Autostereoscopic three-dimensional (3D) displays have steadily improved [1–7]. Furthermore, novel applications of autostereoscopic 3D displays, such as in tabletops and automobiles, have been reported recently [8, 9]. Various methods to characterize the performance of autostereoscopic 3D displays have been reported [10–19]. The performance of autostereoscopic 3D displays significantly depends on the viewing position of users. Therefore, determining the designed viewing distance, viewing zone, or qualified viewing space of an autostereoscopic 3D display is important. The viewing zone and qualified viewing space were determined from the spatial light intensity distribution [5, 10, 12, 13, 17]. Consequently, this study focuses on measuring the spatial light intensity distribution.

A typical setup to measure the spatial luminance distribution of an autostereoscopic 3D display is shown in Fig. 1. Generally, a spotlight measuring device (LMD) is used to measure luminance. The spot LMD has good accuracy, but it is limited to the measurement at a single position. The spot LMD is placed on the xz and rotation stages to measure the spatial luminance distribution at various user positions. The spatial luminance distribution is obtained using a time-consuming process in which the luminance is measured at multiple positions by translating the LMD along the x- and z-axes. For some applications, the light intensity along the vertical direction of the y-axis must be measured, which further increases the overall number of measurement positions.

Figure 1. Top view of a typical setup using a spot light measuring device (LMD) to measure the luminance distribution of an autostereoscopic 3D display at the user position.

The interpupillary distance (IPD) between the left and right eyes is assumed to be approximately 65 mm [20]. Therefore, the interval between the measurement positions of the spot LMD must be at least considerably smaller than the IPD. For example, suppose a spot LMD is used to measure the luminance distribution on an xy plane of 300 mm × 100 mm with an interval of 5 mm. In that case, more than a thousand movements are necessary, even at a specific viewing distance of D₀. The measurement time will further increase when the same procedure is repeated for the various D₀. Therefore, a more practical measurement method with reduced measurement time is necessary. Methods that use other measuring equipment than a spot LMD have been proposed to reduce the measuring time or procedure [14, 16, 21].

To reduce the overall measurement time, a method to measure the two-dimensional (2D) light intensity distribution at the user position was investigated where a white semitransparent diffusing screen or 2D spatial sensor was placed at the user position. The 3D spatial light intensity distribution at the user position was determined from multiple data points of the measured 2D spatial light intensity distribution.

A method to obtain the 2D intensity distribution at multiple positions under each measurement condition was investigated to reduce the measurement time. The proposed method in which a white semitransparent diffusing screen was placed in the user position to measure the light intensity in 2D space is shown in Fig. 2. A sheet of white A4 paper was used as the diffusing screen. The light intensity on the diffusing screen caused by light from the autostereoscopic 3D system was recorded using a commercial digital camera. The camera was set in manual mode with a shutter time of 0.3 s, F5.6, and ISO 640 with a photo resolution of 6,240 × 4,160. The camera was placed 90 cm from the diffusing screen so that the image of the A4 paper was at the center of the recorded image and occupied a third of the recorded image.

Figure 2. Top view of the proposed measurement setup with a diffusing screen and camera. A white, semi-transparent diffusing screen was placed near the user position. The camera was focused on the diffusing screen. The autostereoscopic 3D display was on the translation stage along the z-direction. D₁ represents the distance between the autostereoscopic 3D and the diffusing screen.

Black line mesh with a 20 mm period was printed on the white diffusing screen, which was used to align and control the focus of the camera. A diffusing screen without mesh was used for the measurement.

An autostereoscopic 3D smartphone (ZTE Axon 7 max, 6 inch diagonal size, 1,920 ×1,080 resolution; ZTE, Shenzhen, China) was selected as an autostereoscopic 3D sample. In the selected sample, a lenticular lens sheet was attached to the display to make a two-view autostereoscopic display. The vertical odd and even number lines of the display contributed to the left and right view separately when the left and right view images with a size of 960 × 1,080 were applied.

The test patterns shown in Fig. 3 were displayed on a 3D sample for measurement. The images for left and right views in Fig. 3 were converted to match the configuration of the two-view autostereoscopic display where each eye of the user could see the vertical lines of the odd and even numbers separately. The test patterns of the L_BR_B were used for the calibration to distinguish the light rays from the autostereoscopic 3D smartphone and from other sources.

