## Abstract

Designated eye position (DEP) and viewing zone (VZ) are important optical parameters for designing a two-view autostereoscopic display. Although much research has been done to date, little empirical evidence has been found to establish a direct relationship between design and measurement. More rigorous studies and verifications to investigate DEP and to ascertain the VZ criterion will be valuable. We propose evaluation metrics based on equivalent luminance (EL) and binocular luminance (BL) to figure out DEP and VZ for a two-view autostereoscopic display. Simulation and experimental results prove that our proposed evaluation metrics can be used to find the DEP and VZ accurately.

© 2014 Optical Society of America

## 1. Introduction

With the increasing usage of 3D compatible displays, the optical quality assessment of these displays is more and more important. One of the amazing 3D displays is an autostereoscopic display without using extra glasses for the observers, and such an autostereoscopic display definitely will be the main stream of the 3D display market in the near future. Since a two-view parallax-barrier type autostereoscopic display has been applied in the handheld display market such as handheld game machines, digital cameras and mobile phones for a while, we focus on this kind of autostereoscopic display in this study.

For the autostereoscopic display, the image quality for observers depends on both the viewing distance and viewing angle. Therefore, there are designated eye positions (DEPs) which are the best viewing positions for each eye at the viewing plane. Besides, a viewing zone (VZ), in which an observer is free to move and can still perceive good stereopsis, is another important issue for the autostereoscopic display. Although there have been lots of studies on VZ, deeper researches are still needed for further understanding. Thus this study proposes a novel evaluation method to describe VZ by a novel formula and discussing the affecting factors for VZ of the parallax barrier autostereoscopic display, such as the refraction index of panel glass, the system crosstalk, and the uniformity, by the geometric and the ray tracing methods, respectively.

Viewing zone (some literature named viewing area, viewing diamond or viewing freedom) is a critical topic of the autostereoscopic image qualities; however, it is not a definite terminology and does not have a fixed definition till now. Various definitions of viewing zone (VZ) have been proposed over the decades of researches. N.A. Dodgon [1, 2] defined the viewing zone as: “The positions of the viewer’s eye at which the entire screen appears illuminated determine the useful viewing zone of the display.” H. Ujike, *et al*. [3, 4] pointed out that the Q3DVS (qualified 3D viewing space), QBVS (qualified binocular viewing space) and QSVS (qualified stereoscopic viewing space) should be based on human ergonomics. Hirotsugu Yamamoto, *et al.* [5–7] defined the viewing zone as: “The viewing area where only the left-perspective or right-perspective image is seen without the emitting area disappearing is determined based on the no crosstalk and no disappearance conditions”, and providing clear and solid equations in Yamamoto’s studies. Toni Järvenpää, *et al.* [8] defined the viewing freedom as crosstalk lower than 10% area. Pierre Boher, *et al*. [9] considered the perceived crosstalk for both eyes and proposed “combined 3D contrast” to define the viewing space. Those previous studies deal with VZ from different perspectives, and those results show that there is no general consensus on what the VZ basis is. The limiting or restrictive criterion of the VZ was not made explicit. In our previous studies [10, 11] we proposed a method to find out DEP when the designed optimal viewing distance (OVD) is given and also a geometric method to study VZ around the designed OVD [12]. In this study, we discuss the VZ step by step, and several complicated issues are considered. We show a general method to investigate DEP and VZ by using binocular luminance (BL) and equivalent luminance (EL) even the designed OVD is not given. Our goals in this study is to propose a new objective evaluation method to figure out reasonable VZ and to provide a valuable reference to the autostereoscopic display metrology, in addition to display designers.

## 2. Methods

#### 2.1 Design principle for a two-view autostereoscopic display

The first section of the article is a review of the literature addressing both empirical and theoretical aspects of the DEP and VZ investigations, and reflects the key index for designing principle. This is followed by some background information of the ongoing research in which the present study was carried out and a statement of the VZ issue. Figure 1 shows the top view for a two-view autostereoscopic display design, the rectangular coordinate system is used and the coordinate of the screen center is set as (x, y, z) = (0, 0, 0). P_{D} and P_{B} are the pitch of sub-pixel on image screen and that of parallax barrier, respectively. The distance from display to barrier is defined as f, the distance from barrier to an observer is defined as Z, and the inter-pupil distance (IPD) is marked as P_{E}. First, according to the convergent rule for a monocular condition that every sub-pixel image designed for the specified eye would converge at the same point, and the point is defined as the designated eye position (DEP) [11] as shown in Fig. 1. Therefore, the distance between two DEPs for the right and left eyes should be designed equal to IPD. A convergent relationship between P_{D} and Z can be shown in Eq. (1) [10]:

_{D}is written in Eq. (2):From Eqs. (1) and (2), we can derive the designer’s formulas for a two-view autostereoscopic display as shown in Eqs. (3) and (4):

#### 2.2 Geometric approach

According to the previous studies [5–7], the condition of no pixel disappearing is adopted and the regions defined by the side sub-pixels at the display screen can be drawn as shown in Fig. 2. In this paper, this concept is followed and an additional new condition, under which the observer can perceive all the pixels but not necessarily each entire pixel, is added.

Actually many 3D images are arranged according to sub-pixels instead of pixels, hence we define no sub-pixel disappearing condition instead of no pixel disappearing condition [10, 12]. In other words, at VZ the viewer should perceive each sub-pixel for the specified views. VZ is surrounded by the lines L1, L2, L3, and L4, and each line is linked by the sub-pixel and barrier as shown in Fig. 2. For example, L1 can be plotted by jointing points E and F, and these points can be expressed as in Eqs. (5) and (6). L2 can be plotted by jointing points E’ and F’, and these points can be expressed as in Eqs. (7) and (8).

Thus L1 can be expressed as in Eq. (9) by the pixel aperture ratio a_{D}, the barrier aperture ratio a_{B}, the pitch of sub-pixel P_{D}, the pitch of barrier P_{B}, the distance between the image screen and barrier f, the number of pairs N in the image screen, and the horizontal screen size W. Similarly, the lines L2 to L4 can be obtained. The formulas of L1 to L4 in x-z plane are listed in Eqs. (9) to (12).

_{E}>>P

_{D}, P

_{B}~2P

_{D}and 2P

_{D}N = W, and Eq. (16) is reduced to

_{B}and a

_{D}being less than 1, then (2a

_{B}+ a

_{D})<<(W/P

_{E}), in a practical case, and we finally achieve the quation for ΔZ from Eq. (20)

_{B}and a

_{D}are the only parameters for designers to adjust the VZ for a two-view autostereoscopic display.

#### 2.3 Ray tracing approach

Illustrating by a series of light rays, the ray tracing approach can show the luminance distribution in the space. Although the geometric approach in the previous section can provide a good solution to estimate the VZ in which each eye can perceive all sub-pixels from the specified left- or right-eye image, it cannot show the light fan distribution and is not good enough to describe the optical properties when crosstalk and uniformity issues are considered. In this study, the commercial software Lighttools^{TM} is applied for ray tracing to simulate the luminance distribution in the space, and the commercial software Matlab^{TM} is applied for reconstructing the viewing zones from the ray tracing simulation and measured data through our evaluation metric.

Figure 3(a) shows an example for the measured angular luminance profile from the center points of the two-view images. We measure the angular luminance profiles from the three points on the screen [as shown in Fig. 3(b)] and reconstruct the VZ by our proposed method mentioned below. In contrast to the geometric approach, it must be noted that we usually measure fewer than 500 pixels without any bad effects in practice [13]. In other words, measured points 1 to 3 are neither a single pixel nor a single sub-pixel.

To figure out an evaluation method to describe the luminance perceived by an observer, we propose a novel metric. Figure 4(a) shows an example for our metric notations. Number 1, 2 and 3 represent the measured points on an autostereoscopic display screen. Points 1 and 3 are the side points on the screen, and point 2 is the central one as shown in Fig. 4(b). The right image luminance measured or perceived from point 3 by the observer’s right eye is expressed as *L*_{R-3}. The italic style character *L* represents the luminance, the subscript characters R means for the right eye, and the subscript characters 3 means the luminance comes from point 3. Multiple-point luminance that an observer perceived at her or his right eye as shown in Fig. 4(b) is notated as *L*_{Req}. The equation of *L*_{Req} is expressed in Eq. (22), and we name it as the equivalent luminance (EL), or called total luminance [10], for right eye. EL is an equation to describe the intersection of luminance from the three different points, and EL satisfies the condition of no pixel disappearing which we defined in section 2.2.

