We present methodologies for determining the optimum viewing distance (OVD) for a multi-view auto-stereoscopic 3D display system with a parallax barrier. The OVD can be efficiently determined as the viewing distance where statistical deviation of centers of quasi-linear distributions of illuminance at central viewing zones is minimized using local areas of a display panel. This method can offer reduced computation time because it does not use the entire area of the display panel during a simulation, but still secures considerable accuracy. The method is verified in experiments, showing its applicability for efficient optical characterization.
© 2014 Optical Society of America
Multi-view auto-stereoscopic 3D display systems have been brought into great attention for replacing those based on two-view stereo parallax due to advantages such as capability of providing movement parallax and a widened viewing zone. Various evaluation methodologies for multi-view auto-stereoscopic systems have been reported [1–10]. The key ingredients for designing a multi-view auto-stereoscopic display include the optimum viewing distance (OVD) between a display panel and a viewing zone, and the optimum separation between individual viewing images (OSVI) at the OVD.
Cross-talk, one of the major problems encountered in a multi-view auto-stereogram, needs to be resolved for acceptable quality of viewing images. An estimate of cross-talk demands precise determination of the OVD and evaluation of the OSVI, although methodologies for obtaining such information have rarely been reported.
Most methods reported to estimate the OVD rely on a simple geometrical approach or measurement of an angular distribution of illuminance at viewing zones for which an angle-control optics such as a goniometer is used for optical characteristics evaluation [2,3,8,11,12]. However, methods relying on goniometers demand high precision angular resolution for proper evaluation and also are considered to take relatively long time of angle scanning. Another scheme that utilizes Fourier optics has thus been proposed to provide relatively easy evaluation that is not subject to angle scanning with a goniometer of a limited angular resolution but employs conversion of angle-dependent illuminance distribution (wave vector-dependent illuminance distribution) from light source into spatial distribution of illuminance on the CCD sensor surface with a restricted resolution [3, 12].
However, the methods based on measurement of angular distribution of illuminance employ a couple of point-like areas (about 10 mm2) of a display panel as image light emitting sources, and thus the estimated angular distribution does not reflect the illuminance effects for which the total area of the display panel is taken into account. It is thereby seen that those methods need to be verified under conditions of illumination from the entire area of a display panel for practical applicability.
In this paper, we present two different methods of optical characterization including the OVD, for a multi-view (10 views) auto-stereoscopic 3D display with a parallax barrier. Both methods rely on the approximation of linear distribution of illuminance at central viewing zones for optical characterization in practical cases where the image abberation occurs due to the refractive index of the transparent medium between the display panel and the parallax barrier. The first method uses the entire area of the 3D display panel for OVD estimation via minimization of full-width at half-maximum (FWHM) for illuminance distribution along a quasi-linear line in parallel with the display panel at the central viewing zones. This method delivers a straightforward evaluation of the OVD but suffers from the significant indeterminacy of the OVD.
The second method, the one that we highlight in this paper, is based on an optical ray tracing simulation that enables us to obtain distributions of illuminance along a quasi-linear line at central viewing zones for different viewing distances. Then, one can determine the OVD to be the viewing distance where the statistical deviation of center positions of the spatial distributions of illuminance of individual viewing images is minimized, using only the number of local areas of the display panel. It turns out that this method consumes computation time reduced compared to the first method of using an entire area of a display panel while providing the OVD the nearly same as that obtained by the former method. Experiments performed support the applicability of the latter method for time-efficient and relatively easy characterization of parameters such as OVD and OSVI.
We simulate optical rays traces for the auto-stereoscopic 3D display with a parallax barrier of a view-number of N, which relies on spatial multiplexing of optical rays via a parallax barrier mask. Figure 1 depicts schematic (top view) of the 3D display system designed with geometrical ray traces. WP is the size of the sub-pixel which forms the basic pixels for color distinction, WS is the width of a slit aperture, ΛPB is the spatial period of the slit positions in the parallax barrier, d is the distance between the display panel and the parallax barrier, DVD is the designed distance from the parallax barrier to the viewing position(viewing zone), and SV is the spatial interval between the individual viewing images at the viewing distance. The designed parameter relations can be drawn as given in the following equations, using geometrical proportions in the Fig. 1 schematic.
