Open Access
Add to BibSonomyAbstract
Static convergence and accommodation responses were measured by comparing integral photography images, binocular stereoscopic images, and real objects in a measurement range from 450 to 900 mm. The experimental results were evaluated with a multiple comparison test. It was found that six of the ten observers did not have an accommodation-convergence conflict in viewing integral photography in the range. Moreover, the required resolution was found to be 0.7 or more and less than 1.4 cycles per degree for inducing accommodation. In conclusion, integral photography can provide a natural 3D image that looks like a real object.
© 2017 Optical Society of America
1. Introduction
Stereoscopic images produced using the binocular stereoscopic 3D (S3D) method, which uses binocular parallax, are now popular in movies, etc. In the S3D method, parallax images are input to both eyes of the viewer, so special glasses, lenticular lens, or other such mechanisms are required for presenting different images to the left and right eye. The parallax enables stereoscopic vision. As a result, the convergence reaction of the viewer is consistent with the depth position of the S3D target. However, it has been pointed out that the accommodation position is near the displayed position, so the consequent inconsistency in convergence and accommodation produces visual fatigue [1].
Integral photography is a promising method to display 3D optical images by reproducing exactly the same light rays as emitted from real objects [2]. This method duplicates the conditions of viewing real objects. Therefore, the convergence and accommodation responses have been predicted to be consistent with the depth position of the 3D target. The accommodation response to integral 3D (I3D) displays has been theoretically analyzed by many researchers [3–5]. The reports indicate that satisfying the super multi-view (SMV) condition is the most important requirement for obtaining a proper accommodation response. The SMV condition means that two or more light rays from the point lights of the reconstructed 3D objects reach the pupil of an observer. The accommodation responses to I3D targets have been verified by a theoretical analysis, computer simulation, and experiment [4]. Although the experiment in [4] showed that different depth positions of the I3D target could be captured, the accommodation responses of the observers were not measured. Additionally, the accommodation responses were evaluated [3,6], however, they were not compared with a real object. Therefore, they were not clarified whether they were consistent with the depth position where it should have been. Furthermore, the accommodation responses in monocular viewing of an I3D target has been reported [7]. The experimental setup satisfied the proposed SMV condition [3], and the experimental results indicated that the accommodation responses of over 73% of the participants were induced for the I3D target presented in front of the I3D display. However, no accommodation was induced for the target presented behind the display. The proposed SMV conditions for I3D displays would be very interesting and useful, but experimental verification of the SMV condition is also important. To measure the accommodation of the human eye, we consider that it is necessary to satisfy three conditions. The first condition is that the pupil of the observer should be dilate in order to narrow the depth of field (DOF) of the human eye. The second condition is to avoid the effect of size cues for depth perception. The third condition is that the accommodation results for 3D targets and real objects should be compared to deal with personal differences. Some of these conditions were not satisfied in the previous reports. In particular, we reported on the relationship between depth perception and accommodation responses when viewing I3D targets [8]. In that report, the depth perception and accommodation responses were verified to be in accordance with the depth positions of the reconstructed I3D target [8]. The accommodation responses of binocular or monocular viewing conditions differ because of convergence accommodation. Therefore, we also measured the accommodation responses to an I3D target in a monocular viewing condition [9]. The resulting responses were consistent with the depth position of the target. Under monocular and binocular viewing conditions, the accommodation responses to I3D targets were obtained the same tendency.
It is known that the convergence and accommodation control mechanisms are not entirely independent and have mutual influence. The convergence and accommodation responses to an I3D target were measured to evaluate visual fatigue [5]. However, the experimental results did not include or compare them with responses to real objects. The results were insufficient for evaluating the accommodation-convergence conflict. Moreover, the responses to the I3D target were not measured outside of the DOF. To our knowledge, therefore, there has been no report concerning the relationship between the convergence and accommodation responses to I3D targets inside and outside of the DOF. In this study, we report experimental results of the static convergence and accommodation responses to I3D targets. For comparison, the same measurements were performed with S3D targets and real targets.
