ne-cessity of a multi-layered system. The display window could beenlarged using holographic printing methods.

Uncorrelated Light Fields The additive light field display has anintrinsic limitation, which is analyzed in Section 6.2. This difficultyin compressing uncorrelated light fields is a common issue for theattenuation-based and polarization field displays. The attenuation-based display, however, is relatively free from this problem sincethe front SLM layer could form either a parallax barrier or a pin-hole array. However, when a wide field of view is essential, theattenuation-based display has the same limitation in the absence ofa time-multiplexing method.

Limited DOF & Applications The light field spectrum that isemitted by additive light field displays forms a few lines in the fre-quency domain, which means the depth of field is restricted to theregions nearby the individual layers [Narain et al. 2015]. The lim-ited depth of field could be a barrier for AR applications since vir-tual images are difficult to superimpose over real objects. However,it is able to apply additive light field displays as whiteboards, wind-shields, and in the simulated shooting game shown in Fig. 14. Inaddition, with accommodation cues, additive light field display sys-tems have the potential to be modified for use with head-mounted

Left view

Right view

Front layer

Rear layer

Left view

Right view

Figure 14: Application example of additive light field displays. Wesimulate a shooting game using a static 3D image. The toy house,car, and tree are real objects. The parallax views are captured bymoving the rear layer while the observer’s location remained sta-tionary.

displays. Indeed, head-mounted displays and AR screens usingholographic materials are currently being developed by companiessuch as DigiLens and HoloPro.

7.2 Future Work

HOEs have the potential for the realization of AR. Applying HOEsto conventional display methods will be interesting topics for futurework. For instance, it is feasible to apply HOEs to see-throughhead-mounted displays. HOEs could also function as a transparentprojection screen for a compressive light field projection system[Hirsch et al. 2014].

Methods that include the diffraction effect in optimization algo-rithms could be applied to compressive displays with SLM layers.If the diffraction effect is not severe, the method could enhance thedisplay performance of compressive light field displays.

The principles that govern the additive light field displays couldbe applied to conventional volumetric displays with additive layerssuch as multi-focal plane displays that use switchable lenses [Liuet al. 2008; Love et al. 2009]. A light field stereoscope display withadditive layers has already been simulated by Huang et al. [2015].

Advanced computational techniques for AR could be applied to ad-ditive light field displays. For instance, the introduction of a direct3D interactive system with a Kinect camera [Hilliges et al. 2012]could be an interesting application for an additive light field dis-play. Computer vision algorithm that could recognize and classifyreal objects is another issue [Hagbi et al. 2011] to be explored.

8 Conclusion

We combined compressive light field displays, which is an emerg-ing technology for light field displays, and HOEs. The compres-sive light field displays demonstrated a high level of display perfor-

mances in terms of brightness, resolution, and contrast in applica-tions where conventional glasses-free 3D displays still suffer fromthe trade-off between spatial and angular resolutions. HOEs areversatile optical elements, which have transparency, angular selec-tivity, and an ability for spatial and wavelength multiplexing. In thepresent study, we applied the merits of HOEs to compressive lightfield displays. We implemented and utilized DHOEs as transparentadditive projection screens for compressive displays. Additive lightfield displays enable observers to see real-world beyond a displayin full-color, bright, and high-fidelity 3D images. With advances incomputational technologies, additive light field displays with ARcould be realized in the near future.

Acknowledgements

We would like to thank Soon-gi Park and the anonymous reviewersfor valuable feedback. We also acknowledge the support by Cove-stro AG (formerly, Bayer MaterialScience AG) for providing thephotopolymer Bayfol HX film used for recording the DHOE layers.This work was supported by the IT R&D program of MSIP/KEIT(fundamental technology development for digital holographic con-tents of Korea).

References

AKELEY, K., WATT, S. J., GIRSHICK, A. R., AND BANKS, M. S.2004. A stereo display prototype with multiple focal distances.ACM Trans. Graph. (SIGGRAPH) 23, 804–813.

ANDERSEN, A. H., AND KAK, A. C. 1984. Simultaneous alge-braic reconstruction technique (sart): a superior implementationof the art algorithm. Ultrasonic imaging 6, 1, 81–94.

AZUMA, R. T. 1997. A survey of augmented reality. Presence:Teleoperators and virtual environments 6, 4, 355–385.

CLOSE, D. H. 1975. Holographic optical elements. Opt. Eng. 14,145402.

