Optical See-Through 2D/3D Compatible Display Using Variable-Focus Lens and Multiplexed Holographic Optical Elements

hv photonics

Article Optical See-through 2D/3D Compatible Display Using Variable-Focus Lens and Multiplexed Holographic Optical Elements

Qinglin Ji 1, Huan Deng 1,*, Hanle Zhang 2, Wenhao Jiang 1, Feiyan Zhong 1 and Fengbin Rao 1

1 College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China; [email protected] (Q.J.); [email protected] (W.J.); [email protected] (F.Z.); [email protected] (F.R.) 2 School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China; [email protected] * Correspondence: [email protected]

Abstract: An optical see-through two-dimensional (2D)/three-dimensional (3D) compatible display using variable-focus lens and multiplexed holographic optical elements (MHOE) is presented. It mainly consists of a MHOE, a variable-focus lens and a projection display device. The customized MHOE, by using the angular multiplexing technology of volumetric holographic grating, records the scattering wavefront and spherical wavefront array required for 2D/3D compatible display. In particular, we proposed a feasible method to switch the 2D and 3D display modes by using a variable- focus lens in the reconstruction process. The proposed system solves the problem of bulky volume, and makes the MHOE more efﬁcient to use. Based on the requirements of 2D and 3D displays, we calculated the liquid pumping volume of the variable-focus lens under two kinds of diopters.

Keywords: optical see-through 2D/3D; variable-focus lens; holographic optical elements

Citation: Ji, Q.; Deng, H.; Zhang, H.; Jiang, W.; Zhong, F.; Rao, F. Optical See-Through 2D/3D Compatible 1. Introduction Display Using Variable-Focus Lens Augmented reality (AR) is a technology which allows computer generated virtual and Multiplexed Holographic Optical imagery to exactly overlay physical objects [1,2]. AR display mainly includes optical Elements. Photonics 2021, 8, 297. see-through type [3], video see-through type [4] and reflection type [5,6] display devices. https://doi.org/10.3390/ At present, the optical see-through display device has become the mainstream technical photonics8080297 solution, because it allows the user to directly watch the real environment light through an image combiner, and improves the user’s perception of the real world. As a kind of Received: 28 June 2021 true three-dimensional (3D) display technology, integral imaging has a compact structure Accepted: 23 July 2021 and can provide various physiological depth cues [7,8]. It is conductive for the natural Published: 27 July 2021 integration of virtual 3D images and real scenes, and is suitable to be integrated into AR display devices [9,10]. However, due to optical modulation of the lens array, integral Publisher’s Note: MDPI stays neutral imaging is not compatible with two-dimensional (2D) display. Although 3D display with regard to jurisdictional claims in can provide depth information that is absent in 2D display, the current 3D resolution published maps and institutional affil- is severely degraded. The 2D display has the advantage of high resolution and large iations. viewing angle, but it can’t replace 3D display. Therefore, some researchers have proposed 2D/3D compatible displays, such as switching backlight units by using polarized pinhole array [11,12] and polymer dispersed liquid crystal (PDLC) [13], or using dynamic parallax grating technology [14], but these technologies cannot be applied to optical see-through Copyright: © 2021 by the authors. AR display devices. Licensee MDPI, Basel, Switzerland. The technology that is key to realizing optical see-through AR display is the image This article is an open access article combiner that overlaps the virtual images and the real scenes together. The image combiner distributed under the terms and can be further divided into two categories: reflection-type devices [15,16] and diffraction- conditions of the Creative Commons type devices [17,18]. Compared with reflection-type devices, the diffraction-type devices Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ have many advantages, such as unique angle selectivity and wavelength selectivity and 4.0/). flexibility of design, as well as high diffraction efficiency and transparency. It can replace

