1. Introduction

Through projecting numerous two-dimensional (2D) perspective views of target three-dimensional (3D) object to dense sub-viewing-zones, the glasses-free super multi-view (SMV) technology [1] can provide 3D display with smooth motion parallax. Each displayed 3D spatial spot is formed by superimposing incoherent light beams coming from different 2D views. The interval between adjacent sub-viewing-zones is set smaller than the pupil diameter of the eye. So, at least two different views are delivered to a single eye pupil and the eyes can focus on the spot. The high-density directional (HDD) display is very similar to SMV, but the used 2D views are orthogonal views. The angle pitch must be small enough to satisfy the condition for SMV display, that is, at least two different views are delivered to a single eye pupil [2]. To provide binocular disparity and motion parallax simultaneously, a large number of sub-viewing-zones are necessary for constructing a wide viewing zone which could not only accommodate two eyes of a viewer but also provide a proper free space for the movement of the viewer. Up to the present, all the studies on SMV or HDD do hard to increase the number of sub-viewing-zones by pure spatial-multiplexing, e.g. using display panel with ultra-high resolution [3,4], adopting more display panels [5,6] or both of them [7]. Technologies of this type have a common feature that at least two light beams for one displayed spatial spot pass through the eye pupil simultaneously.

Time-multiplexing is another method for generating multiple sub-viewing-zones where light beams from different 2D views pass through a displayed spatial spot in a time-sequential manner. In 1990, Travis demonstrated the applicability of time-multiplexing on autostereoscopic 3D display [8]. A planar multi-switch liquid crystal shutter was placed before a 2D cathode-ray tube (CRT). Different vertical-strip switches of the shutter were gated sequentially and then imaged into different sub-viewing-zones through a Fresnel lens. The CRT was refreshed synchronously and rapidly with corresponding 2D views. Eyes at different sub-viewing-zones could perceive corresponding 2D views. Based on the persistence of human vision, autostereoscopic display got realized. Subsequently, time-multiplexing of four CRTs was implemented for more sub-viewing-zones by N. A. Dodgson [9]. They designed a complex lens consisting of 6 element lenses to ensure rays from each pixel of a CRT passing through the corresponding “final face”. Each CRT has a specific “final face”, i.e. a rectangular parallel plane where the whole CRT is visible to each point on it. In order to spatially superimposing 2D views projected from different CRTs, CRTs were aligned in an arc. Therefore, these “final faces” presented different angular offsets between each other. The confliction on occupied physical spaces makes the system accommodate only one planar multi-switch shutter. Thus, if the size of switches was small and multiple CRTs were used for SMV, some “final faces” presented too great deviations from the multi-switch shutter, making some pixels of the corresponding CRTs missed by the switches. So, the system of N. A. Dodgson was not extended to SMV displays. J. Y. Son realized time-multiplexing of two CRTs through using a dichronic prism [10], but their system could not accommodate more CRTs due to complicated optical structures.

In this letter, employing an array of planar aligned OLED microdisplays as display panels, a new SMV technology combining the time- and spatial-multiplexing together is proposed. An array of symmetrically and equally spaced apertures is introduced into the spatial-spectrum plane of the microdisplay array. Through an optical structure, all the display panels are imaged into a common 2D region, but apertures are imaged into different sub-viewing-zones in a time-sequential manner. With different apertures gated sequentially and corresponding perspective views refreshed synchronously, the proposed system can provide enough dense sub-viewing-zones for SMV, while bearing with lower requirement on the number of display panels. Different from that in [9], the “final faces” for all OLED microdisplays in the proposed system overlap on the planar spatial-spectrum plane. The deviation problem in [9] is avoided. Benefitted from gating the spatial-spectrum, the superimposition of 2D views becomes precise.

The rest of this paper is organized as follows. In section 2, a spatial-spectrum time-multiplexing technology based on OLED microdisplay is explained. Based on the developed time-multiplexing, section 3 describes the SMV technology with multiple planar aligned OLED microdisplays. Experiments and results are shown in Section 4. Section 5 analyzes the lateral display resolution limit of the proposed system. Section 6 provides conclusions.