Below, we briefly describe the experiment, including the experimental setup for measuring the convergence and accommodation responses, the target presentation method, and the experimental procedure. Then we present the results of measuring the convergence and accommodation responses to I3D targets, S3D targets, and real targets. After that, we discuss the experimental results and conclude the paper by summarizing the features of the convergence and accommodation responses.
2. Overview of the experiment
The convergence and accommodation responses were measured when targets at different depth positions were viewed with both eyes. Three types of target were used, i.e., a real target and 3D targets produced by integral photography and the binocular stereoscopic method. In integral photography, the resolution of the 3D images varies with the depth positions of the 3D targets from the display [10]. For comparison of the convergence and accommodation responses between the I3D and S3D, the resolution and depth positions of the targets were determined. The resolution of the S3D targets was set to almost the same resolution as the I3D targets. A 3D display was positioned 600 mm from the observer. The 3D targets were presented at eight positions between −0.56 and + 0.56 D from the 3D display, where D is the diopter value in units of inverse meters. The target depth was fixed at the time of measurement, and the static convergence and accommodation responses were measured at the same time.
2.1 Experimental setup
The experimental setup (Fig. 1) comprised a system for measuring convergence and accommodation responses and a 3D display device for presenting the targets.
The system for measuring the convergence and accommodation responses was an optometric device (PowerRef3, Plusoptix Inc.) which uses the photo-reflection method [11]. The equipment measures the pupil size of the observer in a measurement range from 4.0 to 8.0 mm in 0.1 mm steps. It also detected the left and right eyes directions when the observer viewed the targets at 0.02 second intervals. After that, the convergence point was calculated using the left and right eyes directions. The distance of the measuring equipment was optically 1.0 m away from the observer, and the measurements were made with infrared light. A hot mirror and mirror were placed in front of the observer between the measuring equipment and the observer. The hot mirror is a complete reflector of infrared light but is transparent to visible light; thus it enables measurement of the convergence and accommodation responses while the observer is intently viewing the target. Note that the measurement was made at a distance of 1.0 m from the observer, so + 1.0 D accommodation was included in the result.
The 3D display device consisted of an LCD panel and a lens array. The LCD had a pixel count of 1920 (H) × 1080 (V), pixel pitch of 55.5 μm, diagonal screen size of 4.8 inches, RGB stripe pixel structure, and was driven at 60 Hz. A lens array arranged in a regular honeycomb pattern has a higher lens density than that of a squarely arranged lens array. Moreover, not as much light gets through the interstices between the lenses of the hexagonal lens array compared with the case of a lens array comprised of circular lenses. The 106 (H) × 69 (V) lens array comprised hexagonal micro lenses arranged in a regular honeycomb pattern with a horizontal pitch of 1.0 mm and a vertical pitch of 0.866 mm. Each lens had a focal length of 3.0 mm. The distance between the LCD panel and the lens array was set at the focal point of the array. The specifications of the measurement system (PowerRef3) and 3D display device are listed in Table 1.
Table 1. Specifications of the experimental setup.
2.2 Target presentation method
To measure the convergence and accommodation responses to three targets, we adjusted four conditions: the depth position of the target, target brightness, target size, and resolution characteristics.
The method of using the 3D display to present the target was as follows. For the I3D and S3D images, the 3D display was set 600 mm away from the observer. The targets generated by each imaging method were presented at eight different depth positions as shown in Fig. 2(a). The target depth positions from the observer were 450 mm (−2.22 D = -(1/0.45) D), 500 mm (−2.00 D), 550 mm (−1.82 D), 600 mm (−1.66 D = the display plane position), 650 mm (−1.54 D), 700 mm (−1.43 D), 750 mm (−1.33 D), and 900 mm (−1.11 D). The depth positions of the targets were determined in order to measure the effect of the convergence accommodation in the DOF of the ocular optics. The DOF of the human eye is ± 0.2 to 0.3 D [12]. The maximum target depth positions from the 3D display were ± 0.56 D. Therefore, the target depth positions were inside and outside the DOF. For the real target, the target was displayed on the 3D display plane and the 3D display was moved to the depth position that was the same as the depth positions of the targets for the 3D imaging methods, as shown in Fig. 2(b). As a result, the three targets were displayed almost the same level brightness.