We consider the case of the slanted parallax barrier in front of a display panel of liquid crystals (LC) for image resolution balance between horizontal and vertical directions, while maintaining a color uniformity at the respective viewing zone. The slanted angle of a parallax barrier used in the design is θ = arctan(1/3) = 18.435°. Our simulation involves parametrization of geometrical positions of optical components that generate, spatially multiplex, and detect light as shown in Fig. 2. In modeling, a light source is assumed to have a Lambertian surface which emits light illuminance that follows the inverse-square law with respect to light propagation distance. Illuminance of light that emits from all pixels of a single view are simply added to obtain resultant total illuminance at a given viewing zone due to the incoherent properties of a light source. Pixels on the LC display are numbered for modeling optical ray traces while each pixel transmittance is assumed to switch between on-(100%) and off-(0%) states.
It is also assumed that, although the parallax barrier that consists of a periodic slit structure lies on the substrate of 0.1 mm thickness, the separation between the display panel and the parallax barrier, denoted by d, can be approximated to be air-filled as shown in Fig. 2. In order to find the OVD, we can find the VD where the FWHM is minimized with an aim of minimizing a cross-talk noise, by scanning the position of an optical detector with a 10 mm step over a ±50 mm range of distance from the parallax barrier to it, across the initial VD. This initial VD for scanning can be assigned approximately either by a position where width of spatial distribution of illuminance appears minimized upon naked eyes or by the DVD which can be obtained via the geometrical relations shown in Eqs. (1) to (3).
Figure 3 shows how we define the FWHM of a given illuminance distribution as a function x. This is the spatial separation between two points where values of illuminance are half its maximum. We simulate ray tracing from light source (bottom) by using all pixels of the display panel for a single view, as shown in Fig. 4, and compute the illuminance at viewing zones to check the OVD and its indeterminacy.
In order to locate the viewing distance (VD) where the FWHM of spatial distribution of illuminance across the viewing zone is minimized, we plot it as a function of the VD whose offset is shifted such that the zero represents the middle of the scanned positions, as shown in Fig. 5. It is revealed that, although the OVD can be determined to be around 10 mm, the VDs of zero through 20 mm give the pretty close values of the FWHM, leading to expectation of high degree of errors (indeterminacy) of the OVD determined. This indeterminacy can be understood by checking the fact that the FWHM slightly varies with VD as shown in Figs. 6(a)–6(d), where the FWHM of measured illuminance distribution for 8th, 9th and 10th view images by using the whole display panel is illustrated at VD =590 mm, 600 mm, 610 mm, and 620 mm, respectively.
To resolve such an indeterminacy problem, we use a series of pixels that produce a single-view image, within a chosen local display area of a certain size for ray tracing simulation. The ray traces calculated using the local display area on the left, in the middle and on the right are shown in Figs. 7(a), 7(b) and 7(c), respectively. The computed ray traces of a main-branch image and those of two of its adjacent subsidiary branch images are presented in each case of using three different local display areas. It is noted that the minimization of cross-talk noise corresponds to the fact that the three spatial distributions along the x-axis for three main-branch images forming from three different local display areas coincide as much as possible with one another. This also applies to the cases of each subsidiary branch images. The parameters used in the simulation include 10 views for an auto-stereoscopic system, and an 80 mm width of the local display area out of the whole display area of the width of 640 mm. The value of 970 mm is used as the middle of the scan for the VD while the SV is designed to be 16.25 mm.