2. Time-multiplexing technology based on OLED microdisplay

The light emission of an OLED pixel presents a large divergence angle. After optical Fourier transformation, the light intensity distribution on the spatial-spectrum plane (P_spectrum) of an OLED microdisplay is approximately homogeneous in the central region, which is a necessary condition to carry out the proposed time-multiplexing technology.

An array of symmetrically and equally spaced apertures will be placed on the P_spectrum plane of an OLED microdisplay k, which constructs a projecting unit. Here five apertures (A_k1, A_k2, A_k3, A_k4 and A_k5) with a horizontal interval of ΔD/5 are taken as an example, as shown in Fig. 1. Through a Projection lens behind the P_spectrum plane, the OLED microdisplay k is imaged to PP' on the focal plane (P_projection) of the Projection lens. A two-step imaging process through the Projection lens and a lens (called Field lens) located at the P_projection plane makes the apertures be imaged onto the observing plane (P_obser) as sub-viewing-zones (SVZ_k1, SVZ_k2, SVZ_k3, SVZ_k4, SVZ_k5). The u₁ and v₁ represent the object distance and image distance of the first imaging. The u₂ and v₂ denote the object distance and image distance of the second imaging. With the apertures being gated sequentially, the 2D perspective views of the target 3D object converging to their corresponding sub-viewing-zones are refreshed by the OLED microdisplay k synchronously. Precisely, at the time t, the aperture A_k1 is gated and other four apertures are closed. A 2D perspective view converging to the geometrical center of SVZ_k1 is displayed by the OLED microdisplay k. Then at t + Δt/5, A_k1 is closed and A_k2 gets opened, synchronously the microdisplay is refreshed with a 2D perspective view converging to the geometrical center of SVZ_k2. And so on, at t + 2Δt/5, t + 3Δt/5 and t + 4Δt/5, A_k3, A_k4 and A_k5 are gated, respectively. Corresponding 2D perspective views converging to the geometrical centers of SVZ_k3, SVZ_k4 and SVZ_k5 are synchronously refreshed by the microdisplay, respectively. Repeating above procedures cyclically, a multi-view display with five sub-viewing-zones gets realized by only one OLED microdisplay when the time cycle Δt is small enough for persistence of human vision. Due to the homogeneity of light intensities on the spatial-spectrum plane, the display intensity of each 2D perspective view is approximately equal when ΔD is not very large.

 

Fig. 1 Optical diagram of the proposed SMV system.

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3. A SMV display system with multiple planar aligned OLED microdisplays

To obtain more sub-viewing-zones, multiple (N) projecting units are arranged side by side transversely along the system optical axis, as shown in Fig. 1. For simplicity, only two adjacent projecting units are drawn in the figure with sequence number k and k + 1. The common optical axis of the Projection lens (f_p) and the Field lens (f_d) is taken as the optical axis of the display system. Through the public Projection lens and Field lens, sub-viewing-zones from different projecting units are lined up along the horizontal x-direction on the P_obser plane. Benefitted from the adopted optical structure, the projected 2D views from all planar aligned OLED microdisplays are superimposed on the P_projection plane precisely, with points P and P' as the common boundary points along the horizontal direction. At each time point, one aperture per projecting unit is gated. For a time cycle consisting of five time points (t, t + Δt/5, t + 2Δt/5, t + 3Δt/5, t + 4Δt/5), totally 5N sub-viewing-zones are obtained. When the sub-viewing-zone interval (βΔD/5) is smaller than the eye pupil diameter, a SMV display gets realized by the proposed display system through time-multiplexing of multiple OLED microdisplays. Here the β = v₁v₂/u₁u₂ is the magnification of the sub-viewing-zone to the aperture. The size of the horizontal viewing zone is βNΔD.