The targets were created as follows. The target was a white 2D Maltese cross pattern. To avoid the effect of size cue for depth perception, its size was set to 1.9 degrees of the visual angle at all depth positions. In the central 2.0 degrees of the visible field, observers are able to concentrate on viewing. The target size on the 3D display, which was at the viewing distance of 600 mm, was 20 mm × 20 mm (Fig. 3(b)). Figures 3(a) and 3(c) show the experimental target at 500 mm and 700 mm.
Fig. 3 Photograph of experimental I3D targets at the viewing distances of 500 mm, 600 mm and 700 mm from the observer. The target size was set to 1.9 degrees of visual angle at all depth positions. The target size was 20 mm × 20 mm at the viewing distance of 600 mm, in Fig. (b).
The S3D target resolution was constant at all depth positions; however, in principle, the I3D target resolution varies according to the depth position [10]. Because the accommodation responses depend on the target resolution [13], the accommodation position is induced to the convergence position by convergence accommodation when viewing a 3D target with low resolution. Therefore, it was necessary to make the S3D target resolution about the same as for the I3D target. The I3D target was generated at each depth position by computer simulated ray tracing, and the S3D target was generated from the I3D target. Generation of the S3D target required information on the pupillary distance and the viewing distance from the observer to the 3D display device. Here, the pupillary and viewing distances were 65 mm and 600 mm, respectively. A 3D display consisting of a high-density lens array would be better for measuring of convergence and accommodation responses. However, the size of our lens array in this experiment was somewhat large. This meant that the observers could see the structure of the lens array at all depth positions. Thus, the real target resolution was the same as the lens array resolution. The effect of the target resolution is described in section 4.
2.3 Experimental procedure
The observers viewed three types of targets (I3D, S3D, or real object); a measurement sequence consisted of the observer viewing the target at the eight depth positions (each observation at a depth position was a trial). In each experimental trial, the convergence and accommodation responses of the observers were measured using PowerRef3. One measurement was done for each sequence in which a randomly selected target (I3D, S3D, or real object) was placed at the eight depth positions. The selected target was positioned at one of the eight depth positions. We measured the convergence and accommodation responses of the observer viewing the target for 10 seconds. The measurement time was determined in consideration of the attention span of the observers. The measurement ended after finishing one sequence. The rest time between the measurement sequences was more than 5 minutes to avoid visual fatigue. To improve the accuracy of the results, the measurements were done four times. Thus, measurements were made 96 times for each observer (3 types of targets × 8 depth positions × 4 repetitions). Each observer was instructed to look at the target in such a way that it was not seen as a double image, without knowing the target depth. Although the experiment was performed in a darkened room, the observer's pupils were dilated; an artificial pupil or other such device was not used. Ten observers ranging in age from 20 to 30 years old participated in the experiment. The visual acuities of the observers were higher than 1.0. All observers did the experiment without any visual correction. We confirmed that they all had normal stereo vision by using a stereo fly test produced by Stereo Optical Company.
3. Experimental results
Figures 4 and 5 show representative results of four observers (A, B, C, and D) for the convergence and accommodation responses to the I3D targets, S3D targets, and real targets. The accommodation response results are shown for both eyes. The horizontal axes of the graphs indicate the target depth positions, and the vertical axes represent the measured convergence or accommodation responses. The diagonal solid line of slope one in the figures indicates the condition that the convergence and accommodation responses are consistent with the target depth positions. The unit of accommodation, D (diopter), and the unit of convergence, MA (meter angle), are both inverses of distance.