COLEMAN, T., AND LI, Y. 1996. A reective newton method forminimizing a quadratic function subject to bounds on some ofthe variables. SIAM Journal on Optimization 6, 4, 1040–1058.

COUFAL, H. J., SINCERBOX, G. T., AND PSALTIS, D. 2000.Holographic data storage. Springer-Verlag.

HAGBI, N., BERGIG, O., EL-SANA, J., AND BILLINGHURST,M. 2011. Shape recognition and pose estimation for mobileaugmented reality. Visualization and Computer Graphics, IEEETransactions on 17, 10, 1369–1379.

HILLIGES, O., KIM, D., IZADI, S., WEISS, M., AND WILSON,A. 2012. Holodesk: direct 3d interactions with a situated see-through display. In In Proceedings of the Conference on HumanFactors in Computing Systems, ACM, 2421–2430.

HIRSCH, M., WETZSTEIN, G., AND RASKAR, R. 2014. A com-pressive light field projection system. ACM Trans. Graph. (SIG-GRAPH) 33, 4, 58.

HONG, S.-H., AND JAVIDI, B. 2004. Improved resolution 3dobject reconstruction using computational integral imaging withtime multiplexing. Opt. Express 12, 19, 4579–4588.

HONG, J., KIM, Y., PARK, S.-G., HONG, J.-H., MIN, S.-W.,LEE, S.-D., AND LEE, B. 2010. 3d/2d convertible projection-type integral imaging using concave half mirror array. Opt. Ex-press 18, 20, 20628–20637.

HONG, J., MIN, S.-W., AND LEE, B. 2012. Integral floatingdisplay systems for augmented reality. Appl. Opt. 51, 18, 4201–4209.

HONG, K., YEOM, J., JANG, C., HONG, J., AND LEE, B.2014. Full color lens-array holographic optical element for three-dimensional optical see-through augmented reality. Opt. Lett. 39,1, 127–130.

HUANG, F.-C., CHEN, K., AND WETZSTEIN, G. 2015. The lightfield stereoscope immersive computer graphics via factored near-eye light field displays with focus cues. ACM Trans. Graph.(SIGGRAPH) 34, 4, 60.

HUANG, Y.-T. 1994. Polarization-selective volume holograms:general design. Appl. Opt. 33, 11, 2115–2120.

JANG, C., LEE, C.-K., JEONG, J., LI, G., LEE, S., YEOM, J.,HONG, K., AND LEE, B. 2016. Recent progress in see-throughthree-dimensional displays using holographic optical elements.Appl. Opt. 55, 3, A71–A85.

JAVIDI, B., AND HUA, H. 2014. A 3d integral imaging opticalsee-through headmounted display. Opt. Express 22, 11, 13484–13492.

KASAI, I., TANIJIRI, Y., ENDO, T., AND UEDA, H. 2001. Apractical see-through head mounted display using a holographicoptical element. Opt. Rev 8, 4, 241–244.

KAUFMANN, H., AND SCHMALSTIEG, D. 2003. Mathematics andgeometry education with collaborative augmented reality. Com-puter & Graphics 27, 3, 339–345.

KIM, H.-J., LEE, S.-K., PIAO, M.-L., KIM, N., AND PARK, J.-H. 2015. Three-dimensional holographic head mounted displayusing holographic optical element. IEEE International Confer-ence on Consumer Electronics (ICCE), 132–133.

LANMAN, D., HIRSCH, M., KIM, Y., AND RASKAR, R. 2010.Content-adaptive parallax barriers: optimizing dual-layer 3ddisplays using low-rank light field factorization. ACM Trans.Graph. (SIGGRAPH Asia) 29, 163:1–163:10.

LANMAN, D., WETZSTEIN, G., HIRSCH, M., HEIDRICH, W.,AND RASKAR, R. 2011. Polarization fields: Dynamic light fielddisplay using multi-layer lcds. ACM Trans. Graph. (SIGGRAPHAsia) 30, 6, 186.

LEE, D. D., AND SEUNG, S. 1999. Learning the parts of objectsby non-negative matrix factorization. Nature 401, 788–791.

LEE, S., JANG, C., CHO, J., YEOM, J., JEONG, J., AND LEE,B. 2016. Viewing angle enhancement of an integral imagingdisplay using bragg mismatched reconstruction of holographicoptical elements. Appl. Opt. 55, 3, A95–A103.

