Abstract

The discontinuity of motion parallax offered by multi-view displays was assessed by subjective evaluation. A super multi-view head-up display, which provides dense viewing points and has short-, medium-, and long-distance display ranges, was used. The results showed that discontinuity perception depended on the ratio of an image shift between adjacent parallax images to a pixel pitch of three-dimensional (3D) images and the crosstalk between viewing points. When the ratio was less than 0.2 and the crosstalk was small, the discontinuity was not perceived. When the ratio was greater than 1 and the crosstalk was small, the discontinuity was perceived, and the resolution of the 3D images decreased twice. When the crosstalk was large, the discontinuity was not perceived even when the ratio was 1 or 2. However, the resolution decreased two or more times.

© 2012 OSA

1. Introduction

Motion parallax is one of the physiological cues of human three-dimensional (3D) perception [1]. Conventional two-view 3D displays [2, 3], including both the glasses and glasses-free types, offer a sense of depth to viewers using two other physiological cues such as vergence and binocular disparity. Multi-view displays [16], which offer glasses-free 3D images to multiple viewers, provide motion parallax in addition to vergence and binocular disparity. Because the number of views provided by multi-view displays is limited practically, motion parallax that they provide is discretized. The smoothness of motion parallax depends on the density of viewing points, i.e., the interval between viewing points. Motion parallax becomes smoother when the density of the viewing points increases, and it becomes more discontinuous when the density decreases. This study reveals the relationships between the smoothness of motion parallax and the density of viewing points.

We previously developed the super multi-view windshield display (SMV–WSD) [7], which is a head-up display (HUD) used in automobiles. It provides driving information as 3D images for near and far distances through a windshield. The driving information can be observed beside real objects such as intersections, signposts, and obstacles on roads. Motion parallax is the last physiological cue for the depth perception of distant objects or images. The super multi-view (SMV) display technique was used because it provides very smooth motion parallax although the SMV display technique was originally developed to resolve the vergence-accommodation conflict that causes visual fatigue while observing 3D images. This is performed by reducing the interval between viewing points to be smaller than the diameter of the pupil of an eye [812]. Smooth motion parallax is important for the superposition of 3D images in the real world. Viewers feel as if 3D images exist in real scenes when 3D images have smooth motion parallax.

Figure 1 shows the discontinuity in motion parallax provided by the multi-view displays. The distance between the 3D image and an observer is denoted by z. The observation distance, which is the distance between the display plane and an observer, is denoted by l. The interval between viewing points is denoted by d. The width of the region for one viewing point is also d. The parallax image viewed by an eye does not change until the eye moves into regions for adjacent viewing points. Because parallax images are displayed on the display plane, the perceived horizontal position of 3D images changes depending on the horizontal eye position. In the case where the 3D image is displayed behind the display plane, when the eye moves horizontally within the region for one viewing point, the 3D image moves in the opposite horizontal direction. On the contrary, in the case where the 3D image is displayed in front of the display plane, the 3D image moves in the same horizontal direction. When the eye moves into the region of an adjacent viewing point, the 3D image jumps horizontally. The width of this fluctuating motion of 3D images on the display plane is given by the length PnPn+1 in Fig. 1, which is denoted by q. The similarity of the triangles PAB and PPnPn+1 gives z: zl = d: q. Thus, the motion parallax fluctuation is given by q = (1 − l /z) d.

 

Fig. 1 Discontinuity in motion parallax that occurred in multi-view displays.

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We previously evaluated the smoothness of motion parallax produced by the SMV–WSD [7]. Subjective evaluation showed that the fluctuation of motion parallax would not be perceived when it was smaller than the pixel pitch of 3D images. Moreover, it was found that the blur due to the crosstalk between viewing points increased the smoothness of motion parallax. However, the evaluation was performed only for a relatively long observation distance (1.95 m). More detailed evaluations should be performed with various observation distances to find conditions necessary to provide smooth motion parallax. In addition, the effects of the crosstalk should be further explored because it is unavoidable in most of the multi-view displays.

Several studies have been conducted to explore the relationship between the density of viewing points and the smoothness of motion parallax provided by multi-view displays [1315]. However, they used a glass-type stereoscopic display with a head-tracking mechanism to simulate multi-view displays because multi-view displays with adequately dense viewing points could not be used. The stereoscopic image was changed according to the horizontal head position to provide motion parallax. Pastoor et al. [13] showed that the maximum magnitude of the parallax shift that occurred at the transition points between adjacent viewing points must not exceed 1.15 min of arc to maintain a good 3D image quality. Runde [14] reported that the spatial sampling of eye positions should not exceed 5 min of arc (i.e., 12 views per degree of visual angle) to obtain smooth motion parallax. Speranza et al. [15] performed experiments in which the 3D image was changed with respect to an observer’s action according to the head movement, hand movement, or independently. They reported that the average of the required density for the three conditions was 3.5 views per cm or approximately 7 views per degree of visual angle. When motion parallax was provided according to the head movement, 7 views per cm was required. Hoshino et al. [16] discussed the discontinuity in motion parallax from the perspective of image acquisition, and they examined the number of cameras required to capture multi-view images.

The previous studies [13‒15] experimentally showed the maximum parallax shift or the minimum density of viewing points required to provide smooth motion parallax. These values undoubtedly depend on the display parameters of multi-view displays. However, the studies did not show the relationship between the display parameters and the perception of smooth motion parallax. In this study, we experimentally derive the detailed relationships between the display parameters, such as, the interval between viewing points, the observation distance, the distance to 3D images, the pixel pitch, and crosstalk between viewing points to provide smooth motion parallax. Most previous studies used the combination of a stereoscopic display and head-tracking mechanism to simulate multi-view displays. This study uses an actual multi-view display so that the effects of the crosstalk between viewing points can be examined. A newly developed super multi-view head-up display (SMV–HUD) is used for the experiments, which provides 36 views and has three distance ranges for 3D image presentation: short-, medium-, and long-distance ranges. In addition, the use of the SMV–HUD permits the evaluations of the effect of motion-parallax discontinuity on the superposition of 3D images in real scenes. The results obtained in this study may be applicable to ordinary multi-view displays.

