## Abstract

In auto-stereoscopic multi-views 3D display systems, the crosstalk and low resolution become problems for taking a clear depth image with the sufficient motion parallax. To solve these problems, we propose the projection-type auto-stereoscopic multi-view 3D display system, in which the hybrid optical system with the lenticular-parallax barrier and multi projectors. Condensing width of the projected unit-pixel image within the lenslet by hybrid optics is the core concept in this proposal. As the result, the point crosstalk is improved 53% and resolution is increased up to 5 times.

©2012 Optical Society of America

## Introduction

The crosstalk is one of problems that cause an unclear stereo vision in the glasses-free 3D display systems [1–15]. This is an obstacle for clear recognition of the viewpoint image. Also, a double image may happen and the fusible stereo power is deteriorated [1–7]. As a result, the low-quality depth is provided. Many research works to solve the crosstalk problem are in progress [8–10]. However, these existing methods suffer from the low resolution despite the improvement of crosstalk [9–15]. So, we propose the projection-type, auto-stereoscopic multi-view 3D display system, in which the hybrid viewing-zone forming optical system with the lenticular-parallax barrier is used in order to improve the resolution and solve the crosstalk problem. The objective of the proposed method is to minimize the width of pixel image projected by the projector, to make a viewing zone width approximately equal to the distance between the adjacent viewing zones, and to have a rectangular intensity distribution. A convolution theory is applied to describe the rectangle viewing zone and to reduce crosstalk. The validity of our method is verified by the ray-optics. By this, we can expect the improvement as follows. Firstly, the rectangle viewing-zone reduces the overlapped area with the adjacent zones, so the crosstalk problem to be solved. Secondly, the viewing-zone has uniform brightness distribution and expands the viewing-zone where we can see the viewpoint image clearly. Additionally, the number of pixels within the lenslet pitch increases in inverse proportion to the effective pixel width. So, it is possible to make the multi-viewpoint image keeping the uniform brightness with high resolution [12–15]. In a quantitative and qualitative manner, this paper describes the properties of a projection display system with the lenticular-parallax barrier to create the high-resolution multi-view images with low crosstalk. In order to verify the logical feasibility of the proposed method, two cases are considered: the pixel and the effective pixel. The crosstalk reduction is analyzed theoretically and verified by the measurements.

## Preliminary Considerations

To achieve a rectangle intensity distribution in the viewing zone, we designed a projection auto-stereoscopic 3D display system and analyzed its properties such as reduced pixel width. The Fig. 1 represents the illustration of the pair image for two viewpoints based on the effective pixel width projected from the projector and formed on the screen after the lenticular sheet.

In this system, a convolution theory helps to understand why the narrower width of pixel forms a rectangle viewing zone and reduces the crosstalk between adjacent viewing zones at the observing plane. The convolution between two apertures is defined as Eq. (1).

In Eq. (1), h(x) and f(x) represent the width of effective pixel formed on the surface of the lenticular sheet and the aperture of the parallax barrier sheet, respectively. Both f(x) and h(x) are given within −0.5<*x*<0.5; their shapes are unit-box. The Fig. 2
show the convolution calculated by Eq. (1), Fig. 2(a) shows the result for identical shapes h(x) = f(x) and Fig. 2(b) shows the case h(x) narrower than f(x), h(x) = f(0.1 x). As shown in Fig. 2(a) and (b), if the pixel is narrower, the result changes from a triangle to a rectangle.

With using convolution and the ray-optics analysis, we can calculate the crosstalk. In Fig. 1, the left half shows the effective pixel formed on the diffusing screen, and the right half shows the viewing zones on the observing plane. *P _{1}* presents the pixel projected on the screen without lenticular lens sheet and adjusted to the pitch of lenslet (

*P*) according to the projected distance

*S*.

_{o}*P*presents the reduced width of

_{2}*P*. The width of pixel is strongly connected with the optical power of the lenslet. The origin of the coordinates is located at the center of the observer.

