Optical characterization of auto-stereoscopic 3D displays: interest of the resolution and comparison to human eye properties

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1 Optical characterization of auto-stereoscopic 3D displays: interest of the resolution and comparison to human eye properties Pierre Boher, Thierry Leroux, Thibault Bignon, Véronique Collomb-Patton ELDIM, 85 rue d Epron, 4200 Hérouville St Clair, FRANCE ABSTRACT Optical characterization of multi-view auto-stereoscopic displays is realized using high angular resolution viewing angle measurements and imaging measurements. View to view and global qualified binocular viewing space are computed from viewing angle measurements and verified using imaging measurements. Crosstalk uniformity is also deduced and related to display imperfections. Keywords: auto-stereoscopic, viewing angle, homogeneity, spatial resolution, angular resolution. INTRODUCTION Since few years the optical characterization of stereoscopic 3D displays has been investigated. Each type of 3D display is requiring different measurement methods due to the different mechanism on which stereoscopy is based. In 2009, we have proposed a new viewing angle instrument for the characterization of auto-stereoscopic displays [-2]. Using this instrument left and right eye contrasts and 3D contrast of twin view displays has been computed everywhere in front of the display and qualified monocular and binocular viewing spaces have been evaluated. In 200, we have shown that the same type of parameter can be calculated for polarization based stereoscopic 3D displays using multispectral polarization measurement with Fourier optics viewing angle instrument [3]. Direct comparison between the two technologies was possible since similar quality parameters can be deduced [4-5]. In 20, active glass 3D TVs have been characterized using temporal and spatial measurements [6-8]. The present paper address again the case of auto-stereoscopic 3D displays that are clearly more complex to realize than the others when high performances are expected. Since this type of display emits different views in different directions all the stereoscopic characteristics can be derived from measurements of the output luminance and colors versus viewing angle. The entire angular aperture is needed to make efficient computation, otherwise very partial capacities of the display are measured. Point by point goniometric measurements cannot be considered because there are too long. In addition an excellent angular resolution is required regarding to the high angular resolution of the human eye and the increasing requirements with the size of the display and the distance of the observer. Fourier optics instrument are extremely well adapted for this task since the full angle of view is measured rapidly and easily. Nevertheless, the angular resolution of standard instruments is limited to about 0.5 which is not sufficient for accurate 3D display characterization. In 2009, we have introduced a new Fourier optics viewing angle instrument with excellent angular resolution (0.03 ) for this specific task [-2]. This instrument has been used to characterize twin view stereoscopic displays and a way to compute the monocular and binocular contrasts in front of the display has been introduced. Only two or three measurement points correctly selected on the display surface are sufficient to compute qualified monocular and binocular viewing spaces in front of the display, to quantify observer viewing freedom in the different directions and the effective crosstalk in the optimized viewing conditions. Local viewing angle measurements are nevertheless not sufficient to detect possible inhomogeneities at the surface of the displays. ELDIM has also proposed to use imaging luminance meter at the optimized observer position in order to measure the crosstalk for all the display surface [9-0]. For a twin view auto-stereoscopic display we have shown that the crosstalk local variations can be understood using the viewing angle measurements and computing the display aspect. Misalignment of the parallax barriers can be outlined and quantified with this method. The proposed paper address the more complex case of multi-view auto-stereoscopic 3D displays where more than two views are displayed simultaneously in the space in front of the display. For this type of display, the purpose is to extend the qualified stereoscopic viewing space in front of the display allowing the observer to see different stereoscopic images pboher@eldim.fr; phone ; fax ; web site: eldim.fr