2. Super-multi-view head-up display

In this section, the newly developed SMV–HUD is explained. It was designed such that it could modify the observation distance to provide the three display-distance ranges. It also enables the simultaneous observation of both 3D images and real objects.

The configuration of the SMV–HUD is shown in Fig. 2(a) , which is the same as that used for the previously developed SMV–WSD [7]. It consists of a multi-view display, a projection lens, and a half mirror. The multi-view display and the projection lens were placed below the half mirror, and an observer perceives 3D images through the half mirror. Figure 2(b) shows an imaging system that was drawn without the half mirror for simplicity. The screen of the multi-view display is imaged by the projection lens to produce a virtual image on a display plane at an observation distance, which is a virtual screen. The projection lens also images multiple viewing points generated by the multi-view display to produce multiple viewing points for the observer.

 

Fig. 2 Super multi-view head-up display (SMV–HUD): (a) system configuration, and (b) imaging system; in the SMV-HUD developed in this study, a Fresnel lens is used as the projection lens, and the multi-view display consists of a flat-panel display and a slanted lenticular lens.

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The equations for the optical system are described. The screen width of the multi-view display is denoted by D0, the width of a viewing region produced by the multi-view display is denoted by W0, and the distance to the viewing region from the screen is denoted by l0. The width of the virtual screen is denoted by D, and the distance between the virtual screen and the observer is denoted by l. The width of the viewing region for the observer is denoted by W. The focal length of the projection lens is denoted by f. The distance from the projection lens to the multi-view display is denoted by s and that from the projection lens to the viewing region for the observer is denoted by h. The equations used to produce the virtual image are as follows:

1/s1/(lh)=1/f,
(lh)/s=D/D0.
The equations used to produce the viewing points for the observer are as follows:

1/h1/(l0s)=1/f,
h/(l0s)=W/W0.

The SMV–HUD was designed to offer short-, medium-, and long-distance ranges for 3D image presentation. The distance range could be modified by replacing the projection lens and changing the distances s and h. The short-distance range considers a PC monitor on a desk; therefore, the observation distance is l = 600 mm, and the screen size is 20.9 in. The medium-distance range considers a TV in a living room; therefore, the observation distance is l = 1.5 m, and the screen size is 42.8 in. The long-distance range considers a large display screen for activities such as public viewing and advertisements; the distance is l = 5.0 m, and the screen size is 170 in.

We surveyed possible flat-panel displays that could be used to construct the SMV–HUD. However, we found that using the liquid crystal panel employed in our previous study [7] was appropriate because of its high pixel density. The resolution was 1,920 × 1,200, and the screen size was 17.0 in. A slanted lenticular lens [17] with a lens pitch of 1.143 mm was used to generate the viewing region whose width was W0 = 4.65 m at a distance of l0 = 29.1 m. The 3D resolution was 320 × 200, and the number of viewing points was 36.

For the projection lens, a Fresnel lens was used because a large-diameter lens was required. Three Fresnel lenses were selected to correspond to the three distance ranges. Table 1 shows the focal lengths and other parameters. The intervals of the viewing points are less than 3 mm for all three configurations.

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Table 1. Display Parameters for SMV–HUD

Figure 3 shows the constructed SMV–HUD. The observer could simultaneously perceive 3D images and real objects through the half mirror. The size of the half mirror was 200 × 125 mm2.

 

Fig. 3 Photographs of the developed SMV–HUD: the display system is configured for (a) short-, (b) medium-, and (c) long-distance ranges for 3D image presentation.

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The light-intensity distributions of viewing points for the observer were measured to evaluate the crosstalk between viewing points. A cooled charge coupled device (CCD) camera was placed on the plane at which the observer’s viewing points were generated. A white image was displayed on one viewing point in which the intensity distribution was measured, and black images were displayed on the other viewing points. The cooled CCD camera was mounted onto a horizontal translation stage, and it was appropriately moved horizontally to encompass the entire viewing region. The measurements were performed for the three system configurations. The results for the three system configurations were similar, and the results for the medium-distance configuration are shown in Fig. 4(a) . Each curve shows the light-intensity distribution obtained by the cooled CCD camera for each viewing point; each curve was drawn using the values of pixels along a horizontal line that has the largest light intensity in the vertical direction. The graph consists of 36 curves corresponding to 36 viewing points. The averages of the measured intervals of the viewing points were 2.1, 2.6, and 2.1 mm for the short-, medium-, and long-distance configurations, respectively. As observed in Fig. 4(a), a considerable crosstalk existed between the viewing points because the slanted lenticular technique intrinsically generates the crosstalk, and the use of the Fresnel lens also increases the crosstalk. In the subjective assessment described in Sec. 3, the interval between the viewing points was increased several times by displaying identical parallax images to successive viewing points. Figures 4(b)4(e) show the intensity distributions of the viewing points with increased intervals, which were calculated from the measured distributions shown in Fig. 4(a). As shown in the graphs, the crosstalk between the viewing points decreased when the interval increased.

 

Fig. 4 Measured light-intensity distributions of viewing points for medium-distance configuration: intervals between the viewing points are (a) 2.6 mm, (b) 5.3 mm, (c) 7.9 mm, (d) 10.6 mm, and (e) 15.8 mm.

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3. Perception of the discontinuous motion parallax

The perception of motion-parallax discontinuity was evaluated using the developed SMV–HUD. The depth perception of 3D images was also evaluated.