Photonics 2021, 8, 297. https://doi.org/10.3390/photonics8080297 https://www.mdpi.com/journal/photonics Photonics 2021, 8, x FOR PEER REVIEW 2 of 9

biner can be further divided into two categories: reflection-type devices [15,16] and diffraction-type devices [17,18]. Compared with reflection-type devices, the diffraction-type Photonics 2021, 8, 297 2 of 9 devices have many advantages, such as unique angle selectivity and wavelength selectivity and flexibility of design, as well as high diffraction efficiency and transparency. It can replace one or several optical elements in the system and is an ideal image combiner [19].one orYeom several et al. optical proposed elements a 2D/3D in the converti systemble and projection is an ideal system image using combiner see-through [19]. Yeom in- tegralet al. proposedimaging based a 2D/3D on convertibleHOE. The use projection of prism system reduced using the see-through number of integral projectors imaging and enabledbased on a HOE.compact The form use of factor, prism but reduced the utilization the number of the of projectors HOE was and only enabled 50%, that a compact is, one halfform of factor, the HOE but thewas utilization used for 2D of thedisplay HOE and was the only other 50%, half that for is, 3D one display half of [20]. the HOE Chou. was et al.used proposed for 2D display a 2D/3D and hybrid the other integral half for imaging 3D display display [20]. based Chou. eton al.a proposedliquid crystal a 2D/3D micro-lenshybrid integralarray (LCMLA), imaging displayin which based the LCMLA on a liquid has the crystal focusing micro-lens effect arrayor no (LCMLA),optical effect in determinedwhich the LCMLA by the haspolarization the focusing state effect of orthe no incident optical effectlight. determinedTherefore, bythe the system polarization added devicesstate of thesuch incident as twisted light. nematic Therefore, cell the and system polarizer added to devicescontrol suchthe polarization as twisted nematic state, and cell increasedand polarizer the toredundancy control the [21]. polarization In our previous state, and work, increased we proposed the redundancy attaching [21 a]. PDLC In our filmprevious to the work, lens wearray proposed HOE toattaching constitute a a PDLC 2D/3D film projection to the lens screen. array The HOE lens to constitutearray HOE a 2D/3D projection screen. The lens array HOE and PDLC film were used to realize integral and PDLC film were used to realize integral imaging 3D display and 2D display, respec- imaging 3D display and 2D display, respectively. However, the PDLC film degraded the tively. However, the PDLC film degraded the transparency of the system, and the opti- transparency of the system, and the optical see-through properties could not be achieved cal see-through properties could not be achieved in 2D mode [22]. in 2D mode [22]. In this paper, we propose an optical see-through 2D/3D compatible display by using In this paper, we propose an optical see-through 2D/3D compatible display by using variable-focus lens and multiplexed holographic optical elements (MHOE). Based on variable-focus lens and multiplexed holographic optical elements (MHOE). Based on angular multiplexing technology, the MHOE records the scattering wavefront of a dif- angular multiplexing technology, the MHOE records the scattering wavefront of a diffuser fuser for 2D display and the spherical wavefront array of micro-lens array (MLA) for 3D for 2D display and the spherical wavefront array of micro-lens array (MLA) for 3D display. display. The incident angles of the projected angles vary with the changes in the varia- The incident angles of the projected angles vary with the changes in the variable-focus ble-focus lens to meet the two Bragg diffraction conditions of 2D and 3D displays. lens to meet the two Bragg diffraction conditions of 2D and 3D displays. Therefore, our Therefore, our approach does not require polarization devices and reduces the systematic approach does not require polarization devices and reduces the systematic complexity, complexity,enhances the enhances effective utilizationthe effective of MHOE utilization and maintains of MHOE optical and see-through maintains properties optical see-throughfor both 2D andproperties 3D displays, for both all 2D of whichand 3D are displays, highly beneficialall of which for are AR highly applications. beneficial for AR applications. 2. Structure and Principle 2. StructureFigure1 and shows Principle the structure of our proposed optical see-through 2D/3D compatible displayFigure system. 1 shows It is the mainly structure composed of our of propos a MHOE,ed optical a variable-focus see-through lens 2D/3D and compatible a projector. displayEssentially, system. the MHOEIt is mainly is a volumetric composed holographicof a MHOE, grating.a variable-focus The scattering lens and wavefront a projector. of a Essentially,diffuser and the the MHOE spherical is a wavefrontvolumetric array holograp of MLAhic grating. are recorded The scattering on the single wavefront volumetric of a diffuserholographic and the grating spherical by two-step wavefront recording array of with MLA angular are recorded multiplexing on the single technology. volumetric The holographicvariable-focus grating lens has by twotwo-step optical recording states of diopterwith angularϕ1 and multiplexingϕ2, and it modulates technology. the lightThe variable-focustransmitted by lens the has projector two optical respectively states of to diopter meet the φ1 two and Bragg φ2, and diffraction it modulates conditions the light of transmittedMHOE. by the projector respectively to meet the two Bragg diffraction conditions of MHOE.