In order to make intervals between all adjacent apertures, including those belong to different projecting units, be fixed at ΔD/5, the size of the lens used for Fourier transformation in each projecting unit must be smaller than ΔD, as shown in Fig. 1. At the same time, lights from each pixel on a microdisplay should cover all apertures in the projecting unit so as to make the whole 2D view be viewable in any sub-viewing-zone. Therefore, a double-lenses (f) structure for Fourier transformation is designed, as shown in Fig. 1. O_k1 and O_k2 are the optical centers of the two coaxial lenses (Lens1 and Lens2), respectively. Their optical axis passes through the geometrical center of the microdisplay perpendicularly. The distance between two lenses is f(m-1)/(m-2), where m is a number larger than 2. The normal emission ray from a marginal point pixel (P_k) of the OLED microdisplay intersects with the two lenses at A_k and B_k, respectively. C_k is the intersection point between lines A_kB_k and O_k1O_k2. The OLED microdisplay has a distance of f/m away from the Len1. According to the geometrical relationship shown in Fig. 1, the size of the Len2 should be less than ΔD along the horizontal direction. Numerically, the following equation shall be satisfied:

The sequential gating of apertures is implemented through a rotating circular metal plate, called “gating plate” in this paper. The gating plate is placed 2mm behind the P_spectrum plane with its rotating axis being parallel with the system optical axis. A pre-designed arc-aperture pattern with an angular pitch of 4.8° is enchased into the gating plate, as shown in Fig. 2. Each arc-aperture is with a width of 3mm along the radial direction and covers a central angle of 4°. An arc-aperture denoted as GA_kl is the gating aperture for the aperture A_kl on the P_spectrum plane. For example, when GA₁₁ rotates to the x-axis, the aperture A₁₁ gets gated. Here, only a part of the gating plate is shown in Fig. 2(a). Specifically, along the radial direction, 5 × 2 kinds of arc-apertures are drawn and other 5 × (N-2) kinds of arc-apertures are arranged by the same rule. At a time point, N apertures from N projection units are gated simultaneously. Along the angular direction, a fan-structure with a central angle 24° is taken as a unit, as schematically drawn in Fig. 2. Totally there are 15 identical units constructing the circular gating plate. The arc gating apertures ensure that all apertures on the P_spetrum plane have an equal gating time wherever their locations on the gating plate are. The gating plate rotates at a constant speed of one cycle per second. The gating time is 11ms and the display frequency of the 3D image is 15Hz.

 

Fig. 2 (a) The schematic drawing of a part of the gating plate with arc-apertures; (b) Photo of the gating plate.

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4. Experiments and results

A display system is set up to implement the idea described above. N = 12 white OLED microdisplays, with a display area $d_x\times d_y=7.56\times 10.08m{m}^2$ and a resolution $600\times 800$, from Yunnan North OLEiD Opto-Electronic Technology Co of China are used. Their shorter sides are set along the horizontal direction. But each microdisplay is integrated with a control chip on a printed circuit board. The total size of the module is 17mm × 22mm. So, ΔD is set as 17.2mm in our experiment. The frame rate of the used microdisplay is 75Hz. To avoid obvious flicking, five time-points are adopted for time-multiplexing and the display frequency is set as 15Hz in the prototype system. Although slight flicker is observed in the experiment, this value is enough for the sense of motion. OLED has a response time at the scale of μs, exhibiting great potentials to manufacture OLED microdisplays with very high frame rates. Once high-speed OLED microdisplays are available, higher displaying frequency will come true en route our system. According to Eq. (1), m = 4 is adopted, Lens1 ($f=60mm$) and Lens2 ($f=60mm$) are processed into rectangular shape (17mm × 22mm). Each projecting unit is packaged into a cuboid structure with a frame size of 17.2 mm × 24 mm × 78mm (W × H × L). The internal structure of an assembled projecting unit is shown in Fig. 3. The baffles (0.1mm thick) shown in Fig. 1, as parts of the cuboid structure, have low reflectivity for light blocking. Five apertures are engraved into a light-blocking membrane. The membrane is braced by an optical glass sheet with five windows which are a little larger than the apertures to guarantee free path for the valuable light rays.

 

Fig. 3 Photo showing the internal structure of a projecting unit (with the upper package and a baffle removed for photograph).