Because the fluctuation of motion parallax is given by q = (1 − l /z) d, the three parameters d, l, and z were changed. The interval between views d was changed by displaying identical parallax images to successive viewing points, as described in Sec. 2. The three display configurations provided three observation distances l. The display distance z was determined from preparatory experiments. The distance z was heavily adjusted to be approximately equal to the observation distance l. Figure 5 shows a test image used for the measurements. The checkered pattern was slanted at an angle same as that of the lenticular lens. The solid checker pattern was not used because it became jaggy when displayed by the slanted lenticular lens. The image size was changed so that the visual angle of the test image would remain constant in order to avoid depth perception due to a psychological factor, i.e., the image size. The visual angle was 4.0°, which was determined from preparatory experiments. The experimental conditions are summarized in Table 2 .

 

Fig. 5 Test image used for measurements.

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Table 2. Experimental Conditions

Subjects were asked whether or not they were aware of unnatural motion parallax while moving their heads horizontally. They were required to choose from two options: unnatural motion parallax was 1) perceived or 2) not perceived. The depth perception of 3D images was also evaluated using a real reference object. The real reference object was a 2D image displayed on a PC monitor. The checkered pattern shown in Fig. 5 was also used for the reference object. However, the visual angle of the reference object was different from that of the 3D test image in order to avoid depth perception due to image size. The visual angle of the reference object was set to 2.0°, which was determined from preparatory experiments. The PC monitor was moved such that the reference object was located at the same distance as the 3D test image. Subjects were queried about their perceived depth positions, and they were required to select from three distances at which they are perceived: 1) the same distance, 2) approximately the same distance, and 3) different distances.

There were 10 subjects. All subjects were screened for normal stereoscopic vision and visual acuity (average of 1.2, and minimum of 0.9). The distance to the test image was randomly varied. Five trials were performed for each display condition. The subjects observed the 3D images using a dominant eye and the other eye was covered with an eye patch to allow the maximum movement of the dominant eye because the viewing region widths were less than 100 mm, as shown in Table 1.

Figures 6 -8 show the results obtained for the short-, medium-, and long-distance ranges, respectively. In each figure, the results for the different intervals of viewing points are shown in different graphs. The horizontal axis represents the distance to the 3D test image. The left-vertical axis represents the average ratio indicating that the subjects perceived unnatural motion parallax, which is indicated by a diamond. The right-vertical axis represents the average ratio of proper depth perception, i.e., the average ratio indicating the subjects’ answers that the 3D image and the reference object were perceived to be at the same depth or approximately the same depth, which is indicated by a circle. The observation distance l is indicated by the dashed vertical line. The three test images shown in Fig. 7(b) were captured by a video camera. Media 1 shows the movie of the 3D test image in which discontinuous motion parallax was clearly observed, Media 2 shows the movie in which moderate discontinuity was observed, and Media 3 shows the movie in which discontinuities were seldom observed.

 

Fig. 6 Measured results of unnatural motion-parallax and proper depth perceptions for short-distance configuration (observation distance l = 0.6 m; screen size = 20.9 in.): the intervals of viewing points are (a) 2.2 mm, (b) 4.4 mm, (c) 6.6 mm, (d) 8.8 mm, and (e) 13.1 mm.

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Fig. 7 Measured results of unnatural motion-parallax and proper depth perceptions for medium-distance configuration (observation distance l = 1.5 m; screen size = 42.8 in.): intervals between viewing points are (a) 2.6 mm, (b) 5.3 mm, (c) 7.9 mm, (d) 10.6 mm, and (e) 15.8 mm: Movies are provided in case of (b) when the distance to 3D image was 0.5 m (Media 1), 0.7 m (Media 2), and 1.5 m (Media 3).

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From the results shown in Figs. 6–8, the depth ranges of 3D images in which the subjects perceived smooth motion parallax, i.e., the ratio of the unnatural motion-parallax perception was low, exist in the vicinity of the virtual screens. For all distance ranges, the depth range increased when the interval between the viewing points decreased. The above results can be explained by the fluctuation of 3D images that is given by q = (1 − l /z) d.

The ratio of the proper depth perception decreased when 3D images were displayed further from the virtual screen (display plane). When compared to the perception of unnatural motion parallax, the depth perception was less affected by the fluctuation of 3D images. The 3D images were perceived at the same or approximately the same distance as that of the reference objects, whereas unnatural motion parallax was perceived.

Because 3D images are quantized by their pixel pitch, the image fluctuation q of 3D images is quantized by the pixel pitch p on the display plane. We found that unnatural motion-parallax perception depends on the ratio of the image fluctuation to the pixel pitch, i.e., q/p. Thus, Fig. 6, Fig. 7, and Fig. 8 were redrawn by considering the horizontal axes as q/p. For each distance range, the results are divided into two cases, i.e., small and large crosstalks, and they are shown in different graphs. Figures 9(a) and 9(b) show the small-crosstalk (the interval between views is 6.6, 8.8, and 13.1 mm) and large-crosstalk cases (the interval between views is 2.2 and 4.4 mm) for the short-distance range. Figures 9(c) and 9(d) show the small-crosstalk and large-crosstalk cases for the medium-distance range, and Figs. 9(e) and 9(f) show those for the long-distance range.

 

Fig. 8 Measured results of unnatural motion-parallax and proper depth perceptions for long-distance configuration (observation distance l = 5.0 m; screen size = 170 inches): intervals between viewing points are (a) 2.2 mm, (b) 4.4 mm, (c) 6.7 mm, (d) 8.9 mm, and (e) 13.3 mm.

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The results for the small-crosstalk cases shown in Figs. 9(a) , 9(c), and 9(e) are considered. When |q/p| is smaller than 0.2, the ratio of unnatural motion-parallax perception is approximately zero. When |q/p| is greater than 1, the ratio is approximately 100%.

 

Fig. 9 Dependence of unnatural motion-parallax perception on q/p: (a) and (b) correspond to short-distance configuration, (c) and (d) correspond to medium-distance configuration, and (e) and (f) correspond to long-distance configuration; (a), (c), and (e) show small-crosstalk cases, and (b), (d), and (f) show large-crosstalk cases.

