2.1.

Experimental Setup

Figure 1 is a schematic diagram of the experiment. The equipment comprised a 3D display device for presenting the target and a system for measuring the accommodation and convergence responses. The 3D display device consisted of an LCD panel and a lens array set 600 mm away from the observer. The LCD had a pixel count of $1920(\mathrm{H})\times 1080(\mathrm{V})$, pixel pitch of $55.5\mu \mathrm{m}$ (458 ppi), diagonal screen size of 4.8 in., and RGB stripe pixel structure, and it was driven at 60 Hz. The lens array was composed of small lenses with 1.0 mm diameter with a focal length of 3.0 mm arranged in a honeycomb pattern.

Fig. 1

Experimental setup.

The system for measuring the accommodation and convergence responses was an optometry device (PowerRef 3, Plusoptix Inc.) that used the photoreflection method.¹¹ The measuring equipment was set up to be optically 1.0 m away from the observer, and the measurements were made with infrared light. A hot mirror and a 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 accommodation and convergence responses while the observer is intently viewing the target. Note that the measurement was made at 1.0 m from the observer, so $+1.0\mathrm{D}$ accommodation was included in the result. Table 1 lists the specifications of the 3D display and measuring equipment.

Table 1

Specifications of 3D display and measuring equipment.

The physiological factors of stereoscopic vision are convergence, accommodation, binocular disparity, and motion parallax. To suppress the motion parallax effect, the depth perception and objective measurement were performed in a state with the observer’s head fixed in a chin rest. In addition, the viewing angle of the target size was fixed at 1.9 deg in all depth positions to avoid size cues for depth perception.

2.2.

Depth Perception

The I3D targets were made from a 2D Maltese cross pattern, as shown in Fig. 2(a). The targets were presented at 13 different depth positions, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, and 780 mm. The targets were randomly presented at each depth position. For measuring the depth perception at three display resolutions (153, 229, and 458 ppi), 153 and 229 ppi targets were made from the 458 ppi target by downconversion with the nearest-neighbor algorithm.

Fig. 2

Target presentation. (a) Integral targets for subjective evaluation. (b) Integral and binocular stereoscopic targets for objective evaluation. (c) Real targets for objective evaluation. (d) Photograph of the experimental I3D targets at the viewing distances of 500, 600, and 700 mm.

The depth perception was measured by Scheffe’s method of paired comparison. The method uses a criterion and an evaluation stimuli. In this experiment, the targets were divided into upper and lower parts and were presented at the same time. The upper and lower targets were used as the criterion and evaluation stimuli, respectively. The depth position of the lower target (evaluation target) was evaluated from $+3$ to $-3$ against the depth position of the upper target (criterion target). The value was positive (negative) when the depth position of the evaluation target was close to (far from) the observer compared with the depth position of the criterion target. And the values (3, 2, 1, and 0) indicated the perceived difference between the depth of the evaluation target and depth of the criterion target, with values of 3, 2, 1, 0 showing large, moderate, small, and no difference, respectively. The targets were presented at the 13 depth positions; therefore, the target combination number of one sequence was 169 times at each resolution. One measurement was done when the observer viewed the target. The target presentation of a measurement consisted of 10 s in which the target was shown for, an interval of 5 s in which no image was shown, followed by 10 s in which the target was shown. The rest time between the measurement sequences was more than 5 min to avoid visual fatigue.

2.3.

Accommodation and Convergence Responses

The accommodation and convergence responses were measured when the targets were viewed with both eyes. Three types of targets 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 targets from the display.¹² To compare the accommodation responses to the I3D and S3D targets, 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. The targets generated by each imaging method were presented at eight different depth positions, as shown in Fig. 2(b). The target depth positions from the observer were 450, 500, 550, 600, 650, 700, 750, and 900 mm. The depth positions of the targets were determined for two reasons. The first reason is that the accommodation responses should be measured in order to consider the effect of the convergence accommodation in the DOF of the ocular optics. The DOF of the human eye is $\pm 0.2$ to 0.3 D.¹³ The maximum target depth positions, 450 and 900 mm, were $\pm 0.56\mathrm{D}$ from the 3D display. Therefore, the target depth positions were inside and outside the DOF. The second reason is that the maximum target depth positions were determined from the results of the depth perception experiment. The details of this reason are discussed in Sec. 3.1. For the real target, the target was displayed on the 3D display plane and the 3D display was moved to depth positions that were the same as those of the targets of the 3D imaging methods, as shown in Fig. 2(c). Thus, the three types of targets were displayed at almost the same level of brightness.

The resolution of the S3D target was constant at all depth positions; however, the resolution of the I3D target varied with the depth position¹² as shown in Fig. 2(d). In the experiment, the calculated I3D target resolutions displayed from 450 to 900 mm were 1.4, 2.4, 5.2, 10.5, 6.1, 3.3, 2.4, and 1.4 cpd. It is reported that the accommodation responses to the S3D target depend on the target resolution.¹⁴ The accommodation position is induced to the convergence position by convergence accommodation when viewing a low-resolution S3D target. 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 assumed to be 65 and 600 mm, respectively.

The observers viewed the three types of target (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 accommodation and convergence responses of the observers were measured using PowerRef 3. 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 accommodation and convergence responses of the observer while he or she viewed the target for 10 s. The rest time between the measurement sequences was more than 5 min 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 (three types of target $\times$ eight depth positions $\times$ four repetitions).

2.4.

Participants

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. The experiment was performed in a darkened room. The observer’s pupils were dilated; however, 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 acuity of the observers was higher than 0.7. We confirmed that they all had normal stereo vision by using a stereo fly test produced by Stereo Optical Company.