Figures 8(a) and 8(b) show how we determine the OVD based on the simulation of ray traces shown in Figs. 7(a)–7(c). The color of data in the graph represents the specific local display area used for the image formation in the simulation while the shapes of data dots, i.e., rectangles, triangles, and circles, correspond to three branch images, i.e., the left subsidiary branch images, the right subsidiary ones, and the main ones between them, respectively. For VD scanning, we deliberately assign the initial VD by a VD which is 10 mm shorter than DVD, to see our methodology produce the OVD same as the DVD. As illustrated in Fig. 8(a), we plot the center position of the quasi-symmetric spatial distribution (along x-direction) of illuminance for each of the three main-branch images and the six of their subsidiary branch images, as a function of the scanned VD. The deviation of the distribution of the center positions for the group of the main-branch images is minimized at the VD of 10 mm. Note that the same value of the VD also finds the minimization of the deviation of the center position distribution of illuminance for each group of the two subsidiary branch images.
Figure 8(b) illustrates the average of all the deviations derived from data shown in Fig. 8(a), as a function of VD. The VD where the averaged deviation is minimized, (namely the OVD) is found to coincide with that estimated using the whole display area and through the minimization of the FWHM, as depicted in Fig. 5. It is also important to note that the VD that leads to the deviation minimum in Fig. 8(b) can be obtained with less indeterminacy than the case shown in Fig. 5.
The determination of the OVD described above is based on the three kinds of view images including the three main-branch images and their corresponding pairs of the subsidiary ones (two adjacent images on the left and the right of a main branch), all of which form approximately in a rectilinear fashion. This is different from the OVD determination methods based on an angular distribution of image illuminance, as found in the previous studies [3, 12]. The additional benefits of our method include the computation time much less than that based on the full area of the display panel. This method can also be effective in determining the OVD even in the case where a parallax barrier in a practical use possesses insignificant defects possibly caused by its convex deformation or imperfect uniformity of gap between a parallax barrier and a display panel over the x direction.
Figure 9 shows the structure of display pixels mapped with image view numbers at a slanted angle of θ = arctan(1/3) used in the experiment. The box surrounded by a white dashed line represents a group of pixels for all image view numbers with red, green and blue colors.
In accordance with the design used in the simulation described above, a slanted parallax barrier supporting 10 views is prepared for the experiments with a LC display panel of a 15.6 inch diagonal (width of about 340 mm) Table 1 shows the parameters relevant to the experimental apparatuses used in the setup.
The width of each local display area is 71.7 mm covering 400 pixels while its height is 53.775 mm that covers 300 pixels. The three local areas are separated from one another by 114.72 mm while the second local area positioned at the center of the whole display panel, as shown in Fig. 10.
A CCD image sensor on a stage movable along a linear line is used to measure the image illuminance, as a function of position along the x-direction, at a given VD . The horizontal (the x-direction) resolution of about 7.4 μm in illuminance measurement is produced by the moving stage with the CCD, which also allows the optical properties of the auto-stereoscopic system to be measured over the horizontal range from −300 mm to +300 mm. The height of the center position of the CCD sensor is kept to be the same as that of the center of the whole display panel while the VD is scanned with a 10 mm step from 520 mm to 620 mm.
Figures 11(a)–11(c) show the measured spatial distribution of illuminance of 10-view images using three different local display areas at a VD of 570 mm which is close to the calculated one based on the determination method described above. In order to see how well the spatial distributions of images (of a given view) that form from the different local display areas are overlapped, we sketch the ray traces from the local display area to the viewing image at the VD of 570 mm, using the results shown in Figs. 11(a)–11(c). As shown in Fig. 12, these sketches imply an imperfect overlapping between images that form from different local display areas, indicating the difference between the experimental configuration and the design used in the simulation. For example, the separation between the display panel and the parallax barrier, which is one of the critical factors to determine the OVD, may differ for the different local display areas used in the experimental setup due to imperfection of flatness of the parallax barrier with respect to the display panel. Moreover, the refraction of light during propagation through the transparent medium between the display panel and the parallax barrier, causes light path change, leading to image aberration at the OVD estimated by the simulation which assumes the gap filled with air.