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Next, the results for the large-crosstalk cases were considered. For the short-distance range, as shown in Fig. 9(b), when |q/p| is smaller than 1, the ratio of unnatural motion-parallax perception is approximately zero for both the intervals of views (2.2 and 4.4 mm.) For the medium-distance range, as shown in Fig. 9(d), the ratio is approximately zero when |q/p| is smaller than 1 in the case when the interval of views is 5.3 mm. The ratio is also approximately zero when |q/p| is smaller than 2 in the case when the interval is 2.6 mm. For the long-distance range, as shown in Fig. 9(f), the ratio is approximately zero when |q/p| is smaller than 0.2 in the case when the interval is 4.4 mm.

4. Evaluation of retinal images

To explain the results obtained in the previous section, we investigated the way in which a retinal image changes because of the eye movement.

Figure 10 illustrates the retinal image formation considering the crosstalk between viewing points. Figure 10(a) shows the case in which the crosstalk is sufficiently small and |q/p| = 1. The point-spread functions (PSFs) on a retina are shown at several eye positions within the region of one viewing point #n. The width of the peaks constituting the PSF corresponds to the width of each cylindrical lens constituting the lenticular lens. At the transition points between adjacent viewing points, two peaks appear, and their separation is p. The dashed line, which is the envelope of the sum of the peaks, shows the PSF. The width of the PSF increases twice at the intermediate points. Figure 10(b) shows the case in which the crosstalk is moderate and |q/p| = 1. In this case, the PSF consists of a main lobe corresponding to the view #n and two side lobes corresponding to the views #n − 1 and # n + 1. The heights of the main and side lobes change depending on the eye position. The widths of the PSFs become approximately constant with appropriate amounts of crosstalk. Because the width of the PSFs is approximately 2p at any viewing position, the resolution of 3D images decreases twice. Figure 10(c) shows the case in which the crosstalk is large and |q/p| = 2. In this case, the PSF consists of three separate peaks because the separation between the peaks is 2p. The widths of the PSFs are 3p–5p. Therefore, the resolution of the 3D images decreases more than thrice.

 

Fig. 10 Retinal image formation at several positions in the viewing region: (a) small crosstalk and |q/p| = 1, (b) moderate crosstalk and |q/p| = 1, and (c) large crosstalk and |q/p| = 2.

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The retinal image formation was examined experimentally. A slant vertical line was displayed by the SMV–HUD. The line was slanted at an angle same as that of the lenticular lens. A cooled CCD camera was used to investigate retinal images. The camera was placed at the distance where the viewing points were produced. The focal length of the lens was 16 mm, and the aperture diameter of the lens was set to 5.7 mm, which was the average pupil diameter of the subjects during evaluation. The resolution of the camera was 772 × 580, and the pixel pitch was 8.3 μm. The focus of the camera was set at the display plane. The camera was mounted onto a horizontal translation stage to facilitate its motion across several viewing points.

First, we investigated the retinal images when smooth motion parallax was perceived in the small-crosstalk cases. The retinal images were captured with the display conditions indicated by ‘A’ in Fig. 9, where |q/p| was approximately equal to 0.2. Figures 11(a)11(c) show the captured images for the short-, medium-, and long-distance ranges, respectively. The camera position was changed from one endpoint to the other endpoint of a region for a viewing point #n, where one endpoint is the transition point of the regions for viewing points #n and #n − 1, and the other endpoint is that of the regions for viewing points #n and #n + 1. The light-intensity distributions in the horizontal direction are shown. At the transition points, two parallax images for adjacent viewing points were observed simultaneously. Because |q/p| is small, the difference between the adjacent parallax images is small, so the fluctuation of the line width depending on the observation position was seldom observed.

 

Fig. 11 Images captured by the cooled CCD camera at several horizontal positions near the viewing point when |q/p| was approximately equal to 0.2 for small-crosstalk cases: (a) for short-distance range, d = 8.8 mm, z = 0.59 m, and q/p = −0.16; (b) medium-distance range, d = 10.6 mm, z = 1.45 m, and q/p = −0.14; and (c) long-distance range, d = 8.9 mm, z = 4.1 m, and q/p = −0.17.

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Then, we captured images with display conditions in which unnatural motion parallax was clearly perceived in the small-crosstalk cases; the captured display conditions are indicated by ‘B’ in Fig. 9. Figure 12 shows the captured images when |q/p| is approximately equal to one for the three distance ranges. At the transition positions, the line width is twice of that at the center position because the difference in the horizontal line position between adjacent parallax images was approximately equal to the line width, i.e., |q| ≈p. Therefore, the horizontal resolution decreased twice at the transition positions. This is the case shown in Fig. 10(a).

 

Fig. 12 Images captured by the cooled CCD camera at several horizontal positions near the viewing point when |q/p| was approximately equal to 1 for small-crosstalk cases: (a) for short-distance range, d = 8.8 mm, z = 0.54 m, and q/p = −0.70; (b) for medium-distance range, d = 10.6 mm, z = 1.2 m, and q/p = −1.0; and (c) for long-distance range, d = 8.9 mm, z = 2.1 m, and q/p = −1.1.