(a) (b)

Figure 1. Schematic diagrams of system structure: (a) 3D image reconstruction when the probe beam satisﬁes the Bragg diffraction condition 1; (b) 2D image display when the probe beam satisﬁes the Bragg diffraction condition 2.

In Figure1a, the probe beam from the projector contains the amplitude information of elemental image array, and illuminates the MHOE after passing through the variable-focus Photonics 2021, 8, x FOR PEER REVIEW 3 of 9

Figure 1. Schematic diagrams of system structure: (a) 3D image reconstruction when the probe beam satisfies the Bragg diffraction condition 1; (b) 2D image display when the probe beam satisfies the Bragg diffraction condition 2. In Figure 1a, the probe beam from the projector contains the amplitude information of elemental image array, and illuminates the MHOE after passing through the variable-focus lens with the diopter of φ1. Then, the MHOE’s Bragg diffraction condition 1 is satisfied, and the spherical wavefront array is diffracted out. The elemental image aligns Photonics 2021, 8, 297 with the element of MHOE to reconstruct the 3D image based on the theory of integral3 of 9 imaging. In Figure 1b, the probe beam from the projector contains the 2D image, and illuminates the MHOE after passing through the variable-focus lens with the diopter of φ2. At this time, the MHOE’s Bragg diffraction condition 2 is satisfied, and the scattering lenswavefront with the is diffracted diopter of outϕ1. Then,to achieve the MHOE’s 2D display. Bragg The diffraction light from condition the real 1scene is satisﬁed, whose andwavelengths the spherical and wavefrontincident angles array don’t is diffracted match the out. Bragg The elemental diffraction image conditions, aligns withdirectly the elementpasses through of MHOE the toMHOE. reconstruct Hence, the the 3D system image basedshows ongood the optical theory see-through of integral imaging. proper- Inties. Figure 1b, the probe beam from the projector contains the 2D image, and illuminates the MHOEIn the reconstruction after passing throughprocess, thethe variable-focusvariable-focus lens lens is with the thekey dioptercomponent of ϕ that2. At plays this time,a role thein the MHOE’s angle selectivity Bragg diffraction of MHOE. condition It can 2accurately is satisﬁed, change and the the scattering incident angles wavefront of the is diffracted out to achieve 2D display. The light from the real scene whose wavelengths and reconstructed beam under different diopter conditions in order to meet the Bragg incident angles don’t match the Bragg diffraction conditions, directly passes through the matching angles. In the 3D mode, the divergent angle of projected beam is 2U1, and it MHOE. Hence, the system shows good optical see-through properties. doesn’t change after passing through the variable-focus lens with the diopter of φ1 = 0D. In the reconstruction process, the variable-focus lens is the key component that plays The conical beam still maintains the divergent angle of 2U1 when it arrives at the MHOE, a role in the angle selectivity of MHOE. It can accurately change the incident angles of the the incident angles of the two boundary beams are θl1 and θr1, respectively, as shown in reconstructed beam under different diopter conditions in order to meet the Bragg matching Figure 2a. The θl1 and θr1 can be expressed as angles. In the 3D mode, the divergent angle of projected beam is 2U1, and it doesn’t change after passing through the variable-focusθ lens=°−+ withβ the diopter of ϕ = 0D. The conical beam l1190 U , 1 (1) still maintains the divergent angle of 2U1 when it arrives at the MHOE, the incident angles of the two boundary beams are θl1 andθ θr=°−−1, respectively,β as shown in Figure2a. The θl1 and r1190 U , (2) θr1 can be expressed as ◦ θl1 = 90 − β + U1, (1) where β is the complement angle between the MHOE surface and the optical axis of θ = 90◦ − β − U , (2) projector. On the 2D mode, the diopterr1 of variable-focus1 lens is φ2. The divergent angle of whereprojectedβ is beam the complementturns into 2U angle2 after betweenpassing through the MHOE the vari surfaceable-focus and the lens. optical The incident axis of projector.angles of the On two the 2Dboundary mode, the beams diopter onto of the variable-focus MHOE are θ lensl2 and is θϕr22., Therespectively, divergent as angle shown of projectedin Figure 2b. beam The turns U2, θ intol2 and 2U θ2r2after can be passing described through as the variable-focus lens. The incident angles of the two boundary beams onto the MHOE are θl2 and θr2, respectively, as shown Uy− ϕ in Figure2b. The U2, θl2 and θr2 can be described= 1 as U2 , (3) U −ny'ϕ U = 1 , (3) 2 n0 θ =°−+90 β U , (4) l 22◦ θl2 = 90 − β + U2, (4) θ =°−−◦ β θr2r=229090− β − UU2,, (5)(5) where y is the height of the projected beam formed onto the back surface of the variable- focuswhere lens, y is nthe0 is height the refractive of the indexprojected of the beam liquid formed in the onto variable-focus the back surface lens. of the variable-focus lens, n’ is the refractive index of the liquid in the variable-focus lens.