3.1.

Depth Perception

Figure 3(a) shows the experimental results of the depth perception when the observers viewed the I3D target. The figure shows results for three display resolutions. The horizontal axis of the graph indicates the target depth positions, and the vertical axis represents the normalized value of the measured depth perception.

Fig. 3

Experimental results of depth perception: (a) evaluation results and (b) resolution limitation of depth perception.

The results show that depth perception was dependent on the display resolution. Moreover, the results for high-resolution 458 ppi display were in more accordance with the depth position of the target compared with the results of the low-resolution 153 ppi display. A statistical test evaluated the results at a significance level of 5%. It showed that the recognized depth perception ranges were 180 (from 540 to 720 mm), 240 (from 480 to 720 mm), and 330 mm (from 450 to 780 mm) when the display resolutions were 153, 229, and 458 ppi, respectively. Here, it was expected that the recognized depth perception range would expand as the display resolution increased. Therefore, the maximum recognized depth positions were plotted in the resolution domain, as shown in Fig. 3(b). The graph shows the I3D resolution characteristics of the three display resolutions as calculated by the equations described in Ref. 12. The horizontal axis of the graph indicates the viewing distance from the observer, and the vertical axis represents the resolution. The circles, triangles, and crosses indicate the maximum recognized depth positions (540 and 720 mm in 153 ppi, 480 and 720 mm in 229 ppi, 450 and 780 mm in 458 ppi). As a result, the resolution of the plotted symbols was $\sim 1.0\mathrm{cpd}$ (cycles per degree). This result suggests that depth perception is obtained at over 1.0 cpd.

3.2.

Accommodation and Convergence Responses

Figure 4 shows the experimental results of the accommodation and convergence responses to the I3D and S3D targets. The plots are average results of the 10 observers. Although the accommodation responses were measured for both eyes, only the results for the dominant (left or right) eye are plotted in the graph. In addition, the accommodation and convergence responses were measured for 10 s per measurement. The measured data included incorrect values when the observers blinked their eyes. Thus, the incorrect values were omitted from the calculation of the average results. To compare the experimental results of the 3D and real targets, the horizontal axes indicate the experimental results for the real target, while the vertical axes represent the experimental results for the 3D targets. The diagonal solid line of slope one means that the responses to the 3D targets are the same as the responses to the real target. Figure 4 compares each response to the I3D and S3D targets with the response to the real target. The accommodation responses to the I3D target were closer to that of the real target than to the S3D target. The convergence responses to the I3D and S3D targets showed almost the same tendency.

Fig. 4

Accommodation and convergence responses to the I3D and S3D targets: (a) accommodation results and (b) convergence results.

Figure 5(a) shows the relationship between the accommodation and convergence responses to the I3D, S3D, and real targets. The circles, crosses, and triangles denote the average results of the 10 observers. The horizontal axis indicates the experimental results for the convergence responses, while the vertical axis represents the experimental results for the accommodation responses. The diagonal solid line of slope one means that the accommodation responses are the same as the convergence responses. All the experimental results were above the diagonal solid line. However, this is not a significant problem because Fig. 5(a) relatively compares the 3D target data with real target data. The results suggest that fewer observers experienced accommodation-convergence conflict when viewing the I3D target than when viewing the S3D target. To clarify the accommodation-convergence conflict, the results were evaluated using a multiple comparison test at a significance level of 5%. We assumed that the accommodation-convergence conflict occurred when the accommodation or convergence responses to the 3D targets were significantly different from those to the real target. This experiment tested for a significant difference between the accommodation responses to the 3D targets and the accommodation responses to the real target. Note that the differences between the 3D targets and real target were assumed significant when the results of the left and right eyes showed a significant difference. The results of the multiple comparison test are listed in Table 2 and shown in Fig. 5(b). In Table 2, the number of observers with accommodation, convergence, and accommodation-convergence conflicts is listed at each depth position. In Fig. 5(b), the horizontal axis indicates the depth positions of the target, while the vertical axis represents the number of observers showing significant difference. It means that the number of observers with accommodation-convergence conflict is equal to the number of observers showing significant difference. The I3D (S3D) results for accommodation indicate that, except for the accommodation responses to the I3D (S3D) target at the viewing distance of 450 mm ($-2.22\mathrm{D}$), there were significant differences relative to the accommodation responses to the real target for fewer than 2 of the 10 (5 of the 10) observers. At 450 mm ($-2.22\mathrm{D}$), there was a significant difference relative to the accommodation responses to the real target for 4 of the 10 (8 of the 10) observers. On the other hand, at most 1 of the 10 (3 of the 10) observers experienced convergence conflict when viewing the I3D (S3D) target in the measurement range from 500 to 750 mm. The responses of 1 of the 10 (5 of the 10) observers showed significant differences for the I3D (S3D) target at 450 mm. The responses of 2 of the 10 (4 of the 10) observers showed significant differences for the I3D (S3D) target at 900 mm. The viewing distances of 450 and 900 mm were $\pm 0.56\mathrm{D}$ from the 3D display, i.e., outside the DOF. It was considered that the convergence responses to the S3D target at 450 mm were induced to the 3D display by accommodative convergence. The accommodation-convergence conflict shown in Fig. 5(b) occurred for the above reasons. On the other hand, at most 1 of the 10 (3 of the 10) observers experienced convergence conflict when viewing the I3D (S3D) target in the measurement range from 500 to 750 mm.

Table 2

Number of observers showing significant difference.

Fig. 5

Evaluation results of accommodation-convergence conflict. (a) The relationship between accommodation and convergence responses. (b) The number of the observers with accommodation-convergence conflict calculated by multiple comparison test.