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All lenses in our system are achromatic lens. A Fresnel lens with an aperture of 279.4mm × 279.4mm from Edmund Optics of America is taken as the Projection lens and a doublet lens with a diameter of 100mm is employed as the Field lens. The problem of wavefront aberration and chromatic aberration accompanying the usage of the Fresnel lens will be discussed in the following section 5. Figure 4 shows the photograph of the experimental display system. Other system parameters include $f_p=609.6mm$, $f_d=200mm$, $u_1=60mm$ and δ = 2.7mm. δ is the side length of the quadrate aperture. Under this condition, β = 0.4659, v₂ = 284mm, and the available horizontal display size PP' = 102mm. Limited by the physical size of the used field lens, the display space of the target 3D object is set to be 60mm × 60mm × 60mm in between plane P₁ and P₂ of Fig. 1. The planes P₁ and P₂ have an equal distance, Δz = 30mm, to the P_projection plane. The horizontal viewing zone constructed by 60 sub-viewing-zones is 96.0mm which is 1.5 times as large as the average interocular distance (64mm) of a viewer. The horizontal interval between adjacent sub-viewing-zones (with a size of 1.26mm × 1.26mm) is 1.60mm. For a pupil of 5mm, i.e. the average diameter, at least two adjacent sub-viewing-zones can be captured. So the SMV effect keeps being active throughout the entire viewing zone along the P_obser. In the experiment, a research-type charge coupled device (CCD, SenSys 1602E from PM of America) with an objective aperture of 5mm is used to capture images displayed by the prototype display system [11]. The CCD can move in the P_observ horizontally. Actually, under normal room brightness, the pupil size of human eyes is 3mm [12]. Under this condition, two adjacent sub-viewing-zone can be captured entirely only when the eye is centered on the boundary between them. Once the eye deviating from the boundary, only one sub-viewing-zone can be captured entirely, which is accompanied by two partial sub-viewing-zones. Intensities of different perspective views captured by one eye are not balanced. i.e. one view is brighter than the others, resulting in SMV effect weakening. More dense sub-viewing-zones are needed to achieve uniform SMV effect in the proposed system for viewers with small size pupils. Adopting OLED microdisplays with higher frame rates or smaller mechanical sizes can realize this goal, which will be done in the future work.

 

Fig. 4 Photograph of the experimental display system.

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A uniform light intensity distribution on the P_spectrum plane is a necessary condition for successful time multiplexing. The inherent light emission characteristics of OLED, i.e. large divergence angle, guarantees this point. The light intensity distribution on the P_spectrum plane is measured through a luminance meter CS-2000A from Konicaminolta. The measured values at the five apertures of a projection unit are 129.8, 130.4, 131.130.2 and 129.6cd/m², confirming a nearly homogeneous light distribution on the P_spectrum plane. So the display intensities of different 2D perspective views are roughly even. The fused 3D image through superimposing incoherent lights is free from intensity fluctuation for a moving eye.

To verify the capability of focusing on 3D images produced by the prototype system, two horizontal lines with a spacing of 40mm along the optical axis are displayed. The line-width is 0.6mm. When the aforementioned CCD is focused on one line along the optical axis, the other line becomes blurred due to out-of-focus, as show in Fig. 5. The results reveal that the prototype system is able to produce 3D images on which the human eye can focus.

 

Fig. 5 Captured images when the two lines are on focus separately.

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Two 3D objects, i.e. pyramid&teapot and a pelvis, are displayed to demonstrate the proposed idea and system. The captured images with the aforementioned CCD being at different positions along the P_observ horizontally are shown in Fig. 6.

 

Fig. 6 Captured images by the CCD located at a series of points along the P_observ horizontally with a spatial interval of 19mm when the proposed display system work.