(a) (b)

Figure 2. The projected beam matching with the Bragg matching angles under different diopters of the variable-focus lens: (a) 3D mode; (b) 2D mode.

Compared with the conventional optical elements, the HOEs possess useful properties originating from their volumetric holographic grating structures, namely their selectivity and multiplex ability. The selectivity means HOEs have optical see-through properties, and it is easy to utilize the multiplex ability to superpose different functions of optical elements in the single volumetric holographic grating. Figure3 illustrates the design and two-step recording process of MHOE used in this paper. Figure3a shows the ﬁrst recording process Photonics 2021, 8, x FOR PEER REVIEW 4 of 9

Figure 2. The projected beam matching with the Bragg matching angles under different diopters of the variable-focus lens: (a) 3D mode; (b) 2D mode.

Compared with the conventional optical elements, the HOEs possess useful properties originating from their volumetric holographic grating structures, namely their selectivity and multiplex ability. The selectivity means HOEs have optical see-through prop- Photonics 2021, 8, 297 4 of 9 erties, and it is easy to utilize the multiplex ability to superpose different functions of optical elements in the single volumetric holographic grating. Figure 3 illustrates the design and two-step recording process of MHOE used in this paper. Figure 3a shows the firstthat recording records the process spherical that wavefrontrecords the array spherical generated wavefront by the array MLA. generated The reference by the MLA. beam Theilluminates reference the beam holographic illuminates plate the with holograp the divergenthic plate angle with of 2theU1 .divergent The indent angle angles of of 2U the1. Thetwo indent boundary angles beams of the are twoθl1 boundaryand θr1. The beams signal are beam θl1 and illuminates θr1. The signal the MLA beam vertically illuminates and thegenerates MLA vertically spherical wavefrontand generates array. spherical The spherical wavefront wavefront array. arrayThe spherical is projected wavefront onto the arrayother is side projected of the holographic onto the other plate, side and of interferes the holographic with the referenceplate, and beam interferes in the with region the of referenceL1. As a result,beam in the the spherical region of wavefront L1. As a result, array isthe recorded. spherical Figure wavefront3b presents array is the recorded. second Figurerecording 3b presents process thatthe second records recording the scattering proc wavefrontess that records of a diffuser. the scattering The reference wavefront beam of ailluminates diffuser. The the reference holographic beam plate illuminates with the divergentthe holographic angle of plate 2U2 with. The the indent divergent angles angle of the oftwo 2U boundary2. The indent beams angles are θ lof2 and the θtwor2. Meanwhile, boundary beams the signal are beamθl2 and illuminates θr2. Meanwhile, the diffuser the signalvertically beam and illuminates generates scatteringthe diffuser wavefront. vertically Theand scattering generates wavefront scattering iswavefront. projected ontoThe scatteringthe other sidewavefront of the holographic is projected plate, onto andthe other interferes side withof the the holographic reference beam plate, in and the regioninter- feresof L2 .with the reference beam in the region of L2.