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Next, the images were captured with display conditions in which |q/p| was approximately equal to 1 for the large-crosstalk cases. The captured display conditions are indicated by ‘C’ in Fig. 9. Figures 13(a)–(c) show the captured images obtained for the short-, medium-, and long-distance configurations, respectively. The captured images were similar at any horizontal position. Because of the large crosstalk, the image captured at the center of the region for the viewing point #n (center photos) contained considerable amounts of parallax images for the viewing points #n − 1 and #n + 1. As shown in the leftmost and rightmost photographs, two adjacent parallax images were simultaneously observed at the transition points. Therefore, the retinal image did not change practically depending on the observation position, so that smooth motion parallax could be perceived. However, the resolution of the retinal image decreased twice at any observation position. This is the case shown in Fig. 10(b). From Fig. 9(f), even though q/p = −0.89, unnatural motion parallax was perceived to a certain extent when the interval between viewing points was 4.4 mm. Figure 13(d) shows the captured images for this display condition. The line width at the center was smaller than those at the transition points. From the measurements of intensity distributions of the viewing points described in Sec. 2, the crosstalk for this condition was smaller than those for the above three conditions. Therefore, variations were observed in the line width so that unnatural motion parallax was perceived to some extent. The images shown in Fig. 13(d) appear to be intermediate images between those shown in the Figs. 13(a)13(c) and Figs. 12(a)12(c).

 

Fig. 13 Images captured by the cooled CCD camera at several horizontal positions near the viewing point when | q/p | was approximately equal to 1 for large-crosstalk cases: (a) for short-distance configuration, d = 2.2 mm, z = 0.35 m, and q/p = −1.1; (b) for medium-distance configuration, d = 2.6 mm, z = 0.75 m, and q/p = −1.0; (c) for long-distance configuration, d = 2.2 mm, z = 1.0 m, and q/p = −0.77; and (d) for long-distance configuration, d = 4.4 mm, z = 1.5 m, and q/p = −0.89.

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We captured images with display conditions in which |q/p| was approximately equal to 2 for the large-crosstalk cases. The captured display conditions are indicated by ‘D’ in Fig. 9. For the short-distance configuration, the captured images are shown in Fig. 14(a) . For the medium-distance configuration, Figs. 14(b) and 14(c) show the captured images when the interval between views was 5.3 mm and 2.6 mm, respectively. The crosstalk between the viewing points generated distinctive side lobes because the shift of the image q is approximately twice as large as the pixel pitch p (|q| ≈2p). For Figs. 14(a) and 14(b), the retinal image markedly changed depending on the observation position so that unnatural motion parallax was perceived. For Fig. 14(c), the crosstalk was greater than those for the above-mentioned two cases. The greater crosstalk increased the heights of the side lobes so that there was a small change in the retinal image and discontinuous motion parallax was not perceived. Although smooth motion parallax was obtained, the width of the distribution became three to four times larger than the line width so that the resolution decreased more than thrice. This is the case shown in Fig. 10(c).

 

Fig. 14 Images captured by the cooled CCD camera at several horizontal positions near the viewing point when | q/p | was approximately equal to 2 for large-crosstalk cases: (a) for short-distance configuration, d = 4.4 mm, z = 0.35 m, and q/p = −2.2; (b) for medium-distance configuration, d = 5.3 mm, z = 0.75 m, and q/p = −2.0; and (c) for medium-distance configuration, d = 2.6 mm, z = 0.5 m, and q/p = −2.0.

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5. Discussion

From the results obtained in Secs. 4 and 5, we found that there is a close relationship between the unnatural motion-parallax perception, the parallax shift ratio |q/p|, the crosstalk between viewing points, and the resolution of 3D images. For the small-crosstalk cases, when |q/p| is less than 0.2, unnatural motion parallax is seldom perceived, and the resolution does not decrease. When |q/p| is greater than 1, unnatural motion parallax is perceived, and the resolution decreases twice at transition points for the viewing points. For the large-crosstalk cases, unnatural motion parallax is not perceived even when |q/p| is 1 or 2 although the resolution decreases two or more times throughout viewing regions. The extent of crosstalk is important. When the crosstalk is sufficiently large, the ratio of unnatural motion-parallax perception largely decreases, as shown in Figs. 9(b) and 9(d). When the crosstalk is not so large, as shown in Fig. 9(f), the ratio does not decrease much. The relationships are illustrated in Fig. 15 . The resolution decreases inversely to |q/p|.

 

Fig. 15 Relationships between unnatural motion-parallax perception, resolution, crosstalk, and parallax shift ratio |q/p|.

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Reference 13 reported that the fluctuations in motion parallax must not exceed 1.15 min of arc. From the experimental conditions described in this article, the pixel pitch was p = 3.91 mm, and the observation distance was l = 3.30 m. This means that |q/p| should be less than 0.28. This result is in good agreement with that obtained in our study. Reference 14 reported that a spatial quantization of 5 min of arc is sufficient. Although the depth of the 3D image was not described in Ref. 14, i.e., the result cannot be directly compared with that obtained in this study, the author mentioned that the result was in accordance with the finding of Ref. 13. Reference 15 reported that 7 views per cm were required to exactly reproduce motion parallax. Because the pixel pitch and depths of the 3D images were not described, this result cannot be compared with our result. Although the previous studies used stereoscopic displays to simulate multi-view displays, this study used the actual multi-view display. Therefore, the effect of the crosstalk between viewing points upon the motion-parallax perception could be examined. The crosstalk increases the smoothness of motion parallax. However, it decreases the resolution.

Here we calculate the depth range of 3D images in which unnatural motion parallax is not perceived. This condition is described as |q/p| < m, where m is a positive real value, for example, 0.2, 1, or 2, depending on the degree of smoothness required for motion parallax. The depth range is given as follows:

z>l/(1+mp/d)(dmp),
l/(1+mp/d)<z<l/(1mp/d)(d>mp).
From these equations, if the interval between the viewing points d were reduced sufficiently, the depth range would increase to infinity in the backward direction. When the interval is not very small, the depth range becomes finite.

The pixel pitches of 3D images generated by the three system configurations were relatively large. Therefore, the pixels were observable, and the perception of unnatural motion parallax depended on the pixel pitch. If the pixel pitch becomes so small that the human eye cannot determine a single pixel, the perception may depend on the minimum resolvable distance of the eyes and not on the pixel pitch. In Eqs. (5) and (6), p may be replaced by the minimum resolvable distance.