In general case, the EL for right eye can be expressed in Eq. (23), where n and m are integers. If measured luminance from any point is zero, the EL will be zero. In other words, if any image cannot be observed by a specified eye at a specified position, then the observation position is not a qualified viewing position.

#### 2.4 Crosstalk map

Crosstalk is a critical issue to destroy stereopsis [14, 15]. To investigate the effect of System Crosstalk (SCT) in the VZ, the authors proposed an acceptable crosstalk map to express the SCT qualified space. The SCT formula for the right eye is expressed as Eq. (24) as defined in ICDM [13]. The reasonable SCT criterion is still a debated issue [16, 17], and it is commonly believed that 3%~10% SCT is an acceptable range for a two-view autostereoscopic display. Therefore, in this paper we set it as an adjustable parameter at around 5%. The monocular luminance *L*_{R}* _{KW}* means that the luminance measured at the right eye when the left and right input channels are full black and full white, respectively, where black and white is expressed as the subscripts

*K*and

*W*, respectively.

#### 2.5 Uniformity map

In addition to SCT, uniformity is another important issue to affect the image quality. A formula to define uniformity of the screen for the right eye is written as [13]:

The *L*_{min} and *L*_{max} represent the minimum and maximum luminance of the measured points. In the study, the measured points include only the three points as shown in Fig. 3(b). Although the human perception for display uniformity depends on the spatial frequency and background luminance of the test pattern [18], the acceptable value of uniformity is 80% according to EBU report [19]. We believe that 80% is a strict specification when a user views the display from normal direction, so we set the acceptable value of uniformity higher than 60%.

#### 2.6 Binocular issue

Although binocular issue has been considered in Eqs. (3) and (4), only monocular condition is included in sections 2-1 to 2-4. We still need a formula to express the binocular luminance in the ray tracing approach. Binocular luminance is a formula to describe the luminance perception from both eyes. The authors have proposed a human factor study to evaluate the binocular luminance, the study [20] suggested that the logarithmic average method is used to describe the binocular luminance. In Fig. 5, binocular luminance, that is defined as in Eqs. (26) and (27), is labeled as *L*_{Bi}. If consider central point only, binocular luminance is label as *L*_{Bi-2}. It is worthy of noting that *L*_{Bi} locates at the center of two eyes, so the position of *L*_{Bi} is not really a light convergent point.

#### 2.7 Refractive index effect

In current two-view parallax barrier autostereoscopic display applications, LCD is utilized as the parallax barrier to make the display as 2D/3D switchable. In LCD, the cover glasses with higher refractive index would refract the light into the air and affect the OVD and VZ [10–12]. Therefore, we should consider the effect of refractive index (n_{B}) to approach the real situation. The new OVD at the main lobe is then modified as

In the previous study [10], the result shows that the refractive index of the barrier would change not only the OVD at the main lobe, but also for the side lobes. In the case that the refraction index of the cover glass is considered, the optical characteristics of the system becomes more realistic but complicated. Geometric method is difficult to be used to analyze the optical characteristics.