(a) (b)

FigureFigure 3. 3. Two-stepTwo-step recording recording process process of of MHOE: MHOE: ( (aa)) First First recording recording with with the the MLA; MLA; ( (bb)) second second recording recording with with the the diffuser. diffuser.

3.3. Experiments Experiments and and Results Results 3.1.3.1. Fabrication Fabrication of of Variable-Focus Variable-Focus Liquid Liquid Lens Lens and and MHOE MHOE InIn experiments, experiments, we we fabricated fabricated a a variable-focus variable-focus liquid liquid lens. lens. The The operating operating mechanism mechanism ofof the the liquid liquid lens lens is is that that its its focal focal length length is is controlled controlled by by pumping pumping liquid liquid in in and and out out of of the the lenslens chamber, chamber, which, which, in in turn, turn, changes changes the the curv curvatureature of of the liquid profile. proﬁle. Therefore, Therefore, the the volumevolume of pumping liquidliquid isis controlled controlled to to adjust adjust the the diopter diopter of theof the liquid liquid lens lens to satisfy to satisfy two twoBragg Bragg diffraction diffraction conditions. conditions The. radiusThe radius of curvature of curvature (R) and (R volume) and volume change change∆V follow ΔV followthe relationship the relationship [23]: [23]:

π 2 22r 2 ! r 2 ! 2 π 22ddd2 d d d ∆Δ=VVR= 222R2 − −− −2R RRRRR2 − −2R 2+ +R2 − − ,, (6) (6) 3 4 4 4 34 4 4 where d is the diameter of the lens aperture. The variable-focus liquid lens is considered as wherea thin lens,d is the and diameter its effective of the diopter lens aperture. (ϕ) can be Th calculated:e variable-focus liquid lens is considered as a thin lens, and its effective diopter (φ) can be calculated: (n0 − 1) ϕ = , (7) R where the refractive index of the liquid in the experiment is n0 = 1.33. Figure4a shows the changes in the radius of curvature R and diopter ϕ with the variation in volume change ∆V. In the practical experiment, the ϕ was 14.29D and the R was 23 mm, which we chose while ∆V was 8.6 mL. Figure4b,c show the lens effects with the lens diopter of 0D and 14.29D, respectively. Photonics 2021, 8, x FOR PEER REVIEW 5 of 9

()n '1− ϕ = , (7) R

where the refractive index of the liquid in the experiment is n’ = 1.33. Figure 4a shows the changes in the radius of curvature R and diopter φ with the variation in volume change Photonics 2021, 8, 297 ΔV. In the practical experiment, the φ was 14.29D and the R was 23mm, which we chose5 of 9 while ΔV was 8.6mL. Figure 4b,4c show the lens effects with the lens diopter of 0D and 14.29D, respectively.

(a) (b) (c)

Figure 4. Variable-focus liquidliquid lens:lens: ((aa)) CurvesCurves of of the the radius radius of of curvature curvature and and the the diopter diopter of of liquid liquid lens lens with with the the variation variation in thein the volume volume change; change; (b )(b imaging) imaging effect effect at 0D;at 0D; (c) ( Imagingc) Imaging effect effect at 14.29D.at 14.29D.