Such an image aberration can be quantified by representing the VD where light rays of a given view from different local display areas intersect with each other. Figure 13 shows the VD where optical rays of a given view from two different local display areas intersect with each other, as a function of x-position of the images for main-branch images and the pairs of their subsidiary ones. It is believed that the image aberration occurs between the main-branch images and the subsidiary ones, due to the two reasons. One of them is the refractive index that can cause image abberation along the x-direction at a given VD. The other is the variation of the gap between the display panel and the parallax barrier for the different local display areas, which reaches the maximum of about 150 μm. This leads to an estimation that the effective OVD for this 3D display system lies in the range from 575 mm to 615 mm. This image aberration can be reduced to some extent via using smaller local areas of a display panel upon the requirement that the optical characterization in this method should show good agreement with that obtained by the first method of using the whole display area.
In order to determine the effective OVD, we take the procedures as follows: we obtain the set of x-positions of the centers of the spatial distributions of light rays of a given single view at a given VD, and get its variation range Vsv, by subtracting the minimum value from the maximum one of the set for the main branch images and their corresponding pairs of subsidiary ones, respectively; we then obtain Vsv for all branches of all the views (10 views in this work) at the VD and take their average over all the views, which is denoted by V̄; we repeat the above procedures for the different VD, as shown in Fig. 14. It is seen that the effective OVD of the 10-view 3D display system can be determined to be about 600 mm with V̄ =1.33 mm.
For comparison, we also utilize the method described above (through minimization of FWHM of the spatial distribution of illuminance using the whole area of the display panel) for determining OVD of the 10-view 3D display system. Note that this method is subject to the considerable indeterminacy of the OVD determined, as shown in Fig. 15. The OVD indeterminacy in Fig. 15 can be represented by the normalized parameter, i.e.,Fig. 14, we can draw the definition of a similarly normalized parameter for such an indeterminacy, i.e., Fig. 14, benefits from the enhanced certainty in the OVD determination over the method illustrated in Fig. 15.
Furthermore, we can determine the OSVI by estimating SV at the effective OVD determined. Figure 16 shows the x-positions of centers of individual spatial distributions of illuminance of individual view images at the OVD determined above, as a function of view image number. The least squares method is utilized to obtain the slope of the linear fits to the measured positions of those centers as a function of view image number. The fitted slope that can be interpreted as the SV is 16.4 mm, which is in good agreement with the designed value of 16.25 mm. This self-consistent result of the methodologies described above supports to provide a way of defining and measuring the spatial interval of individual viewing images.
Finally, we examine the effects of a refractive index of a substrate glass on which a pattern is made for a parallax barrier, and imperfect flatness of a parallax barrier with respect to a display panel, on OVD determination. Based on the simulation, we computed averaged deviation of center positions of spatial distributions for the 1st image view from left, center and right area of the display panel for slightly curved parallax barriers. Figures 17(a) and 17(b) show the cases of parallax barriers curved in a convex and concave fashion, respectively. The VD that causes minimum average deviation, moves from 10 mm (as shown in Fig. 8(b)) to around −10 mm in a case of the convexly curved parallax barrier and to around 30 mm in a case of the concavely curved one. This reveals that the error estimation of OVD determined needs to include effects of both a substrate refractive index and imperfectness of the parallax barrier flatness.
For a multi-view auto-stereoscopic 3D display system with a parallax barrier, we present a method to determine the OVD and the SV through minimization of deviation of center positions of illuminance distributions of view images, using a number of local areas of a display panel. This method takes into account the quasi-linear distribution of illuminance at a central viewing zone of a given VD, which is different from the previous methods that rely on the angular distributions.
This method has the advantage of reduced indeterminacy in the OVD determination compared to the case of using the whole display area (through the FWHM minimization) and the reduced computation time due to the fact that no entire area of a display panel is used for the OVD estimation. In addition, a good agreement in the OVD determination is reached between the method of using a whole display area (by FWHM minimization) and the proposed method.
Further study can include the aberration effects induced by the refractive index of a medium between a display panel and a parallax barrier, and can focus on adaptation of this proposed method to calibration of a pupil tracking 3D system.
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