2 depending on his position. In the proposed paper, we show that the method already demonstrated for twin view displays can be applied to such multi-view displays. We introduce a computation method for the viewing space that must be performed step by step in order to understand perfectly the stereoscopic performances of such displays. The method is illustrated by real measurements performed on one Alioscopy 8 views lenticular lens auto-stereoscopic display. We show in particular that binocular crosstalk between two successive views is not sufficient to account for the observer sensation. Full crosstalk computation taking into account all the views together is mandatory for that. The viewing angle computations are confirmed using imaging measurements at different positions in front of the display. The need of high angular resolution for the viewing angle measurements is also confirmed. 2. Fourier optics viewing angle instrument 2. EXPERIMENTAL TECHNIQUES ELDIM was founded in 99 to promote an innovative display measurement equipment based on Fourier optics. A specific optic is designed in order to convert angular field map into a planar one allowing very rapid measurements of the full viewing cone (cf. figure ). This fast viewing angle measurement was first publicly introduced at Eurodisplay'993 in Strasbourg []. Each light beam emitted from the sample surface with an angle θ with regards to the normal of the surface is focused on the Fourier plane at the same azimuth and at a position x = F tan(θ). The angular emission of the sample is then measured simply and quickly without any mechanical movement. In practice, the Fourier optic is an achromatic combination of different lenses (6 to 9) that collects quasi all the light coming from the display and focus each angle on an intermediate Fourier plane (cf. figure ). A field lens and an imaging lens are then used to re-image the first Fourier plane on the CCD sensor. The design used by ELDIM includes a field iris before the sensor which is complex conjugate of the display surface and allows adjusting the measurement spot size independently to the angular aperture. As a consequence, the measurement spot size varies with the angle. This cosine compensation is mandatory to get good collection efficiency even for large incidence angles. The size of the measuring spot is easily adapted by the iris diameter. For 3D display characterization, we need to be able to measure all the views of the display without moving the instrument. So, the spot size must be sufficiently large to include tens of pixels for each view of the display. With the system dedicated to autostereoscopic display VCMaster-3D, a maximum spot diameter of 4mm is achieved. The optimum working distance is fixed to 5mm. This distance ensures that the measured spot is always centered at the same location for each incidence angle but it is not critical parameter. The main feature of the new instrument is its very high angular resolution. Figure. Principle of Fourier optics for angular measurements and photograph of the VCMaster3D instrument. The angular resolution of a viewing angle measurement plays a key role in auto-stereoscopic 3D display characterization as the light arriving in the eyes of the observer needs to be predicted precisely. It defines the capacity to distinguish between two different light beams coming from the same location but with very close directions. To be realistic the accuracy of the calculation in the plane of the observer must be near the one provided by the human eye pupil diameter ( to 4mm depending on illumination conditions). We can easily compute the position uncertainty Δx versus the angular resolution Δθ depending on the observer distance D using the equation Δx = D tan(δθ). The need of angular accuracy increases with the observer distance and becomes extremely demanding for 3D TV application as shown in figure 2. An angular resolution of 2.5 that is usually found in standard goniometric solutions, is not sufficient even for short working distance phone cell displays. The left and right eyes cannot even been distinguished for TVs in this case. Even the 0.25 angular resolution

3 Position uncertainty (mm) obtained with conventional Fourier optic viewing angle system is not sufficient except for applications requiring short working distances (phone cells, tablets and monitors). For these reasons, ELDIM has developed a new Fourier optics instrument VCMaster3D with ultra-high angular resolution. Our target was to cover all displays sizes and especially 3D TVs (cf. figure 2). This specification depends on the optical setup and of the number of pixels of the CCD detector. For VCMaster3D system the angular resolution is improved by one order of magnitude thanks to a specific optical design including aspheric lenses and a 6M pixels CCD camera. It is measured below [2]. Phone Monitor TVs 00 Interocular distance 0 Iris size angular resolution (deg) Figure 2. Position uncertainty versus observer distance for different angular resolution: mean iris diameter and interocular distance are also reported. 2.2 Luminance and color imaging Observer distance (mm) Imaging colorimeters are all based on CCD sensors and generally color filters. The difference between the systems lays into the accuracy, the signal over noise ratio, the spatial resolution and the quality of the imaging optics. ELDIM UMaster system (cf. figure 3.b) is based on a Peltier cooled CCD sensor with true 6-bit analog digital converter. Five color filters dedicated to each CCD sensor are mounted on a motorized color wheel. A second motorized wheel with flat densities is also available for automatic adjustment to the luminance of the target. The imaging optics is telecentric on the sensor side (cf. figure 3.a), which ensures the same incidence for all the rays crossing the filters and therefore the same spectral response. In addition the flux is quasi-independent of the object distance while conventional optic can suffer from up to 20% reduction at short distance [3]. Different objectives with various angular apertures are available (±8, ±6 and ±30 ). For global approach, another important parameters is the size of the entrance iris of the optical system. In the system of figure 3.a, it can be adjusted to a value comparable to the human iris diameter without problem. With a conventional imaging objective the size of the first lens defines this parameter and is generally much larger than the human iris.