Fig. 4 Convergence response [Red: integral photography target (I3D: ○); Blue: binocular stereoscopic target (S3D: △); Green: real target (RO: × )].
Fig. 5 Accommodation response [Red: integral photography target (I3D: ○); Blue: binocular stereoscopic target (S3D: △); Green: real target (RO: × )].
The experimental results of the convergence responses for each observer were above the diagonal solid line in Fig. 4. Nevertheless, the convergence responses to the 3D targets and to the real targets showed about the same tendency as the diagonal solid line. Concerning the convergence responses at the viewing distance of 450 mm (−2.22 D), the S3D target results for observer C were apparently different from those for viewing the real targets. In this case, the difference was 0.5 MA or more relative to the convergence responses to the real targets.
In the measurement results shown in Fig. 5, there were also individual differences in the magnitude of the accommodation responses. In addition to differences between target types, there were differences in the accommodation responses between the left and right eyes. The accommodation responses to the I3D targets were more similar to those to the real targets while the responses to the S3D showed less similarity to the real targets.
4. Discussion
The individual differences in the results of the convergence and accommodation responses made it difficult to understand the relationship with the target depth positions. Therefore, to remove the effects of these individual differences, we used those of the real targets as a reference for comparing the responses to the 3D targets. Then we examined the responses from the point of view of the slope and through a multiple comparison test. Additionally, the requirements of the spatial frequency needed to obtain proper accommodation responses were considered from the viewpoint of previous and our experimental results.
4.1 Convergence response
For instance, the convergence responses to the real target taken from Fig. 4 are plotted along the horizontal axis in Fig. 6, and the convergence responses to the I3D targets and those to the S3D targets are plotted on the vertical axis. To normalize the measured I3D and S3D convergence results by the measured real object result, the experimental results can be relatively evaluated as to the advantage of the convergence responses between the I3D and S3D images.
Fig. 6 Comparison of convergence responses to 3D targets relative to the real targets (Red: integral photography targets; Blue: binocular stereoscopic targets).
The diagonal solid line of slope one in the figure represents where the convergence responses to the 3D targets are the same as for the real target. Approximate straight lines obtained by the least squares method are also shown for each target type. The slopes of the approximating lines for each observer are listed in Table 2. The average slopes for all observers were 0.975 for the I3D targets and 0.894 for the S3D targets. For both methods, there was a difference between the slopes of 0.081. The I3D targets produced convergence responses that were closer to the real target than to the S3D targets in terms of the slope.
Table 2. Slopes of approximating lines for the 3D convergence and accommodation responses versus those of the real targets
Figure 7 shows the results of a multiple comparison test at a significance level of 5% on the convergence responses to I3D targets, S3D targets, and real targets at each viewing distance. The horizontal axis of the graph indicate the target depth positions, and the vertical axis represent the number of responses showing no significant difference. This experiment tested for a significant difference between the convergence responses to the 3D targets and the convergence responses to the real targets. Although the overall tendency was almost the same for every target type, the results were obviously different between the I3D and S3D targets at the viewing distances of 450 mm and 900 mm in particular. The responses of nine of the ten (five of the ten) observers showed no significant differences for the I3D targets (S3D targets) at 450 mm. The responses of eight of the ten (six of the ten) observers showed no significant differences for the I3D targets (S3D targets) at 900 mm. The viewing distances of 450 mm and 900 mm were ± 0.56 D from the 3D display, i.e., outside of the DOF. It was considered that the convergence responses to the S3D targets at 450 mm were induced to the 3D display by accommodative convergence, such as the result of observer C.
Fig. 7 Multiple comparison test results for convergence responses to 3D targets relative to the real targets (Red: integral photography targets; Blue: binocular stereoscopic targets).