The heights of peaks in PSFs in Fig. 14 can be calculated from the light-intensity distributions of the viewing points shown in Fig. 4 and the pupil diameters of the eyes. The amount of light within the light-intensity distribution of the viewing point, which passes through a circular aperture whose diameter is equal to the pupil diameter, provides the height of the peak corresponding to this viewing point. The measured light-intensity distributions for the viewing points, e.g., as shown in Fig. 4, and the average pupil diameter during subjective evaluations were used to calculate the peak heights. We confirmed that the calculated peak heights showed a good agreement with the measured PSFs shown in Fig. 14.

We examined the relationships between the proper depth-perception ratio and the parallax shift ratio |q/p|. However, the proper depth-perception ratio cannot be clearly explained using |q/p|.

The experimental results presented in this study were obtained using the dominant eye. Motion parallax is classified as depth perception using a monocular eye [1]. This study examined the effects of motion parallax discontinuity on depth perception. However, depth can also be perceived using vergence and binocular disparity. These two physiological factors might influence depth perception by discontinuous motion parallax. Because the widths of the viewing regions of the SMV-HUD are limited, sufficient movable lengths cannot be provided in the horizontal direction for observation by both eyes. The width of the viewing region needs to be enlarged to perform experiments on observation by both eyes.

In this study, the SMV–HUD display was developed to explore the display conditions required to provide smooth motion parallax. Its smallest interval between viewing points is smaller than a pupil diameter, implying that SMV condition was satisfied. However, the accommodation responses were not apparently triggered because the subjects reported that their observed images were similar to those captured by the CCD camera (shown in Sec. 4), whose focus was at the display plane. The subjects observed the 3D images only with their dominant eye, so the vergence did not function and did not trigger the accommodation responses. The widths of the intensity distributions for the viewing points were greater than the intervals between the viewing points, as shown in Fig. 4(a). Therefore, the crosstalk between the viewing points would probably affect the evocation of the accommodation responses. If the accommodation functioned, the parallax images for adjacent viewing points would be superimposed on the retina to improve the smoothness of motion parallax.

6. Conclusion

We developed an SMV–HUD with three system configurations that produce 3D images in short-, medium-, and long-distance ranges. The display conditions that provide smooth motion parallax were evaluated using the developed SMV–HUD. We found that the ratio of the image shift between adjacent parallax images to the pixel pitch of 3D images dominated the perception of the discontinuous motion parallax. When the ratio was smaller than 0.2, the discontinuity was not perceived. When the ratio was greater than 1, the discontinuity was perceived and the 3D resolution decreased twice at transition points of the regions for adjacent viewing points. When the crosstalk between viewing points was large, the discontinuity was not perceived even when the ratio was 1 or 2. However, the resolution decreased by a factor of at least two throughout the viewing region.

References and links

1. T. Okoshi, Three-Dimensional Imaging Techniques (Academic Press, New York, 1976).

2. N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011). [CrossRef]  

3. N. A. Dodgson, “Autostereoscopic 3D Displays,” Computer 38(8), 31–36 (2005). [CrossRef]  

4. T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68(5), 548–564 (1980). [CrossRef]  

5. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009). [CrossRef]   [PubMed]  

6. J.-Y. Son and B. Javidi, “Three-dimensional imaging methods based on multiview images,” J. Display Technol. 1(1), 125–140 (2005). [CrossRef]  

7. Y. Takaki, Y. Urano, S. Kashiwada, H. Ando, and K. Nakamura, “Super multi-view windshield display for long-distance image information presentation,” Opt. Express 19(2), 704–716 (2011). [CrossRef]   [PubMed]  

8. Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE 3012, 154–166 (1997). [CrossRef]  

9. T. Honda, Y. Kajiki, K. Susami, T. Hamaguchi, T. Endo, T. Hatada, and T. Fujii, “Three-dimensional display technologies satisfying ‘super multiview condition,” SPIE Crtical Reviews CR76, 218–249.

10. Y. Takaki, “High-Density Directional Display for Generating Natural Three-Dimensional Images,” Proc. IEEE 94(3), 654–663 (2006). [CrossRef]  

11. Y. Takaki and N. Nago, “Multi-projection of lenticular displays to construct a 256-view super multi-view display,” Opt. Express 18(9), 8824–8835 (2010). [CrossRef]   [PubMed]  

12. Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express 19(5), 4129–4139 (2011). [CrossRef]   [PubMed]  

13. S. Pastoor and K. Schenke, “Subjective assessment of the resolution of viewing directions in a multi- viewpoint 3D TV system,” Proc. SID 30, 217–223 (1989).

14. D. Runde, “How to Realize a Natural Image Reproduction using Stereoscopic Displays with Motion Parallax,” IEEE Trans. Circ. Syst. Video Tech. 10(3), 376–386 (2000). [CrossRef]  