4 Filters Display Diaphragm CCD sensor Figure 3. Principle of imaging videocolorimeter telecentric on sensor side and photograph of UMaster system. 2.3 Multi-view auto-stereoscopic 3D displays One commercial 42 inches Alioscopy multi-view display is used for the tests. These auto-stereoscopic displays are made with a conventional high resolution LCD display and a lenticular array in order to display 8 different views. Each cylindrical lens covers 8 sub-pixels very accurately has shown in figure 3. The advantage of cylindrical lenses is the efficiency and the high luminance obtained for each view. The resolution was 920x080 and the announced best working distance is 4 meters. Figure 4. Principle of 8 view auto-stereoscopic 3D displays from Alioscopy. Figure 5. Luminance measurements of 3D display at center: the 8 views and the black and white states are measured.

5 Luminance (Cd/m2) Luminance (Cd/m2) 3. Angular measurements 3. EXPERIMENTAL RESULTS Viewing angle measurements are made at center and on the left and right sides of each display. For each location, the eight views and black and white states are measured. Examples of luminance patterns measured at center of the display are reported in figure 5. The angular emission of each view is precisely measured. Maximum of emission is around 70Cd/m 2. White state is around 0Cd/m 2 which indicates a quite important overlap between views. These features are particularly clear on the horizontal cross sections of the same measurements reported in figure K W Incidence angle (deg) Incidence angle (deg) Figure 6. Horizontal cross section of the luminance measurements of figure Contrast& crosstalk computation using angular measurements a) Coordinate system Using the angular measurements we can compute the light arriving from this display location to an observer located anywhere in front of the display. The observer is defined by its coordinates in the XYZ referential. The origin O is always the display center (cf. figure 7). The X axis, Y axis and Z axis define the transverse, sagittal and coronal planes. The observer position is supposed to be the center of its two eyes. The two eyes are always assumed parallel to the X axis. The inter-pupillar distance is fixed (generally 6.25cm). For each observer position we compute two couples of polar angles (θ L, φ L) and (θ R, φ R) corresponding to the positions of the left and right eyes of the observer. The display light emission measured on each view and for black or white states along these directions can be directly deduced.

6 Figure 7. Definition of the system of coordinates and of the different planes for the observer location. The stereoscopic quality of the 3D display for an observer is directly related to his capacity to see clearly the correct images in his right and left eyes. In order to get a quantitative measurement of the perceived quality, different approaches have been proposed. In 2009, we have propose to evaluate the 3D contrast defined as the luminance ratio of wanted light to total leaked/unwanted light []. Interocular 3D contrast based on ray light distribution analysis method has also been proposed [4], but the lack on normalization do not allow comparison of different types of displays. Interocular 3D purity has also been proposed [5], which is defined as the luminance ratio of wanted light to all light that reaches the observer eye s. In this approach, the monocular purity is in perfect cases when 3D contrast is infinite but the meaning is essentially the same. In addition the combination of left and right views is the same as what we have proposed previously [, 5]. In the following we have used the 3D contrast (or the inverse of the crosstalk) that present several advantages. In particular, the acceptable crosstalk values have been defined in several studies [6-7]. b) Angular and monocular contrasts The angular contrast for each view with regards to the others is obtained using the formula (): Yi (, ) YK (, ) N Ci (, ) (, ) ( Y (, ) (, )) i j YK N ji () Y i(θ,φ) is the luminance at location (θ,φ) when white is applied to view i and black on the other views, Y K(θ,φ) is the luminance at location (θ,φ) when black is applied to all the views simultaneously, and N is the total number of views of the display. Ci(θ,φ) is related to the inverse of the crosstalk χ i of view i. One example of computation in the case of the Alioscopy display is reported in figure 8.a. Figure 8. Monocular contrast for view as right view computed in the transversal plane for central point measurement (left) and three points positions (right): area size 4x6m, resolution 2mm.