4.2 Accommodation response
The accommodation responses differed between the left and right eyes, as shown in Fig. 5. For instance, the accommodation responses to the real targets in Fig. 5 are plotted on the horizontal axis in Fig. 8, and those to the I3D targets and S3D targets are plotted on the vertical axis. To normalize the measured I3D and S3D results by the measured real object result, the experimental results can be relatively evaluated as to the advantage of the accommodation response between the I3D and S3D images. Moreover, this removes the accommodation lag depending on the observers.
Fig. 8 Comparison of accommodation responses to 3D targets relative to the real targets (Red: integral photography targets; Blue: binocular stereoscopic targets).
The diagonal solid line of slope one in the figure represents where the accommodation responses to the 3D targets are the same as for the real targets. Approximating straight lines obtained by the least squares method are also shown for each target type, and the slopes of the approximating lines for each observer are listed in Table 2. Although the slopes differed for the left and right eyes, the accommodation responses to the I3D targets were closer to that of the real targets than to the S3D targets. The averages of the accommodation response slopes for each eye were 0.852 (left eye) and 0.759 (right eye) for the I3D targets and 0.537 (left eye) and 0.550 (right eye) for the S3D targets. For both methods, there was a difference in the slopes for the two eyes of about 0.2 to 0.3. Therefore, the accommodation responses to the I3D targets were closer to the responses to the real targets.
The differences between the 3D targets and real targets were evaluated using a multiple comparison test at a significance level of 5%, as shown in Fig. 9. The horizontal axis of the graph indicate the target depth positions, and the vertical axis represent the number of responses showing no significant difference. This experiment tested for a significant difference between the accommodation responses to the 3D targets and the accommodation responses to the real targets. Note that the differences between the 3D targets and real targets were assumed significant when the results of the right and left eye showed a significant difference. The I3D results (S3D results) in Fig. 9 indicate that, except for the accommodation responses to the I3D targets (S3D targets) at the viewing distance of 450 mm (−2.22 D), there was no significant difference relative to the accommodation responses to the real targets for at least eight of the ten (five of the ten) observers. At 450 mm (−2.22 D), there was no significant difference relative to the accommodation responses to the real targets for six of the ten (two of the ten) observers. The DOF of the human eye is ± 0.2 to 0.3 D [12]; therefore, the viewing distances from 500 to 750 mm were considered to be the DOF of the ocular optics. The accommodation responses to the S3D targets were expected to induce the depth positions of the targets by taking convergence accommodation. However, the accommodation responses to the S3D targets were only induced in five of ten observers at 500 mm and 550 mm. The experimental S3D targets were created from the I3D targets for adjusting the resolution characteristics and assumed 65 mm for the pupillary distance of the observers. The depth positions of the S3D targets were anticipated to be different when the assumed pupillary distance was not the same as the pupillary distance of the observers. In the DOF, however, the convergence responses to the S3D targets were in accordance with the depth positions of the real targets, as shown in Fig. 7. For the above reasons, it was considered that the assumed pupillary distance and the accommodation responses to the S3D targets were reasonable. The convergence responses to the I3D and S3D targets were almost the same, as shown in Fig. 7. Therefore, the accommodation responses to the I3D targets were more strongly induced than those of the S3D targets in the DOF. These results suggest that the I3D targets had fewer significant differences with respect to the real targets than the S3D targets had.
Fig. 9 Multiple comparison test results for accommodation responses to 3D targets relative to the real targets (Red: integral photography targets; Blue: binocular stereoscopic targets).