Figure 55a,ba,b showshow thethe experimentalexperimental setupssetups forfor thethe two-steptwo-step recordingrecording ofof MHOE.MHOE. TheThe fabricatedfabricated variable-focus liquidliquid lenslens was was placed placed in in the the optical optical path path of of the the reference reference beam beam to tochange change the the incident incident angles angles of theof the reference reference beam beam to match to match the Braggthe Bragg diffraction diffraction conditions. conditions.The detailed The detailed parameters parameters are shown are shown in Table in1. Table The pitch 1. The and pitch focal and length focal of thelength recorded of the recordedMLA are 1MLA mm are and 1 3.3 mm mm, and respectively, 3.3 mm, respectively, and the scattering and the angle scattering of the diffuserangle of isthe 20 ◦dif-. fuser is 20°.

(a)

(b)

Figure 5. Experimental setupssetups forfor the the two-step two-step recording recording of of MHOE: MHOE: (a) ( Recordinga) Recording of MLA,of MLA, (b) record-(b) recording of a diffuser. ES, electronic shutter; SF, spatial filter; CL, collimating lens; BS, beam splitter; ing of a diffuser. ES, electronic shutter; SF, spatial ﬁlter; CL, collimating lens; BS, beam splitter; M1, M1, M2, mirror; HP, holographic plate. M2, mirror; HP, holographic plate.

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Table 1. Parameters of the experiment for recording process.

Table 1. ParametersComponents of the experiment for recordingParameters process. Values θl1 57.2° ComponentsBragg matching Parameters angles 1 Values θr1 32.8° Bragg diffraction conditions ◦ θθll21 45°57.2 BraggBragg matching matching angles angles 1 2 ◦ θr1 32.8 Bragg diffraction conditions θr2 45° ◦ θl2 45 Bragg matchingWidth angles 2L1 23 mm◦ Recording region θr2 45 Width L2 18 mm Width L1 23 mm Recording region Pitch 1 mm MLA Width L 18 mm Focal length2 3.3 mm Pitch 1 mm MLADiffuser Scattering angle 20° Focal length 3.3 mm Thickness 15 ± 1 µm Diffuser Scattering angle 20◦ Sensitive wavelength 532 nm Photopolymer plate SensitivityThickness 10 15 mJ/± 1cm²µm Sensitive wavelength 532 nm Averaged refractive index 1.47 Photopolymer plate Sensitivity 10 mJ/cm2 RefractiveAveraged index refractive modulation index >0.02 1.47 Refractive index modulation >0.02 In order to obtain high diffraction efficiency, we actually used two holographic plates and recorded each optical element independently. The MHOE was obtained by In order to obtain high diffraction efficiency, we actually used two holographic plates andusing recorded a frame each (GCM-1301M optical element in Daheng independently. Optics) to The clip MHOE the two was holographic obtained byplates using to- agether. frame (GCM-1301MThe fabricated inMHOE Daheng was Optics) tested with to clip reference the two beams holographic under the plates corresponding together. TheBragg fabricated diffraction MHOE conditions. was tested Figure with 6a,b reference show beamsthe diffraction under the effects corresponding of the MLA Bragg and diffractiondiffuser, respectively. conditions. FigureThe real-world6a,b show scene the diffraction behind the effects MHOE of is the clearly MLA observed and diffuser, with- respectively.out visual obstruction, The real-world which scene verifies behind the thesee-through MHOE is properties clearly observed of MHOE, without as shown visual in obstruction,Figure 6c. Figure which verifies6d shows the the see-through relation be propertiestween normalized of MHOE, diffraction as shown efficiency in Figure 6andc . Figureangle6 ddeviation. shows the The relation diffraction between efficiency normalized starts diffraction to decline efficiency sharply andat about angle ±5°. deviation. The an- Thegular diffraction difference efficiency between starts the two to decline Bragg matching sharply at angles about is± 12.2°,5◦. The which angular is large difference enough betweento avoid the the twocrosstalk Bragg between matching the anglestwo display is 12.2 modes.◦, which is large enough to avoid the crosstalk between the two display modes.