7 As expected from the viewing angle measurements (cf. figure 6), along the transversal plane, the contrast for view is highly periodic. There is no optimized distance from this simple computation since the data concern only the display center. To check the optimized working distance, the computation must be extended to M measurement locations making the same computation for each measurement location and taking the minimum value at each position in the space in front of the display as reported in formula (2): i M j C Min (, ) (2) jc i The result reported for view and three measurement positions is also reported in figure 8.b. Now the well-known hexagonal regions generally used for display optimization appear clearly and the Qualified Monocular Viewing Space (QMVS) can be defined. In agreement with the characteristics reported by the manufacturer, the working distance is around 4 meters for this display. Additional regions much closer to the display in the figure 8.b, do not correspond to optimized conditions. In this case, the contrast is high for the three points but not everywhere on the display surface. c) Binocular contrast To quantify the stereoscopy, this computation need to be made for the left and right of the observer. The stereoscopic vision is correct only if the contrast for the two eyes are maximum simultaneously. It is why we have proposed to combine the contrast of the different views using a geometric average []. The 3D contrast between view i and view j can then be computed using: C i j i j (, ) C R ( R, R )* C ( L, L ) (3) One example of such simulation is reported in figure 9.a and 9.b. The 3D contrast between view and 2 is closed to the monocular contrast for view showing the good geometric adjustment of the display. Nevertheless, the 3D contrast between view and 3 is not negligible in the same regions. This is due to an important overlap between views that extends to the third neighbor (cf. figure 6.b). L Figure 9. Binocular contrast between view and 2 (left) and view and 3 (right) computed in the transversal plane using three point positions: area size 4x6m, resolution 2mm. d) Combined binocular contrast or 3D contrast To get an overall measurement of the Qualified Binocular Viewing Space (QBVS), we have proposed to combine the two eye contrasts to get a quality factor for the observer []. The combined binocular contrast when view i is seen by right eye and view j by left eye is defined by: C N N i, i j i i j j (, ) C C R ( R, R)* C ( L L, L i i ) (4) Corresponding combined binocular contrasts for step and step 2 computed in the transversal plane are reported in figures 0.a and 0.b. The QBVS extends all along the horizontal at a distance between 3.8 and 4.2m. The disruptions corresponds to the pseudoscopic configuration (between view 8 and view). An important modulation of the contrast is nevertheless anticipated which comes for the angular emission profiles. We can also notice that the combined binocular contrast for step 2 is non-negligible and extends exactly in the same region. This is due to the important overlap between views.

8 binocular contrast Figure 0. Combined binocular contrast with step between view (left) and step 2 between views (right) computed in the transversal plane using three point positions: area size 4x6m, resolution 2mm. e) Impact of the overlap for the stereoscopy To illustrate the effect of the overlap between views, it is also interesting to analyze the behavior in a coronal plane in the middle of the QBVS (4 meters) (cf. figure 0). The transition from one couple of view to another can be obtained both with a horizontal or vertical shift of the observer. In addition, for a given couple of views, for example views 2&3, the overlap between views produces a non-negligible binocular contrast in the same region for views 2&4 and views &3 as shown in figure versus the lateral position in the coronal plane at 4 meters. Even the impact of the fifth view can be sensitive in this case (cf. figure ). Figure 0. binocular contrast between view and 2 (left) and combined binocular contrast step between views (right) computed in the coronal plane at 4 meters of the display using three point positions: area size 2x2m, resolution mm between view & view Lateral position (mm) Figure. Binocular contrast between view 2&3, 2&4, &3 and 2&5 versus lateral position in the coronal plane at 4 meters: computed using three point positions, resolution 2mm.