In [3], Jung et al. proposed a theoretical analysis of accommodation in viewing I3D displays in which the accommodation is induced to satisfy the SMV condition. They proposed the following equation for the maximum viewing distance Zmax satisfying the SMV condition:
where pp is a pixel pitch of the display, f is the focal length of a lens of the lens array, and dp is the pupil diameter. In our experimental setup, pp and f were 55.5 μm and 3.0 mm, and dp was assumed to be 5.0 mm. We clarified that our experimental condition does not satisfy the SMV conditions using Eq. (1). In spite of the result of the unsatisfied condition of the SMV, our measurement results indicated that accommodation responses to the I3D targets were almost same as that to the real object. In other research [5,6], the experimental viewing distances, 0.5 m and 1.0 m, were over the theoretical maximum viewing distances, 0.43 m and 0.41 m. However, the accommodation responses to the I3D targets were induced to the depth positions of the target. On the other hand there are contradicted results that accommodation responses to the I3D targets were not same as those to the real object even though the viewing distance satisfied the proposed SMV condition [7]. The experimental results for images presented the behind the 3D display did not induce proper accommodation responses to the depth position of the 3D targets [7]. We think the proposed SMV condition analysis is very powerful tool to analyze the 3D images, however it may not be always sufficient for analysis of the accommodation responses to the I3D display. In Eq. (1), the number of light rays from only one lens of the lens array is considered for the evaluation of the SMV condition. However, the I3D images were composed of light rays from a few lenses, which is different from the SMV condition assumed in Eq. (1). We think that our I3D may satisfy the SMV condition when we consider light rays from multiple lenses, not just light rays from a single lens. Additionally, the I3D images are also not the same as the images of multi-view imaging. As a result, we consider that the experimental results of the I3D target were different from those of S3D targets. Therefore, the induction of accommodation of I3D displays should be subjected to not only theoretical analyses but also experimental analyses. The importance of the experiment was also evidenced by the results indicating that the accommodation responses were different between the left and right eyes.4.3 Correlation of convergence and accommodation responses
Here, we discuss the experimental results concerning the correlation of the convergence and accommodation responses. It is known that the convergence and accommodation control mechanisms are not entirely independent, but have mutual influence. The accommodation responses to the S3D targets have been explained by taking convergence accommodation and the DOF of ocular optics into account [14]. The DOF of the human eye is ± 0.2 to 0.3 D [12]. In other words, the focal point lies on the retina due to convergence accommodation within that range. In this experiment, the target depth positions were in the range of ± 0.33 D away from the 3D display device for depth positions of from 500 to 750 mm, and mostly within the DOF described above. For the target depth positions of 450 mm and 900 mm, on the other hand, the positions were ± 0.56 D away from the 3D display device. The depth positions in the experiment were inside and outside the DOF in the depth direction. For the case outside the DOF, it was predicted by the accommodation-convergence conflict that the accommodation and convergence responses to the S3D targets were not in accordance with the depth positions of the S3D targets. On the other hand, it was expected that the accommodation and convergence responses to the I3D targets were in accordance with the depth positions of the I3D targets. Although the convergence responses to the I3D targets were in agreement with those of the real objects in Fig. 7, the accommodation responses were slightly different than the responses to the real objects, as shown in Fig. 9. The number of the observers without the accommodation-convergence conflict were calculated using a multiple comparison test (Fig. 10). The horizontal axis of the graph indicate the target depth positions, and the vertical axis represent the number of responses showing no significant difference. The results that conflicts of I3D targets (S3D targets) existed only for four of the ten (eight of the ten) observers at a viewing distance of 450 mm. Therefore, the accommodation-convergence conflict seemed to be less in the I3D targets compared with the S3D targets.
Fig. 10 The number of the observers without accommodation-convergence conflict calculated by multiple comparison test (Red: integral photography targets; Blue: binocular stereoscopic targets).
As shown in Fig. 11, the I3D target resolution decreased with distance from the 3D display because of the performance limitations of the 3D display used in this experiment. The horizontal axis of the graph indicate the target depth positions, and the vertical axis represent the spatial frequency. The accommodation responses to the I3D targets were not entirely consistent with those to the real targets. At the viewing distance of 450 mm in particular, there was a large offset from the responses to the real targets in the results for the I3D targets as well as for the S3D targets. The accommodation position was induced by the edges of the target; therefore, it will be necessary to develop a 3D display device for which a decrease in resolution does not occur. Therefore, it is considered that the accommodation positions of high-resolution I3D targets will be close to the target depth positions, just like those to real targets. For the S3D target, on the other hand, it is known that the range of accommodation responses is broadened by convergence accommodation as the target resolution decreases [13]. It was considered, therefore, that the decrease in target resolution was a major factor in the accommodation responses to the S3D targets changing as when viewing the real targets. A higher 3D resolution increases the accommodative convergence effect, so the accommodation responses differ from those to the real targets, and tracking within the DOF can be expected.