Figure 3. Three test patterns of the 3D display. The left and right squares represent the images for the left and right views, respectively.

Considering that the autostereoscopic 3D smartphone was intended to be used at arm’s length, the distance between the 3D sample and diffusing screen was changed from 15 to 40 cm at intervals of 1 cm by moving the 3D sample. At each distance D₁, the light intensity on the diffusing screen was recorded using a digital camera for each test image.

The other measurement setup that uses complementary metal oxide semiconductor (CMOS) to record the 2D spatial light intensity distribution is shown in Fig. 4. A digital camera CMOS with dimensions of 43.8 mm × 32.9 mm (Nikon GFX 50R, medium format; Nikon, Tokyo, Japan) was used. The lens was removed from the camera and the camera was set to manual mode with a shutter time of 1/250 s and an ISO 125. The surface of the CMOS was set on the xy plane and the camera was placed on the x-, y-, and z-translation stages. CMOS recorded the light intensity on the xy plane caused by the 3D sample for each test pattern as the position of CMOS changed horizontally along the x-axis.

Figure 4. Top view of the other proposed measurement setup using complementary metal oxide semiconductor (CMOS). The CMOS was placed on the xy plane at the user position. The blue lines represent the light rays originating from the autostereoscopic display and reaching the CMOS.

Figure 5 shows examples of the original recorded images of the diffusing screen with a mesh of 2 cm, when the test patterns of the L_BR_W and L_WR_B were displayed on the autostereoscopic sample in the setup shown in Fig. 2. As the interval between the mesh lines of the original recorded images was 152 pixels, 76 pixels corresponded to 10 mm. From the photo with a resolution of 6,240 × 4,160, only an area of 2,000 × 1,200 pixels recording the image of the A4 diffuser was used. The original recorded image of 2,000 × 1,200 pixels covered an area of 264 mm × 158 mm.

Figure 5. Images of the diffusing screen recorded in the setup shown in Fig. 2 at various distances, D₁. The test patterns for autostereoscopic samples are (a) L_BR_W and (b) L_WR_B. The vertical and horizontal black lines in the photos represent a mesh with a 20 mm period drawn on the white diffusing screen.

The light intensity on the diffusing screen without the mesh was recorded for the L_BR_W and L_WR_B test patterns as the autostereoscopic sample was moved at a distance D₁ of 15–40 cm with an interval of 1 cm. A 3D spatial light intensity data array was obtained for each of the test patterns of the L_BR_W and L_WR_B by reducing the original recorded images by a factor of 1/7.6 and combing 26 images along the z-direction. In the 3D data array of 264 × 158 × 26 for L_BR_W and L_WR_B, an xy array of 264 × 158 represents the gray level of each recorded image. The units of the x- and y-axes of this 3D data array are mm, whereas the unit of the z-axis is cm. Various characteristics of a 3D sample display can be determined from this 3D spatial relative light intensity data array. Relative light intensity was derived from the gray level, assuming a gamma value of 2.2.

To show the effectiveness of the proposed method, an example of a contour map of the xz plane of the 3D data array at y = 80 mm is shown in Fig. 6(a). The relative light intensity distribution at y = 80 mm and z = 25 cm is shown in Fig. 6(b). Contour maps of the xz plane of the 3D data array at y = 20, 80, and 120 mm are shown for relative light intensity and crosstalk in Fig. 7. The crosstalk of the right view was calculated as Intensity(L_BR_W) / [Intensity(L_BR_W) + Intensity(L_WR_B)] at each position. The typical trends of an autostereoscopic two-view 3D display, where the interval between the bright and dark areas along the x-axis increased at a larger D₁ and the distribution shape was almost uniform along the y-axis, are shown in Figs. 5–7. In Fig. 7(b), the viewing positions of each eye to view 3D images with small crosstalk can be identified from the measured data.

Figure 6. Examples of graphs derived from the measured 3D spatial relative light intensity data array. (a) Contour map of the xz plane at the intersection of y = 80 mm for the L_BR_W and L_WR_B test patterns. (b) Relative light intensity distribution at y = 80 mm and z =25 cm for test patterns L_BR_W and L_WR_B. The horizontal axis represents the horizontal position on the diffusing screen.