## 3. Simulation and experiment results

#### 3.1 Simulation without considering the refractive index of glasses

In this study, handmade autostereoscopic displays are used to test the novel method, while ITRI’s measurement equipment and Lighttools^{TM} are used to capture and simulate the raw data of angular luminance profile. Then, Matlab^{TM} is used to reconstruct the VZ from the raw data. To verify Eq. (15), we build six Lighttools models, in which pitches of sub-pixeles P_{D} are 0.009 cm, N = 2880, IPD = 6.5 cm, OVD = 146.25 cm, pitch of barrier P_{B} = 0.017975cm, with six different barrier and pixel aperture ratios (a_{B}, a_{D}) being (0.334, 0.5), (0.334, 0.7), (0.334, 0.3), (0.5, 0.3), (0.5, 0.5), and (0.5, 0.7), for model 1 to model 6, respectively. In Figs. 7(a) and 7(b), the *L*_{req} is drawn along the x direction at z = 146.25cm. In model 1, the calculated ∆X by using Eq. (15) is 7.59 cm and the simulated ∆X by using Eq. (22) is 7.598 cm, as shown in Fig. 7(a). For model 2, the calculated ∆X is 8.89 cm and the simulated ∆X is 8.798 cm, as shown in Fig. 7(b). The viewing zone formula calculation is consistent with simulation, and we can find that ∆X and pixel aperture ratio are in direct proportion, this trend comply with our viewing zone formula. According to Eq. (15), the crosstalk free VZ condition is to set ∆X equal to IPD, and therefore (2a_{B} + a_{D}) is equal to 1. This diamond-shaped VZ will appear repeatedly along x direction at OVD, and its widths still fit the ∆X and ∆Z formulas. It is worthy of noting that diamond-shaped region will appear repeatedly at around OVD, the reason is that the rays from pixel will pass through the other barrier slits, thus will appear as the other diamond-shaped region at the other locations around OVD. The designed dimond-shaped region is named as the “main lobe”, and the others are called the “side lobes” [10]. As was mentioned above, the viewing zone is defined as the full region that equivalent luminance is not equal to zero. If we consider the widely used definition FWHM (full width at half maximum) to define the area, the viewing region in x direction would be smaller than that defined in Eq. (15) (as shown in Figs. 7(a) and 7(b)). The FWHM results show that the geometric approach is not good enough to describe VZ. As VZ shown in Fig. 2 that the intersection points A and D are not at the same x coordinate, the ∆Z is harder to be defined. Figures 7(c) and 7(d) show the side view at the y-z plane, and ∆Z in main lobes are 45.5 cm and 53.75 cm for (a_{B}, a_{D}) = (0.334, 0.5) and (0.334, 0.7), respectively. Tables 1 and 2 show the comparsions between the geometry and the EL metrics. Table 1 shows that calculation using Eq. (15) is consistent with EL metric simulation with 1%~2% error, and the error is defined as the absolute value of ((Calculated result)-(Simulated result))/(Calculated result). Also, Table 2 shows that the calculated ∆Z(1) and ∆Z(2) of main lobes for different formula by using Eqs. (16) and (21), respectively. And a good consistent result with <5% error is achieved for ∆Z(1) in Error ratio (1). Since ∆Z(2) is calculated from ∆X, a larger Error ratio (2) than Error ratio (1) is expected in Table 2.

The authors use model 2 parameters by applying the designer’s formulas in Eqs. (3) and (4) to find that the designed OVD = 146.25 cm. Besides, two views are symmetrical to the x = 0. We can calculate the (x, y, z) coordinates for the DEPs in the main lobe for the right and left eyes to be (3.25, 0, 146.25) and (−3.25, 0, 146.25), respectively. The coordinates (0, 0, 146.25) should be obtained if we consider the binocular effect in the main lobe.

The authors also use model 2 parameters by applying the Eq. (22) for observed points 2 or 3, and Fig. 8 shows equivalent luminance maps for the right eye. We calculate the maximum luminance poisition, and the results show that both of the two positions would be out of the designed OVD. Figures 9 and 10 show maps for different SCT and different uniformity criteria, respectively. Figure 11 shows qualified viewing zone for SCT<3% and uniformity>60%, the results show that the location of peak luminance would be not affected by qualified crosstalk and uniformity maps. Those results as shown in Figs. 8–11 indicate that if we consider monocular issue only, we can’t find the precise point through the metric, especially when the designed OVD is not given.

Since monocular condition can’t help an inspector to find out the designed OVD and DEP, the authors try to use binocular luminance through Eq. (26). Binocular issue can help to approach the right position but with uncertain z if only one central point data is given (as shown in Fig. 12). The multi-point binocular luminance result as shown in Fig. 13 provide a better result even the designed OVD is unknown. The peak luminance location (x, y, z) = (0, 0, 144~148) is closed to the designed binocular luminance location (x, y, z) = (0, 0, 146.25). Thers is only 1~2% tolerance between the geometric evaluation by Eqs. (3) and (4) and the calcalated result utilizing our metric.

#### 3.2 Simulation with considering refractive index of glasses

To approach a real case [10–12], the refractive index of glass should be considered [11, 12]. Given the refractive index n_{B} = 1.515, the designed OVD calculated by Eq. (28) is modified as 96.42 cm. The result, as shown in Fig. 14, proves that the designed OVD estimated by Eq. (28) is closed to the predicted location.