4.4 Requirements of I3D display for inducing accommodation
In the experimental setup, the distance between the LCD panel and the lens array was set at the focal point of the array. The maximum spatial frequency of the I3D target is limited by the pixel pitch pp of the LCD panel. The maximum spatial frequency can be expressed as follows:
where β is the maximum spatial frequency, g represents the distance between the LCD panel and the lens array, L is the viewing distance, and z is the distance from the lens array to the I3D target. Furthermore, the I3D target is sampled at the lens pitch of the lens array. It is therefore necessary to consider the lens pitch of the lens array. The maximum spatial frequency of the I3D target is restricted by the Nyquist frequency βn determined by the lens pitch pL,From the above equations, the upper limit of the spatial frequency γ of the I3D target produced at an arbitrary depth position can be expressed as follows [10]:The resolution characteristics of previous I3D displays [3,5–7] and our I3D display [8,9] were calculated using Eq. (4). The results are shown in Fig. 12, and the specifications of the various I3D displays are summarized in Table 3. The horizontal axis of the graph indicate the target depth positions, and the vertical axis represent the spatial frequency. The gap between the lens array and display panel is assumed to be the same as the focal length of the lens of the lens array. The symbols 'Δ' means that the points are the presented target depth positions. Note that the focal length of the lens array in [7] was assumed to be 10.0 mm, because the authors did not describe it in their paper. We did not draw the symbols of the target depth position for [5] because the authors only described that the target depth positions were in the DOF. The lens pitch of our I3D display was calculated as 0.5 mm, because the arrangement of the lens array was honeycomb pattern. Our I3D display has better resolution characteristics compared with other I3D displays. Although the red line of [6] seems to indicate high resolution characteristics, the characteristics are not as good as our I3D display’s. This is because the viewing distance of [6] was longer than our condition. To compare the target depth position, target depth positions in our study were more numerous than in the other studies. Additionally, the depth range was wider than in the other studies. Although most of the other studies [3,5,6] only measured the accommodation responses to the I3D target inside of the DOF [7], and we measured the accommodation responses to the I3D target inside and outside the DOF.Table 3. Specifications of previous and our I3D displays and target depth positions from displays.
The experimental results shown in Fig. 10 indicate that six or more observers did not have an accommodation-convergence conflict when viewing the I3D displays. In our experimental results, the minimum required resolution of the I3D display for inducing accommodation was 1.4 cycles per degree (cpd). On the other hand, it is reported that the accommodation responses to an I3D target presented −0.42 D in front of the I3D display were induced to the depth position of the target [7]. The theoretical target resolution of the −0.42 D depth position was about 0.7 cpd, as shown in Fig. 12. However, accommodation was not induced to the target presented the behind of the display [7]. From the results of [7], the spatial frequency of 0.7 cpd was not sufficient to induce accommodation to the I3D target. Therefore, we suggest that the minimum requirements of the spatial frequency to obtain proper accommodation responses are 0.7 cpd or more and less than 1.4 cpd.