LEE, B. 2013. Three-dimensional displays, past and present.Physics today 66, 4, 36–41.

LI, G., JEONG, J., LEE, D., YEOM, J., JANG, C., LEE, S.,AND LEE, B. 2016. Space bandwidth product enhancement ofholographic display using high-order diffraction guided by holo-graphic optical element. Opt. Express 23, 26, 33170–33183.

LIPPMANN, G. 1908. Epreuves reversibles donnant la sensationdu relief. j. phys 7, 4, 821–825.

LIU, S., CHENG, D., AND HUA, H. 2008. An optical see-throughhead mounted display with addressable focal planes. In Proc.ISMAR, 33–42.

LOVE, G. D., HOFFMAN, D. M., HANDS, P. J., GAO, J., KIRBY,A. K., AND BANKS, M. S. 2009. High-speed switchable lensenables the development of a volumetric stereoscopic display.Opt. Express 17, 18, 15716–15725.

MAIMONE, A., LANMAN, D., RATHINAVEL, K., KELLER, K.,LUEBKE, D., AND FUCHS, H. 2014. Pinlight displays: widefield of view augmented reality eyeglasses using defocused pointlight sources. ACM Trans. Graph. (SIGGRAPH) 33, 4, 89.

NARAIN, R., ALBERT, R. A., BULBUL, A., WARD, G. J.,BANKS, M. S., AND O’BRIEN, J. F. 2015. Optimal presen-tation of imagery with focus cues on multi-plane displays. ACMTrans. Graph. (SIGGRAPH) 34, 4, 59.

OLWAL, A., LINDFORS, C., GUSTAFSSON, J., KJELLBERG, T.,AND MATTSSON, L. 2005. Astor: An autostereoscopic opticalsee-through augmented reality system. In Proc. ISMAR, 24–27.

PARK, G., JUNG, J.-H., HONG, K., KIM, Y., KIM, Y.-H., MIN,S.-W., AND LEE, B. 2009a. Multi-viewer tracking integralimaging system and its viewing zone analysis. Opt. Express 17,20, 17895–17908.

PARK, J.-H., HONG, K., AND LEE, B. 2009b. Recent progressin three-dimensional information processing based on integralimaging. Appl. Opt. 48, 34, H77–H94.

SALEH, B. E., TEICH, M. C., AND SALEH, B. E. 2007. Funda-mentals of photonics, vol. 22. Wiley New York.

SASAKI, H., YAMAMOTO, K., WAKUNAMI, K., ICHIHASHI, Y.,OI, R., AND SENOH, T. 2014. Large size three-dimensionalvideo by electronic holography using multiple spatial light mod-ulators. Sci. Rep. 4, 6177.

STATE, A., LIVINGSTON, M. A., GARRET, W. F., HIROTA,G., WHITRON, M. C., PISANO, E. D., AND FUCHS, H.1996. Technologies for augmented-reality systems: Realizingultrasound-guided needle biopsies. ACM Trans. Graph. (SIG-GRAPH), 439–446.

TAKAKI, Y., AND NAGO, N. 2010. Multi-projection of lenticulardisplays to construct a 256-view super multi-view display. Opt.Express 18, 9, 8824–8835.

TAKAKI, Y., AND OKADA, N. 2009. Hologram generation by hor-izontal scanning of a high-speed spatial light modulator. Appl.Opt. 48, 17, 3255–3260.

TAKAKI, Y., AND YAMAGUCHI, Y. 2015. Flat-panel see-throughthree-dimensional display based on integral imaging. Opt. Lett.40, 8, 1873–1876.

WETZSTEIN, G., LANMAN, D., HEIDRICH, W., AND RASKAR,R. 2011. Layered 3d: Tomographic image synthesis forattenuation-based light eld and high dynamic range displays.ACM Trans. Graph. (SIGGRAPH) 30, 1–11.

WETZSTEIN, G., LANMAN, D., HIRSCH, M., AND RASKAR, R.2012. Tensor displays: Compressive light field synthesis usingmultilayer displays with directional backlighting. ACM Trans.Graph. (SIGGRAPH) 31, 1–11.

YEOM, J., JEONG, J., JANG, C., LI, G., HONG, K., AND LEE,B. 2015. Three-dimensional/two-dimensional convertible pro-jection screen using see-through integral imaging based on holo-graphic optical element. Applied optics 54, 30, 8856–8862.