15. F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE 5664, 72–82 (2005). [CrossRef]  

16. H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech. 10(3), 366–375 (2000). [CrossRef]  

17. C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997). [CrossRef]  

References

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  1. T. Okoshi, Three-Dimensional Imaging Techniques (Academic Press, New York, 1976).
  2. N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
    [CrossRef]
  3. N. A. Dodgson, “Autostereoscopic 3D Displays,” Computer38(8), 31–36 (2005).
    [CrossRef]
  4. T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
    [CrossRef]
  5. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt.48(34), H77–H94 (2009).
    [CrossRef] [PubMed]
  6. J.-Y. Son and B. Javidi, “Three-dimensional imaging methods based on multiview images,” J. Display Technol.1(1), 125–140 (2005).
    [CrossRef]
  7. Y. Takaki, Y. Urano, S. Kashiwada, H. Ando, and K. Nakamura, “Super multi-view windshield display for long-distance image information presentation,” Opt. Express19(2), 704–716 (2011).
    [CrossRef] [PubMed]
  8. Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE3012, 154–166 (1997).
    [CrossRef]
  9. T. Honda, Y. Kajiki, K. Susami, T. Hamaguchi, T. Endo, T. Hatada, and T. Fujii, “Three-dimensional display technologies satisfying ‘super multiview condition,” SPIE Crtical Reviews CR76, 218–249.
  10. Y. Takaki, “High-Density Directional Display for Generating Natural Three-Dimensional Images,” Proc. IEEE94(3), 654–663 (2006).
    [CrossRef]
  11. Y. Takaki and N. Nago, “Multi-projection of lenticular displays to construct a 256-view super multi-view display,” Opt. Express18(9), 8824–8835 (2010).
    [CrossRef] [PubMed]
  12. Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express19(5), 4129–4139 (2011).
    [CrossRef] [PubMed]
  13. S. Pastoor and K. Schenke, “Subjective assessment of the resolution of viewing directions in a multi- viewpoint 3D TV system,” Proc. SID 30, 217–223 (1989).
  14. D. Runde, “How to Realize a Natural Image Reproduction using Stereoscopic Displays with Motion Parallax,” IEEE Trans. Circ. Syst. Video Tech.10(3), 376–386 (2000).
    [CrossRef]
  15. F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
    [CrossRef]
  16. H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech.10(3), 366–375 (2000).
    [CrossRef]
  17. C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE3012, 179–186 (1997).
    [CrossRef]

2011 (3)

2010 (1)

2009 (1)

2006 (1)

Y. Takaki, “High-Density Directional Display for Generating Natural Three-Dimensional Images,” Proc. IEEE94(3), 654–663 (2006).
[CrossRef]

2005 (3)

N. A. Dodgson, “Autostereoscopic 3D Displays,” Computer38(8), 31–36 (2005).
[CrossRef]

F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
[CrossRef]

J.-Y. Son and B. Javidi, “Three-dimensional imaging methods based on multiview images,” J. Display Technol.1(1), 125–140 (2005).
[CrossRef]

2000 (2)

H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech.10(3), 366–375 (2000).
[CrossRef]

D. Runde, “How to Realize a Natural Image Reproduction using Stereoscopic Displays with Motion Parallax,” IEEE Trans. Circ. Syst. Video Tech.10(3), 376–386 (2000).
[CrossRef]

1997 (2)

C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE3012, 179–186 (1997).
[CrossRef]

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE3012, 154–166 (1997).
[CrossRef]

1980 (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
[CrossRef]

Ando, H.

Clarke, J. A.

C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE3012, 179–186 (1997).
[CrossRef]

Dodgson, N. A.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

N. A. Dodgson, “Autostereoscopic 3D Displays,” Computer38(8), 31–36 (2005).
[CrossRef]

Favalora, G. E.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

Holliman, N. S.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

Honda, T.

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE3012, 154–166 (1997).
[CrossRef]

Hong, K.

Hoshino, H.

H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech.10(3), 366–375 (2000).
[CrossRef]

Javidi, B.

Kajiki, Y.

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE3012, 154–166 (1997).
[CrossRef]

Kashiwada, S.

Lee, B.

Martin, T.

F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
[CrossRef]

Nago, N.

Nakamura, J.

Nakamura, K.

Okano, F.

H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech.10(3), 366–375 (2000).
[CrossRef]

Okoshi, T.

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
[CrossRef]

Park, J.-H.

Pockett, L.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

Runde, D.

D. Runde, “How to Realize a Natural Image Reproduction using Stereoscopic Displays with Motion Parallax,” IEEE Trans. Circ. Syst. Video Tech.10(3), 376–386 (2000).
[CrossRef]

Son, J.-Y.

Speranza, F.

F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
[CrossRef]

Stelmach, L.

F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
[CrossRef]

Takaki, Y.

Tam, W. J.

F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
[CrossRef]

Tanaka, K.

Urano, Y.

van Berkel, C.

C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE3012, 179–186 (1997).
[CrossRef]

Yoshikawa, H.

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE3012, 154–166 (1997).
[CrossRef]

Yuyama, I.

H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech.10(3), 366–375 (2000).
[CrossRef]

Appl. Opt. (1)

Computer (1)

N. A. Dodgson, “Autostereoscopic 3D Displays,” Computer38(8), 31–36 (2005).
[CrossRef]

IEEE Trans. Broadcast (1)

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-dimensional displays: a review and applications analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

IEEE Trans. Circ. Syst. Video Tech. (2)

D. Runde, “How to Realize a Natural Image Reproduction using Stereoscopic Displays with Motion Parallax,” IEEE Trans. Circ. Syst. Video Tech.10(3), 376–386 (2000).
[CrossRef]

H. Hoshino, F. Okano, and I. Yuyama, “A study on resolution and aliasing for multi-viewpoint image acquisition,” IEEE Trans. Circ. Syst. Video Tech.10(3), 366–375 (2000).
[CrossRef]

J. Display Technol. (1)

Opt. Express (3)

Proc. IEEE (2)

Y. Takaki, “High-Density Directional Display for Generating Natural Three-Dimensional Images,” Proc. IEEE94(3), 654–663 (2006).
[CrossRef]

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
[CrossRef]

Proc. SPIE (3)

Y. Kajiki, H. Yoshikawa, and T. Honda, “Hologram-like video images by 45-view stereoscopic display,” Proc. SPIE3012, 154–166 (1997).
[CrossRef]

C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE3012, 179–186 (1997).
[CrossRef]

F. Speranza, W. J. Tam, T. Martin, and L. Stelmach, “Perceived smoothness of viewpoint transition in multi-viewpoint stereoscopic displays,” Proc. SPIE5664, 72–82 (2005).
[CrossRef]

Other (3)

T. Honda, Y. Kajiki, K. Susami, T. Hamaguchi, T. Endo, T. Hatada, and T. Fujii, “Three-dimensional display technologies satisfying ‘super multiview condition,” SPIE Crtical Reviews CR76, 218–249.