9 f) 2D standards characteristics The 2D characteristics of the display can be computed using the same method as previously and the angular emissive properties of the white and black states. The mean luminance value for the two eyes in ON state and OFF state are given by: M i i i i i i YK (, ) Y i K ( R, R ) Y K ( L, L ) (5) 2M Y W M i i i i i i (, ) Y i W ( R, R ) Y W ( L, L ) (6) 2M Where M is the number of measurement locations, and Y i w(θ,φ) and Y i K(θ,φ) are the luminance for white and black states at location i. Corresponding values for the display in the transversal plane are reported in figures 2.a & 2.b. The standard contrast is maximized near normal incidence but the white state suffers from spatial modulation. This effect is due to the overlap of the different views and produce parasitic moiré effect for the observer [8]. The standard contrast can then be calculated at all the observer positions and compared to the 3D contrast. It is around 700 for the present displays, a value much higher than the 3D contrast that is limited by the crosstalk between the different views. Figure 2. Averaged luminance for white state (left) and black state (right) using three point positions: area size 4x6m, resolution 2mm 3.3 Imaging measurements We have positioned our imaging system at 4 meters from the center of the display and made luminance measurements shifting the system on 200mm with a step of 5mm. The angular aperture of the system was sufficient to cover all the display surface even for the larger lateral shifts. The experiment has been repeated for view, view 2, view 3 and black and white state and the data corresponding the entire surface of the display extracted in all the cases. The monocular contrast of each view has been computed using formula (7): Yi ( X, Y ) YK ( X, Y ) Ci ( X, Y ) ( N ) (7) Y ( X, Y) Y ( X, Y ) ( N ) Y ( X, Y ) W i X and Y are the coordinates on the display surface (cf. figure 7). This formula corresponds to formula () if we assume that white state is the sum of the different views. The different monocular contrasts have been computed versus position. Four monocular contrasts for two views and two positions are reported in figure 3. The positions correspond to the optimized left and right eye positions for view 2 and view 3. As expected from the angular computations (cf. figure 8&9), the monocular contrast is maximized for one view but not negligible for the other due to the overlap between views. Some local defects can also be observed and in particular two brighter oblique lines corresponding probably to the lens direction and the orthogonal direction. Since we have measured the viewing angle properties at display center it is interesting to extract the behavior of the monocular contrast for the different views versus the lateral position. The result is reported in figure 4. The fact that the two peaks of monocular contrast for view 2 and 3 are separated by 65mm confirm that the optimized distance for stereoscopy is 4 meters. K

10 Monocular contrast Figure 3. Monocular contrast measured for two views and two positions from imaging luminance measurements; camera distance 4m, iris diameter 8mm. We have compared the monocular contrast measured at center with the imaging experiment with the simulations made at 4 meters using the angular measurements made at center. Results are reported in figure 4 for view 3. The agreement is excellent showing the coherency of the characterization. In addition it is easy to simulate the effect of a reduction of the angular resolution on the angular measurements and to repeat the same computation. The reduction of resolution is obtained by averaging the original angular measurements on variable angular aperture. Different simulations are also reported in figure 5. The relative small impact of a reduction of angular resolution to 0.3 can be explained by the smooth behavior of the angular emission characteristic of simple cylindrical lenses. Nevertheless, the absolute value for the monocular contrast cannot be reproduced and the crosstalk will be overestimated in this case. The impact of angular resolution of 0.6 or even 3 is much more important in agreement with the expectations (cf. figure 2) mm 6 4 View View 2 View X position (mm) Figure 4. Monocular contrast measured at display center versus lateral position from imaging luminance measurements for view 2, 3 and 4; camera distance 4m, iris diameter 8mm.

11 monocular contrast Imaging 0.03deg 0.3deg 0.6deg 3deg Lateral position (mm) Figure 5. Monocular contrast of view 3 measured and computed from the angular measurements versus lateral position: center; camera distance 4m, the original angular resolution is reduced for the other computations. Figure 6. Imaging luminance measurement with a 3D pattern: display aspect (left) and luminance isocurves (right). 4. CONCLUSIONS A multi-view auto-stereoscopic 3D display has been characterized in details in the paper. We show that angular measurements at two or three locations on the display with a good angular resolution are sufficient to predict all the stereoscopic properties of the display. The best working distance angle and the viewing freedom in the three directions are predicted using the combined binocular (or 3D) contrast. In addition, the investigation of monocular and binocular contrast of the different views allow to understand and quantify the crosstalk. In the display under investigation, the relatively large overlapping between the different views induces for one single view at its optimized viewing position a large amount of parasitic light that is coming from all the other views. In order to illustrate this effect in practical configuration, we have made one imaging measurement on a specific 3D pattern that includes 5 different white squares on a black background. For each view the five squares are shifted by 5 pixel along the horizontal and vertical positions. The luminance measurement is made with the imaging system located at 4 meters of the display and at the exact lateral position for one specific view. The measurement result is reported in figure 6. The crosstalk due to the other views is visible on the isocurve presentation with includes a logarithmic scale (cf. figure 6.b). The expected view (the white squares) is