#### 3.3 Experiment result

To prove the relationship between a_{B}, a_{D} and VZ in Eq. (15), we built three experiments, in which P_{D} are 0.010583 cm, N = 800, IPD = 6.5 cm, OVD = 33 cm, P_{B} = 0.02113cm, W = 16.933 cm, with three different barrier and pixel aperture ratios (a_{B}, a_{D}) being (0.334, 0.5), (0.334, 0.7), and (0.5, 0.7) for model 7 to model 9, respectively. Since illumination of VZ is to be observed in this experiment, a design with brighter backlight and shorter OVD would be better for detecting the VZ. In this experiment, we prepared a handmade backlight with 4620 nits (measured by Konica-Minolta CS-200 luminance meter), barrier is printed by MANIA-BARCO silver-writer, and set the designed OVD as 33cm.

To indicate the VZ from the right-side and left-side pixels, the authors added a light blocking plate on the barrier to block the light from the central area. To figure out the VZ easier, we also added two color filters to distinguish the light from two sides. Figure 15 shows the VZ experiment, and it is noted that the areas with color filters are not a single sub-pixel as we assume in the section 2-2; therefore, a longer △Z than that calculated by Eq. (16) is expected. In addition, the two color filters are designed to distinguish the light for the same view from two sides but not designed to separate the light from different views.

Figures 16(a)–16(f) show the experiment results for model 7 to 9, a Penny (one cent) of 1.905 cm in diameter is put on the illumination plate to evaluate the size of VZ. From Figs. 16(b), 16(d), and 16(f), we can find the width △X for model 9 is larger than that for model 8, △X for model 8 is larger than △X for model 7, and △X is proportional to a_{B} and a_{D}. The relationship in Eq. (15) could be confirmed in this experiment.

We also built a handmade two-view autostereoscopic display by using the same parameters of model 2, and the result is shown as in Fig. 17. To verify the reconstructed result which is calculated from measured data, we compare the reconstructed data and captured pictures at around OVD as shown in Fig. 18.

Figures 18(a)–18(f) show the comparative results. In Figs. 18(a)–18(c), the test patterns of B/W in Fig. 18(a) and natural picture in Fig. 18(b) are captured at the maximum equivalent luminance locations as shown in Fig. 18(c) where (x, y, z) = (17.5, 0, 103) in the first lobe ( + 1). If we move to the lower equivalent luminance position, the worse quality image will appear as in Figs. 18(d) and 18(e) at the location (x, y, z) = (15.5, 0, 103).

## 4. Conclusion

3D display metrology serves as the bedrock for 3D display industry. Much research, such as 3D human factors, ergonomics and 3D optical system design, cannot be conducted without reliable measurement for system evaluation. In this paper, we present an evaluation method for a two-view parallax barrier type autostereoscopic display and propose novel evaluation metrics based on EL and BL. Both design theory and simulation to figure out DEPs and VZ are developed. The new metric is proved to be consistent with geometric method with 1%~2% error in △x calculation and <5% error in △z calculation for a VZ investigation. The design theory based on geometric approach is simple and good for estimating DEPs and VZ, and the simulation based on ray tracing approach can evaluate DEPs and VZ more accurately especially by considering binocular issue. The BL simulation result shows that no error in x direction and <2% tolerance in z direction for DEP verification in a case that designed OVD is not given. The metric can also be coupled with image quality consideration, such as crosstalk and uniformity. Experimental results to verify the proposed evaluation metrics and simulation results have also been shown. This study provides not only the evaluation metrics for DEPs and VZ of a autostereoscopic display in a very clear and coherent manner, but also relates the image quality assessment to the design parameters which will be a valuable reference to the autostereoscopic display metrology as well as system designers.

## Acknowledgments

This research was supported by the Ministry of Economic Affairs of Taiwan, R.O.C. under the project 101-EC-17-A-05-01-1111, Electronics & Optoelectronics Research Lab of ITRI, the National Science Council, R.O.C. under project NSC-102-2221-E-002-205-MY3 and NTU under the Aim for Top University Projects 102R3401-1 and 102R7607-4.

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