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5. Discussions on the display resolution limit

The size of apertures, i.e. the δ, is a key parameter. As a diffraction-limited incoherent imaging system, the optical transmission function is $tri(\lambda f_p{f}_x/\delta )$ when the OLED microdisplays are imaged onto the P_projection plane, where f_x is the spatial frequency. Using the center wavelength (585nm) of the OLED spectrum for calculation, the displayed resoluble light spot on the P_projection plane is ${\epsilon }_d=\left(0.32/\delta \right)mm$. In the SMV system, the displayed 3D image presented to the viewer is a set of spatial light spots, which are formed by superimposing incoherent cone-shaped light beams coming from different 2D perspective views. These light spots can be categorized as locating on a series of virtual 2D display planes, which are parallel with the P_projection plane. The lateral size of a displayed light spot on the corresponding virtual display plane depends on the projection size of the cone-shaped beam. For such a diffraction-limited imaging system, the cone-shaped beam has a minimum projection size on the P_projection plane and keeps expanding as it leaves away from the P_projection plane, no matter along the forward direction or the reverse direction. As shown in Fig. 7, the cone-shaped beam is marked by a pink shadow zone. On the planes (P₁ and P₂) farthest away from the P_projection plane, the projection sizes of the cone-shaped beam will have two extremum values. The larger one is taken as the lateral resolution limit of the proposed display system. Based on geometrical optics approximation, the cone-shaped beam can be approximated by a straight-edge beam, constructed by all rays passing through both SVZ_m zone and Q₁Q₂ zone. In the horizontal plane, its distribution zone is between polygonal lines S₁Q₁M₁ and S₂Q₂M₂, as shown in Fig. 7. Here Q₁ and Q₂ are the boundary points of the projected light spot on the P_projection plane. M₁ and M₂ are the boundary points of the SVZ_m. S₁ and S₂ are the intersection points of lines M₂Q₁ and M₁Q₂ with the plane P₁. T₁ and T₂ are the intersection points of lines M₁Q₁ and M₂Q₂ with the plane P₂. Therefore, S₁S₂ and T₁T₂ can be approximated as the displayed light spots on the P₁ plane and P₂ plane, respectively. Their lateral sizes, ${\epsilon }_1$ and ${\epsilon }_2$, are deduced geometrically by:

 

Fig. 7 Geometrical diagram showing the displayed spot sizes of the 2D display planes in the 3D display space.

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According to Eq. (2), trade-off between the resolution limit of the P_projection plane (0.32/δ) and the size of sub-viewing-zone (βδ) leads to an optimum resolution limit. Figure 8 presents the evolution of ${\epsilon }_1$ and ${\epsilon }_2$ with the aperture size. An optimum lateral resolution limit of 0.2639mm is obtained at δ = 2.7mm. In the experiment, the aperture size is set as 2.7mm × 2.7mm. The 2D image projected from an OLED microdisplay consists of 200 × 200 spots displayed by 352 × 352 effective pixels (i.e. $600\times 60/102$), which corresponds to a reachable lateral display resolution of 0.3 mm × 0.3mm.

 

Fig. 8 The evolution of resolution limits of P₁ and P₂ planes with the aperture size.

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In the present work, only one row of microdisplays is employed and a horizontal parallax only (HPO) display is demonstrated. When high-speed OLED microdisplays are available, equal spaced apertures along the vertical direction can be added and gated in conjunction with multiple rows of projecting units to implement a full parallax 3D display by our system.

To accommodate 12 OLED microdisplays, a Fresnel lens with a large size is taken as the Projection lens in the proposed system. Since only the central 75% of the aperture of the Fresnel lens gets utilized, the wavefront aberration and the chromatic aberration accompanying the usage of the Fresnel lens do not degrade the image quality obviously in the present experiment. When more OLED microdisplays are employed, this kind of degradation must be taken into account. The methods for alleviating the induced image distortion discussed in [13] shall be employed.

6. Conclusions

In conclusion, through spatial-spectrum time-multiplexing of a planar array of 12 OLED microdisplays, 60 sub-viewing-zones for one 3D object are obtained. The interval between adjacent sub-viewing-zones is 1.6mm and a SMV display gets realized. The influence of the aperture size on the display resolution limit is discussed. An optimum lateral resolution limit of 0.2639mm is obtained. The horizontal viewing zone reaches 96mm which is about 1.5 times as large as the average interocular distance (64mm) of the viewers.