_{1}*G*represents the position of the viewpoint. Number

_{j}*j*represents the number of viewpoints. Number

*j*is the total number (

_{max}*N*) of designed viewpoints. Base Distance (BD) represents the interval between the centers of adjacent viewpoints. As such,

*d*represents the distance between the parallax barrier and the screen;

*A*represents the aperture of parallax barrier;

*B*indicates the width of the barrier;

*S*represents the distance from the of parallax barrier to the observing plane. From the given conditions,

*P*and BD, the values of

_{1}, S*d, A*and

*B*can be defined as follows.

In Fig. 1, *h* represents the collective number of views in the horizontal direction. The maximum value of *h* is defined the permitted horizontal resolution of each view image. And *m* represents the number of point light sources. The number *m* ranges from 1 to *k*. It is composed of a bundle of rays with a uniform density. *P _{h,j,m}* is the centric coordinates for the point light sources within the pixel image on the diffusing sheet;

*X*indicates

_{h,j,m}*x*coordinates of the rays reached the horizontal axis at the observing plane;

*A*represents the centric coordinates of the aperture of the parallax barrier plate which corresponds to the

_{h}*h*-th collective number;

*E*indicates the light intensity at

_{h,j,m}*X*. The light intensity decreases in inverse proportion to the squared cosine of divergence angle and the distance from

_{h,j,m}*P*to

_{h,j,m}*X*. The viewing zone is formed as follows. The light bundle radiated from the

_{h,j,m}*m*-th point light source within the

*j*-th pixel passes the

*A*-th aperture of the parallax barrier at

_{h}*X*with the light intensity

_{h,j,m }*E*The range of

_{h,j,m}.*X*is confined to the defined, the horizontal viewing range of observer,

_{h,j,m}*x*; the accumulated value for this, ∑

_{min,max}*E*is defined as the light intensity distribution of the viewing zone. Equation (5) is the mathematical definition for the light intensity distribution of the viewing zone of light sources

_{h,j,m}*P*or

_{1}*P*.

_{2}*L*is given initial light intensity of point light source.

The area of crosstalk between the adjacent viewing zones is the area shared by *X _{h,(j + 1,2,3…N),m}* and

*X*. Therefore, the ratio of light intensity for the

_{h,j,m}*j*-th viewpoint can be defined as Point Crosstalk (PC). Equation (6) is the mathematical definition for PC. When the ratio of occupation by the light intensity of the considered view is higher, PC amount decreases; when its light intensity occupies less than the adjacent views, PC increases.

The ratio of the range of viewing zone that satisfies the minimum PC compared with the distance between the adjacent viewpoints is defined as ‘the minimum P*C.* section / *B.D* width’. This is referred to as the optimal viewing zone ratio. When this ratio is higher, the observer can view the wider clear image within the viewing zone.

The projection auto-stereoscopic multi-view 3D display system, proposed in this paper has a merit in terms of the crosstalk elimination between the adjacent viewing-zones. An additional merit is that it is possible to create high-resolution viewpoint images by use of a number of projectors. This supplementary merit can solve the low-resolution problem for the previous glasses-free multi-view 3D system based on flat-panel-display. The maximum number of projectors can be defined as the natural number of ‘the lenslet pitch / the maximum width of condensed pixel image’. To locate the pixels horizontally, the projectors should be aligned equidistantly; *I* is the distance between the centers of the *P _{2}* and

*ID*is the outermost interval between the centers of projection lens. The relation between them can be defined as the Eq. (7). In Eq. (7),

*n*and

_{d}*n*represent the refractive index of lenslet and air, and

_{m}*t*represents the thickness of lenticular lens sheet, and

*P*represents the pitch of lenslet. The layout corresponding to Eq. (7) is shown in Fig. 3 . The supposed maximum number of projectors is 1, 3 and 5.