(a) (b) (c) (d)

FigureFigure 6. 6.Performance Performance testing testing of of MHOE: MHOE: (a ()a Diffraction) Diffraction effect effect of of the the MLA; MLA; (b ()b diffraction) diffraction effect effect of of the the diffuser; diffuser; (c )(c optical) optical see-throughsee-through properties properties of of MHOE; MHOE; (d ()d relationship) relationship between between normalized normalized diffraction diffraction efﬁciency efficiency and and angle angle deviation. deviation.

3.2. Experimental Results 3.2. Experimental Results We developed the experimental system based on the proposed scheme as shown in We developed the experimental system based on the proposed scheme as shown in FigureFigure7a. 7a. The The projector projector has has the the resolution resolution of of 1280 1280× ×800. 800. The The projected projected image image for for the the 3D 3D modemode is is provided provided as as shown shown in in Figure Figure7b. 7b. The The character character “3” “3” and and letter letter “D” “D” are are in in front front of of thethe MHOE MHOE with with the the depth depth of of 35 35 mm mm and and behind behind the the MHOE MHOE with with the the depth depth of of− 35−35 mm, mm, respectively. In addition, a 2D text “Sichuan University” is prepared for 2D display as shown in Figure7c.

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respectively.respectively. In addition, In addition, a 2D atext 2D “Sichuantext “Sichuan University” University” is prepared is prepared for 2D for display 2D display as as shownshown in Figure in Figure 7c. 7c.

(a) (a) (b) (b) (c) (c) FigureFigure 7. (a) 7.Experimental (a) Experimental system; system; (b) elemental (b) elemental image imageimage array; array;array; (c) 2D (( ccimage.)) 2D2D image.image.

On theOn 3D the display 3D display mode, mode, the projected the projected beam beam meets meets the Bragg the Bragg Bragg diffraction diffraction diffraction condition condition condition 1. 1. 1. The 3DThe image 3D image is reconstructed, is reconstructed, and fourand four different differentdifferent perspectives perspectives from fromtop left, top topleft, right, top right, bottombottom left and left bottom and bottom right rightviewing viewing points points are shown areare shown in Figure in FigureFigure 8a. Obvious8 8a.a. ObviousObvious horizontal horizontalhorizontal and verticaland vertical parallaxes parallaxes can be can clearly be clearly seen. seen.Additionally, Additionally, the character the character “3” is “3” bigger is bigger than than letterletter “D”, “D”, which which demonstrates demonstrates that “3”that that is “3” “3” reconstructed is is reconstructed reconstructed in front in in front frontof the of of MHOE the the MHOE MHOE while while while “D” “D” “D” is behindis behind the MHOE. the MHOE. On the On 2D the display 2D2D displaydisplay mode, mode,mo thede, projected the projected beam beam satisfies satisﬁessatisfies the Bragg the BraggBragg diffractiondiffraction condition conditioncondition 2, and 2, 2, and Figureand Figure Figure 8b8 bshows shows8b shows the the displayed displayedthe displayed 2D image.image. 2D image. TheThe real realThe object objectreal “dice”object “dice”“dice”behind behind behind the the MHOE MHOE the isMHOE always is always is visiblealways visible on visible both on both 2Don and both2D 3Dand 2D display 3Dand display 3D modes, display modes, which modes, veriﬁeswhich which the good optical see-through properties of the system. verifiesverifies the good the good optical optical see-th see-throughrough properties properties of the of system. the system.

(a) (a) (b) (b) Figure 8. Experimental results of 2D/3D compatible display with optical see-through properties: (a) FigureFigure 8. Experimental 8. Experimental results results of 2D/3D of 2D/3Dcompatible compatible display displaywith optical with see-through optical see-through properties: properties: (a) 3D images display captured from four different viewing directions; (b) 2D image display. 3D images(a) 3D display images captured display captured from four from different four different viewing viewingdirections; directions; (b) 2D image (b) 2D display. image display.