5. Conclusion
We measured the convergence and accommodation responses to integral 3D (I3D) targets. For comparison, the same measurements were performed with binocular stereoscopic 3D (S3D) targets and real targets. The 3D display was positioned 600 mm from the observer. The targets were presented at eight depth positions between −0.56 and + 0.56 D from the 3D display. The depth ranges covered both inside and outside DOF of the human eye, and the size of the target was kept to the same visual angle in order to minimize the size effect. The experimental results were evaluated with a multiple comparison test. The convergence responses of nine of the ten (five of the ten) observers showed no significant differences for the I3D targets (S3D targets) at 450 mm outside of the DOF. The accommodation responses of six of the ten (two of the ten) observers showed no significant differences for the I3D targets (S3D targets) at 450 mm outside of the DOF. It was also found that the accommodation-convergence conflict in viewing the I3D targets did not occur in more than six of the ten observers in a measurement range from 450 to 900 mm. Additionally, the requirements of the spatial frequency needed to obtain proper accommodation responses were considered from the viewpoint of previous and our experimental results. As a result, the minimum required resolution of the I3D display for inducing accommodation was found to be 0.7 cpd or more and less than 1.4 cpd. These results suggest that integral photography can provide a natural 3D viewing experience that is close to that of viewing a real object.
References and links
1. S. Yano, M. Emoto, and T. Mitsuhashi, “Two factors in visual fatigue caused by stereoscopic HDTV images,” Displays 25(4), 141–150 (2004). [CrossRef]
2. M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phis. 4, 821–825 (1908).
3. J.-H. Jung, K. Hong, and B. Lee, “Effect of viewing region satisfying super multi-view condition in integral imaging,” SID Symposium Digest Tech. Papers 43(1), 883–886 (2012).
4. A. Maimone, G. Wetzstein, M. Hirsch, D. Lanman, R. Raskar, and H. Fuchs, “Focus 3D: compressive accommodation display,” ACM Trans. Graph. 32(5), 1–13 (2013). [CrossRef]
5. H. Deng, Q.-H. Wang, C.-G. Luo, C.-L. Liu, and C. Li, “Accommodation and convergence in integral imaging 3D display,” J. SID 22(3), 158–162 (2014).
6. Y. Kim, K. Hong, J. Kim, H. K. Yang, J.-M. Hwang, and B. Lee, “Accommodation measurement according to angular resolution density in three-dimensional display,” Proc. SPIE 7956, 79560Q (2011). [CrossRef]
7. Y. Kim, J. Kim, K. Hong, H. K. Yang, J.-H. Jung, H. Choi, S.-W. Min, J.-M. Seo, J.-M. Hwang, and B. Lee, “Accommodative response of integral imaging in near distance,” J. Disp. Technol. 8(2), 70–78 (2012). [CrossRef]
8. H. Hiura, S. Yano, T. Mishina, J. Arai, K. Hisatomi, Y. Iwadate, and T. Ito, “A study on accommodation response and depth perception in viewing integral photography,” in Proceedings of 3D Systems and Applications (3DSA, 2013), paper P2–2.
9. H. Hiura, T. Mishina, J. Arai, and Y. Iwadate, “Accommodation response measurements for integral 3D image,” Proc. SPIE 9011, 90111H (2014). [CrossRef]
10. H. Hoshino, F. Okano, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15(8), 2059–2065 (1998). [CrossRef]
11. F. Gekeler, F. Schaeffel, H. C. Howland, and J. Wattam-Bell, “Measurement of astigmatism by automated infrared photoretinoscopy,” Optom. Vis. Sci. 74(7), 472–482 (1997). [CrossRef] [PubMed]
12. S. Marcos, E. Moreno, and R. Navarro, “The depth-of-field of the human eye from objective and subjective measurements,” Vision Res. 39(12), 2039–2049 (1999). [CrossRef] [PubMed]
13. Y. Okada, K. Ukai, J. S. Wolffsohn, B. Gilmartin, A. Iijima, and T. Bando, “Target spatial frequency determines the response to conflicting defocus- and convergence-driven accommodative stimuli,” Vision Res. 46(4), 475–484 (2006). [CrossRef] [PubMed]
14. N. Hiruma and T. Fukuda, “Accommodation response to binocular stereoscopic TV images and their viewing conditions,” SMPTE J. 102(12), 1137–1144 (1993). [CrossRef]