## Experimental Result

For the verification of crosstalk decrease by the reduced light source width in the projection 3D display system, the following experiment was implemented. The projector used for experiment is EPSON TW4500 model. It supports Full HD resolution (1920X1080). Table 1
shows the constraints on the experiment, which are consisted with the optical property with regard to the lenticular lens sheet, lenslet and light sources *P _{1}* and

*P*.

_{2}Figure 4(b)
shows the measurement of the width of the light source *P _{1}* on the screen. Figure 4(a) shows the cross section of lenticular lens used in the experiment. Figure 4(c) shows the decreased image of the light source

*P*width formed through the lenslet.

_{2}For the measurement of the viewing zone distribution and crosstalk of five viewpoint images in the horizontal direction for the light sources *P _{1}* and

*P*, the following experiment was implemented: The measurement system was equipped with the 5-inch and the 42-inch screens. The 5-inch system was used for the measurement of image properties of the light source width, and the 42-inch system was used for the verification of reduced crosstalk. The constraint conditions applied in the experiment are the horizontal projection distance

_{2}*S*, the observing distance

_{o}*S = 1,100 mm*, and the interval between the viewpoints, BD

*= 15 mm.*The viewing-zone forming optical system is located away from the

*P*and the

_{1}*P*light source surfaces by the distance,

_{2}*d*= 74.5 mm, and has the properties with the aperture width

*A = 0.95 mm*and barrier width

*B = 3.80 mm.*

The measurement of the image width was made by use of the 5-inch hybrid lenticular-parallax optical system. The pixel is projected, and as the detector is moved by 1mm steps along the *x*-axis (from −50 mm to + 50 mm) from the center of the 5-inch screen, the brightness depending on the position of detector was measured. Additionally, the viewing zone distribution and crosstalk for the same viewpoint image from the light sources *P _{1}* and

*P*are compared with each other. The verification of the crosstalk improvement by the reduced light source is implemented by use of the 42-inch system. The layout of the 42-inch system is the same as that for 5-inch system. The Fig. 5 represents the optical properties of each image penetrating through the apertures of the optical system and the 5-inch system comprised for the analysis of crosstalk. The viewpoint image projected from the projector consists of five images. The measurement distance and observing position is applied similarly for two cases (Fig. 5(a), (b)). The area of the effective light source

_{2}*P*is the reduced effective pixel. This implies that the light beams with the uniform density radiated from the light source

_{2}*P*contribute mainly near the center of the aperture of the optical system. Accordingly, the viewing zone from the light source

_{2}*P*becomes narrower and clearer than that from the light source

_{2}*P*, in case that the pitch of lenslet is used for the light source. In the highlighted magnified section in Fig. 5(a), (b), it can be checked that

_{1}*P*is narrower than the

_{2}*P*.

_{1}The Fig. 6
represents the measurement and the simulation results for viewing zone intensity distribution of the five viewpoints formed by the *P _{1}* light source. The

*x*-axis represents the measurement range of the detector, and the

*y*-axis represents the light intensity on the viewpoint. An arbitrary unit (AU) is used in the graph. The distance between the centers of viewpoints is 15 mm, which corresponds to the designed value. The viewing zone of the perpendicular parallax barrier has the triangular shape and represents the integrated brightness distribution. The brightness distribution in the lower part of graph is distorted by noise from the detector or by the ambient-light.

The Fig. 7 shows the PC based on the data of Fig. 6. The x-axis represents the range of the detector, and the y-axis represents the PC value for each viewpoint. At 200%, the contribution from the adjacent viewpoints is two times stronger than that by the specific viewpoint. The minimum PC is approximately 20%. It is probably caused by the noise from the detector and the neighboring light.

The Fig. 8 shows the measured light intensity distribution which corresponds to the simulation. This verifies that the reduction of the light source width decreases the viewing zone width. The brightness at the two ends is higher than in the center of viewing zone.