S. Pastoor and K. Schenke, “Subjective assessment of the resolution of viewing directions in a multi- viewpoint 3D TV system,” Proc. SID 30, 217–223 (1989).

T. Okoshi, Three-Dimensional Imaging Techniques (Academic Press, New York, 1976).

Supplementary Material (3)

» Media 1: MOV (3532 KB)     
» Media 2: MOV (3349 KB)     
» Media 3: MOV (3200 KB)     

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Figures (15)

Fig. 1
Fig. 1

Discontinuity in motion parallax that occurred in multi-view displays.

Fig. 2
Fig. 2

Super multi-view head-up display (SMV–HUD): (a) system configuration, and (b) imaging system; in the SMV-HUD developed in this study, a Fresnel lens is used as the projection lens, and the multi-view display consists of a flat-panel display and a slanted lenticular lens.

Fig. 3
Fig. 3

Photographs of the developed SMV–HUD: the display system is configured for (a) short-, (b) medium-, and (c) long-distance ranges for 3D image presentation.

Fig. 4
Fig. 4

Measured light-intensity distributions of viewing points for medium-distance configuration: intervals between the viewing points are (a) 2.6 mm, (b) 5.3 mm, (c) 7.9 mm, (d) 10.6 mm, and (e) 15.8 mm.

Fig. 5
Fig. 5

Test image used for measurements.

Fig. 6
Fig. 6

Measured results of unnatural motion-parallax and proper depth perceptions for short-distance configuration (observation distance l = 0.6 m; screen size = 20.9 in.): the intervals of viewing points are (a) 2.2 mm, (b) 4.4 mm, (c) 6.6 mm, (d) 8.8 mm, and (e) 13.1 mm.

Fig. 7
Fig. 7

Measured results of unnatural motion-parallax and proper depth perceptions for medium-distance configuration (observation distance l = 1.5 m; screen size = 42.8 in.): intervals between viewing points are (a) 2.6 mm, (b) 5.3 mm, (c) 7.9 mm, (d) 10.6 mm, and (e) 15.8 mm: Movies are provided in case of (b) when the distance to 3D image was 0.5 m (Media 1), 0.7 m (Media 2), and 1.5 m (Media 3).

Fig. 8
Fig. 8

Measured results of unnatural motion-parallax and proper depth perceptions for long-distance configuration (observation distance l = 5.0 m; screen size = 170 inches): intervals between viewing points are (a) 2.2 mm, (b) 4.4 mm, (c) 6.7 mm, (d) 8.9 mm, and (e) 13.3 mm.

Fig. 9
Fig. 9

Dependence of unnatural motion-parallax perception on q/p: (a) and (b) correspond to short-distance configuration, (c) and (d) correspond to medium-distance configuration, and (e) and (f) correspond to long-distance configuration; (a), (c), and (e) show small-crosstalk cases, and (b), (d), and (f) show large-crosstalk cases.

Fig. 10
Fig. 10

Retinal image formation at several positions in the viewing region: (a) small crosstalk and |q/p| = 1, (b) moderate crosstalk and |q/p| = 1, and (c) large crosstalk and |q/p| = 2.

Fig. 11
Fig. 11

Images captured by the cooled CCD camera at several horizontal positions near the viewing point when |q/p| was approximately equal to 0.2 for small-crosstalk cases: (a) for short-distance range, d = 8.8 mm, z = 0.59 m, and q/p = −0.16; (b) medium-distance range, d = 10.6 mm, z = 1.45 m, and q/p = −0.14; and (c) long-distance range, d = 8.9 mm, z = 4.1 m, and q/p = −0.17.

Fig. 12
Fig. 12

Images captured by the cooled CCD camera at several horizontal positions near the viewing point when |q/p| was approximately equal to 1 for small-crosstalk cases: (a) for short-distance range, d = 8.8 mm, z = 0.54 m, and q/p = −0.70; (b) for medium-distance range, d = 10.6 mm, z = 1.2 m, and q/p = −1.0; and (c) for long-distance range, d = 8.9 mm, z = 2.1 m, and q/p = −1.1.

Fig. 13
Fig. 13

Images captured by the cooled CCD camera at several horizontal positions near the viewing point when | q/p | was approximately equal to 1 for large-crosstalk cases: (a) for short-distance configuration, d = 2.2 mm, z = 0.35 m, and q/p = −1.1; (b) for medium-distance configuration, d = 2.6 mm, z = 0.75 m, and q/p = −1.0; (c) for long-distance configuration, d = 2.2 mm, z = 1.0 m, and q/p = −0.77; and (d) for long-distance configuration, d = 4.4 mm, z = 1.5 m, and q/p = −0.89.

Fig. 14
Fig. 14

Images captured by the cooled CCD camera at several horizontal positions near the viewing point when | q/p | was approximately equal to 2 for large-crosstalk cases: (a) for short-distance configuration, d = 4.4 mm, z = 0.35 m, and q/p = −2.2; (b) for medium-distance configuration, d = 5.3 mm, z = 0.75 m, and q/p = −2.0; and (c) for medium-distance configuration, d = 2.6 mm, z = 0.5 m, and q/p = −2.0.

Fig. 15
Fig. 15

Relationships between unnatural motion-parallax perception, resolution, crosstalk, and parallax shift ratio |q/p|.

Tables (2)

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Table 1 Display Parameters for SMV–HUD

Tables Icon

Table 2 Experimental Conditions

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

1/s1/( lh )=1/f,
( lh )/s=D/ D 0 .
1/h1/( l 0 s )=1/f,
h/( l 0 s )=W/ W 0 .
z>l/( 1+mp/d ) ( dmp ),
l/( 1+mp/d )<z<l/( 1mp/d ) ( d>mp ).

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