Figure 7. Three contour maps on the xz plane at the intersection of y = 20, 80, and 120 mm of (a) the relative light intensity derived from the measured 3D spatial relative light intensity data array at L_BR_W test pattern and (b) the crosstalk of the right view.

From the aforementioned results, the light intensity distribution in a volume of 264 mm × 158 mm × 26 cm was only obtained from 26 recorded images. Suppose the spot LMD was translated along the xy plane with an interval of 5 mm and along the z-direction with an interval of 1 cm to cover an area of similar size. In that case, the ratio of the number of measurements would be more than 264 / 5 × 158 / 5 = 1,600 times larger.

Though the setup shown in Fig. 2 is very effective for fast measurement, it has a limitation. The light intensity through the white semitransparent diffusing screen is influenced by incident light and the characteristics of the white semitransparent diffusing screen itself. Therefore, additional measurements using a spot LMD are necessary after the candidate positions for accurate measurement are selected.

Figure 8 shows the results of the setup in Fig. 4, where CMOS with dimensions of 43.8 mm × 32.9 mm was used to record the 2D spatial light distribution. The CMOS was placed 250 mm from the 3D sample display and horizontally translated at an interval of 30 mm. The size of the original images obtained using CMOS was 8,256 × 6,192 pixels. A decrease in light intensity was observed at the boundary of each image when their light intensities were compared side by side. This decrease resulted from the fact that the camera frame blocked some rays from reaching the CMOS boundary. Therefore, only data at the CMOS center area of 30 mm × 20 mm were used by selecting a portion of 5,550 × 3,774 pixels from the original image of 8,256 × 6,192 pixels.

Figure 8. Results using the setup shown in Fig. 4. (a) 2D spatial light intensity data recorded by complementary metal oxide semiconductor (CMOS) for an area of 30 mm × 20 mm as CMOS translated with a step of 30 mm for the L_BR_W and L_WR_B test patterns. (b) Relative light intensity at the horizontal intersection of the dotted red line. The horizontal axis represents the relative position of the CMOS, where each CMOS data with a horizontal length of 30 mm, was horizontally shifted by multiples of 30 mm considering the horizontal CMOS position at each measurement.

The images at the CMOS area of 30 mm × 20 mm are shown in Fig. 8(a). The light intensities of the recorded images along the horizontal direction are shown in Fig. 8(b). The largest gray area for one test pattern overlapped with the smallest gray area for the other test pattern, similar to the graph in Fig. 6(a). The intervals between the largest and smallest light intensities were also similar, as shown in Figs. 6(b) and 8(b). This implies that the setup shown in Fig. 2 is still handy for determining 3D spatial light intensity and the maximum or minimum intensity positions, where accurate measurements will be performed. On the other hand, the uniformity of the positional or angular transmittance of the diffusing screen is not guaranteed, and the comparison of the peak heights is meaningless when the diffusing screen is used.

The setup in Fig. 4 using CMOS can measure more reliable spatial light intensity data at multiple positions compared with the setup in Fig. 2 using a semitransparent diffusing screen. The setup using CMOS will effectively reduce the overall measurement time compared with that using only a spot LMD. The reduction in measurement time depends on the available CMOS size.

This study investigated a novel measurement scheme where 2D light intensity distribution was obtained using a semitransparent diffuser or CMOS to reduce the measurement times. Since the light intensity distribution of autostereoscopic 3D display has unique distribution trends at the user position, candidate positions for accurate measurement can be selected from the measured 2D distribution or the estimated 3D distribution, if necessary.

While a spot LMD could accurately measure luminance, the measurement procedure at the 3D space of the user position was quite time-consuming. The accuracy of data measured by the diffusing screen was not as good as that measured by the spot LMD. However, the overall measurement time could be reduced and measurement data with good accuracy could be possible at the selected positions by using the measurement of 2D light intensity distribution together with measurement using the spot LMD.

This research was supported by Research Program funded by the Seoul National University of Science and Technology.

The author declares that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Research data are not shared.