The Fig. 9
shows the PC based on Fig. 8. The minimum PC of the viewpoint image is around 20%. As compared with PC of the light source *P _{1}*, the minimum PC area is expanded. Accordingly, the viewpoint image by the light source

*P*has the low crosstalk within the viewing zone, which means a clearer image for the observer.

_{2}The interval where the image is clearest, that is, where PC is minimized, increases more than with the light source *P _{1}*. The minimum PC section for the light source

*P*is expanded. The Fig. 10 represents the light sources

_{2}*P*and

_{1}*P*in the 42-inch system measured at the observer position. The viewpoint image with

_{2}*P*has the lower crosstalk than that with

_{2}*P*.

_{1}The ratio of light beam widths before and after the lenticular sheet is 18.7%. The segment of the viewing zone where the viewpoint images can be clearly seen is the area where the PC is minimized. Before the reduction, in case of the light source *P _{1}*, the BD width is 15mm. Also, the low PC (PC<30%) is observed within 3mm. The optimal viewing zone ratio is 0.2. After the reduction, in case of the light source

*P*, the minimum PC range is 11mm. The optimal viewing zone ratio is 0.73. Therefore, the PC is improved by

_{2}*53%*. The maximum number of projectors available is 5, and the resolution of viewpoint image can be increased by five times. The Fig. 11 represents measured position between the centers of projection lens for each projector, when the number of projectors is 1, 3 and 5. When

*I*= 1/2, 1/3, and 2/5, the positions of the light sources

*P*are 0 mm, 0.34 mm, and 0.41 mm from the center of lenslet, respectively. The outermost interval

_{2}*ID*between the centers of projection lenses of projectors corresponds to 0mm, 389.95mm and 469.45mm, respectively, from Eq. (7).

## Discussion

In Fig. 8, the shape of the viewing zone for every viewpoint follows the same pattern; the brightness at the ends is higher than in the center of viewing zone. We supposed that the shape of the viewing zone is strongly affected by the optical property of pixel image as the energy distribution. The Fig. 12 shows the simulated energy distribution on the cross-section of the effective pixel image after the lenticular sheet. In the simulation, the same the parameters are considered as in the proposed system.

As we can see in Fig. 12, the energy distribution on the cross-section within the width of effective pixel image has the curved form which is similar to Fig. 8. The thickness of lenticular sheet is the focal plane having a minimized beam waist in this system, and the paraxial focal plane is located behind the focal plane because of the spherical aberration. The curved shape is changeable by the cross-section plane selected in the range of depth of focus. This means that we can make an energy distribution flat, if the thickness of lenticular lens sheet is controllable. In this system, the thickness of the lenticular lens sheet affects the viewing zone shape.

## Conclusion

In this paper, the cause of crosstalk between the viewing zones in the glasses-free projection 3D display system was analyzed quantitatively and qualitatively, and as a way of solving the problem, the projection glasses-free 3D display system was proposed, based on the hybrid optical system with lenticular-parallax barrier. The characteristic of this system is that the crosstalk improvement can be realized by the reduced pixel width and the high-resolution viewpoint image by use of a number of projectors. The pixel width reduced through the lenticular lenses is convoluted with the aperture of the parallax barrier sheet, and forms the rectangular viewing zone distribution. The width of the formed viewing zone decreases the overlapped area with the adjacent viewing zones. Therefore the point crosstalk is improved. The rectangle viewing zone distribution expands the section of optimal viewing-zone ratio with a uniform brightness. Also, if the number of projectors is equal to the number of effective pixels focused within the pitch of the lenslet *N _{views}*, the resolution of viewpoint image increases by

*N*times. As a proposal for the application of this research, this system can expect to be applicable to the clear stereovision screen with a size of 42 inches or larger.

_{views}## Acknowledgment

This work was supported in part by the IT R&D program of MKE/KEIT [KI10035337, development of interactive wide viewing zone SMV optics of 3D display] and in part by the Korea Institute of Science and Technology under the Tangible Social Media Platform Project.

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