4. Conclusions4. Conclusions In thisIn paper, thisthis paper,paper, an optical an an optical optical see-through see-through see-through 2D/3D 2D/3D 2D/3D compatible compatible compatible display display display system system system is proposed is proposedis proposed by by usingbyusing using a a variable-focus variable-focus a variable-focus lenslens andlensand a MHOE.aand MHOE. a MHOE. The The scattering scatteringThe scattering wavefront wavefront wavefront and sphericaland sphericaland wavefrontspherical wavefrontwavefrontarray arearray recorded array are recorded are in therecorded MHOE in the in usingMHOE the MHOE angular using using multiplexingangular angular multiplexing technology multiplexing technology to achieve technology 2D/3Dto to achieveachievedisplay, 2D/3D 2D/3D respectively. display, display, respectively. The respectively. variable-focus The variable-focus The variable-focus lens is used lens to islens adjust used is usedto the adjust incident to adjust the incident angles the incident of the anglesprojectedangles of the of projected beam.the projected By beam. analyzing beam. By analyzing the By relationship analyzing the relationship the between relationship the between liquid between change the liquid the and liquid thechange radius change of and theandcurvature radius the radius ofof thecurvature of variable-focus curvature of the of lens,variable the thevariable-focus optimal-focus lens, diopter lens,the optimal ofthe the optimal variable-focus diopter diopter of the lensof varia- the is pickedvaria- ble-focusble-focusup to lens match islens picked the is picked Bragg up to diffractionup match to match the conditions.Bragg the Bragg diffraction Thediffraction incident conditions. conditions. angles The of incident The the projectedincident angles angles beam of theofare projected the calculated projected beam and beam are measured. calculated are calculated When and the measured.and MLA measured. and When diffuser When the wereMLA the recordedMLA and diffuserand on diffuser holographic were were recordedplatesrecorded on based holographic on onholographic angular plates multiplexing plates based based on technology,angular on angular multiplexing the multiplexing variable-focus technology, technology, lens isthe placed varia-the invaria- the ble-focuspathble-focus lens of the islens placed reference is placed in the beam in path the to pathof adjust the of re thetheference incidentreference beam angles beam to adjust ofto theadjust the reference incident the incident beamangles angles through of of the referencethe variationreference beam inbeam through the through liquid the pumping variation the variation volume.in the in liquid the During liquid pumping reconstruction, pumping volume. volume. theDuring incident During recon- anglesrecon- struction,struction,of the the projected incident the incidentbeam angles angles satisﬁed of the of projec the Braggprojected beamted matching beam satisfied satisfied angles the Bragg underthe Bragg matching the samematching angles amount angles of underunderliquid the same pumpingthe same amount amount volume, of liquid of and liquid pumping the sphericalpumping volume, wavefront volume, and theand array spherical the of spherical the wavefront MLA wavefront and thearray scattering array of of the MLAwavefrontthe MLA and theand of diffuserscattering the scattering are wavefront reconstructed. wavefront of diffus Asof diffus aer result, areer reconstructed. are 3D imagesreconstructed. with As proper a Asresult, a horizontalresult, 3D im- 3D andim- vertical parallaxes are reconstructed on 3D display mode and 2D image is displayed on ages ageswith withproper proper horizontal horizontal and verticaland vertical parallaxes parallaxes are reconstructedare reconstructed on 3D on display3D display 2D display mode, and both modes show good optical see-through properties. The images; modemode and 2Dand image 2D image is displayed is displayed on 2D on disp 2D laydisp mode,lay mode, and bothand bothmodes modes show show good good opti- opti- quality would be further improved if a variable-focus liquid lens with multi-chamber is used. The proposed system can be a good candidate in AR application.

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Author Contributions: Conceptualization, Q.J.; methodology, H.D., H.Z. and W.J.; software, F.Z.; validation, Q.J. and F.R.; data curation and writing-original draft preparation, Q.J.; writing—review and editing, H.D. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant numbers 61972147 and 61775151, and the China Postdoctoral Science Foundation, grant number 2021M690287. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest.

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