12 superposed with additional parasitic views with different magnitudes and positions. One can understand well how this parasitic crosstalk is prejudicial for a clear vision of the stereoscopy with this display. The study performed in the paper allows to predict and understand the magnitude of these parasitic effects and to compare with other auto-stereoscopic 3D displays. ACKNOWLEDGEMENTS The authors thanks Mr. Didier Debons from NEO TELECOMS for his friendly lending of the 3D display used in the tests. REFERENCES [] Boher, P., Leroux, T., Bignon, T., Collomb-Patton, V., A new to characterize auto-stereoscopic 3D displays using Fourier optics instrument, Electronic Imaging, Proceedings SPIE 7237, 37 (2009). [2] Leroux, T., Boher, P., Bignon, T., Glinel, D., VCMaster3D: a new Fourier optics viewing angle instrument for characterization of auto-stereoscopic 3D displays, SID Symposium Digest of Technical Papers, 40, 5 (2009) [3] Boher, P., Leroux, T., Bignon, T., Collomb-Patton, V., Multispectral polarization viewing angle analysis of circular polarized stereoscopic 3D displays, Electronic Imaging, San Jose, Proc. SPIE 7524, 26 (200) [4] Boher, P., Leroux, T, Collomb-Patton, V., Bignon, T., Ginel, D., A common approach to characterizing autostereoscopic and polarization-based 3-D displays, Journal of the SID, 8/4, 293 (200) [5] Leroux, T, Boher, P., Collomb-Patton, V., Bignon, T., Characterization of auto-stereoscopic and polarization based 3D displays: a common approach, IMID Seoul Korea, October 3-5, 46- (2009) [6] Boher, P., Leroux, T, Collomb-Patton, V., Bignon, T., Optical Characterization of Shutter Glasses Stereoscopic 3D displays, Proceedings SPIE 7863, 36 (20) [7] Boher, P., Leroux, T, Collomb-Patton, V., Characterization of one Time-Sequential Stereoscopic 3D Display - Part I: Temporal Analysis, Journal of Information Display, vol., N 2, 8/4, 57 (200) [8] Boher, P., Leroux, T, Collomb-Patton, V., Characterization of one Time-Sequential Stereoscopic 3D Display - Part II: Quick Characterization Using Homogeneity Measurements, Journal of Information Display, vol., N 2, 8/4, 2 (200) [9] Leroux, T., Boher, P., Bignon, T., Quality control of auto-stereoscopic 3D displays using video luminance meter, IDW, Nagoya, December 7-9 (20) [0] Boher, P., Leroux, T., Bignon, T., Collomb-Patton, V., Full optical characterization of auto-stereoscopic 3D displays using local viewing angle and imaging measurements, Proceedings SPIE 8288, 82880S (202 [] Leroux, T., Fast contrast vs. viewing angle measurements for LCDs, Proceedings 3th Int. Display Research Conference (Eurodisplay 93), 447 (993) [2] Boher, P., Bignon, T., Leroux, T., Auto-stereoscopic 3D display characterization using Fourier optics instrument and computation in 3D observer space, IDW, Niigata, December (2008) [3] Boher, P., Leroux, T, Collomb-Patton, V., Bignon, T., On the color accuracy of an imaging system using color filters, J. of Information Display, vol. 3, N, 7-6, March (202) [4] Horikoshi, T., Uehara, S, Taira, K., Hamagishi, G., Nomura, T., Mashitani, K.,Koike, T.,Yuuki, A., Watanabe, N., Hisatake, Y., Ujike, H., Stereoscopic viewing space analysis based on optical measurements, Proceedings Eurodisplay, 6-9, (2009). [5] Horikoshi, T., Uehara, S; Koike, T., Kato, C., Taira, K.,Hamagishi, G.,Mashitani, K.,Nomura, T., Yuuki, A., Watanabe, N., Hisatake, Y., Ujike, H., Characterization of 3D Image Quality on auto-stereoscopic Displays Proposal of Interocular 3D Purity, SID Symposium Digest of Technical Papers, 4, (200) [6] Nakao, K; Higano, T., Kanda, N.; Wakemoto, H.;, Critical level of Crosstalk for Visual Perception of 3D and Viewing Space Mapping, SID Symposium Digest of Technical Papers, 43, (202) [7] Tsirlin, I., Wilcox, L., Allison, R., The Effect of Crosstalk on the Perceived Depth From Disparity and Monocular Occlusion, IEEE Trans. on Broadcasting, 57, N 2 (20) [8] Uehara, S., Hiroya, T., Shigemura, K., Asada, H., Reduction and Measurement of 3D Moiré Caused by Lenticular Sheet and Backlight, SID Symposium Digest of Technical Papers, 40, (2009)