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This work presents a new methodology to design patterned circular polarizers consisting of in-cell polarizers, in-cell retarders and biaxial films to achieve very wide viewing freedom for stereoscopic 3D color LCDs. The biaxial films with least materials and simple fabrication concepts are employed for off-axis compensation of the in-cell retarders. In the best result, the crosstalk ratio is less than 0.035 or 0.0082 respectively for over ± 60° or ± 40° viewing cone of the 3D display. As to the normal view of the proposed structure with glasses or LCD rotation, the crosstalk ratio is less than 0.11%, with 93.5% improvement as compared with the ± λ/4 patterned polarizer. The dispersion properties of materials have been considered in all simulations to mimic real situations.
©2010 Optical Society of America
1. Introduction
3D display is an emerging technology for LCD industry. Compared to autostereoscopic display, stereoscopic display has a better performance for horizontal viewing angle and distance, with little image crosstalk. Patterned polarizer is the key technology for stereoscopic display. Tsai et al. applied polycarbonate film with laser processing to produce patterned retarder, so the cost can be further reduced [1]. Polymerized liquid crystal provides more compatible process for LCD industry, Wu et al. fabricated the patterned retarder with λ/4 and 3λ/4 phase difference by a single alignment layer and a single orientation of optical axis [2]; Yoshihara et al. produced ± λ/4 phase differences by an orthogonal set of optical axes [3]. In order to improve the performance of mobile devices, Roosendaal et al. adopted an in-cell patterned retarder characterized by specific retardation values and optical axis orientations for transflective LCDs [4]. Recently, in-cell uniaxial retarder was utilized because of its high stability and temperature endurance during the whole LCD process. Doornkamp et al. indicated two common ways to achieve in-cell patterned retarder: one is photoalignment with two different optical axis orientations but the same retardation value; the other is two-step polymerization at two different process temperatures [5].
As to stereoscopic displays, the in-cell absorptive polarizer and patterned retarder were embedded inside the LCD panel to reduce the misalignment between LCD pixels and patterned retarder stripes for off-axis illumination [6,7]. Thus the vertical viewing angle can be expanded. Oh et al. proposed λ/4 and 3λ/4 phase differences for in-cell patterned retarder [8]; however, λ/4 and 3λ/4 will results in severe wave dispersion and inconsistent color shift for left eye and right eye images. So far, the in-cell patterned retarder uniformly aligned by PI mechanical rubbing is more compatible than patterned alignment technique for LCD makers with existing facilities [2]. A quarter-wave plate cooperating with a patterned half-wave plate aligned by PI rubbing was used in [9] to achieve ± λ/4 phase differences. However, there is still unwanted crosstalk caused by oblique incidence in the patterned retarder on LCD and the retarders on glasses. In this paper, we proposed three novel designs of broadband and wide-view patterned polarizers to reduce the crosstalk due to off-axis illumination and chromatic phase difference.
Broadband wide-view circular polarizers were proposed by the corporation of uniaxial A and C plates [10]. And wide-view polarizers were proposed by using biaxial retardation films [11,12]. These methods are specifically suitable for the retardation film made by stretched process. However, the in-cell patterned retarder for stereoscopic display is made by polymerized uniaxial liquid crystal and it is complicated to fabricate the compensation film inside the LCD panel. As the result, we provide the methodology to compensate oblique phase change of the in-cell patterned retarders by out-cell biaxial retardation films as shown in Fig. 1 . This is a much easier and practical way to reduce the crosstalk with least materials.
2. Design consideration for stereoscopic display
The content for stereoscopic display presentation comprises left-eye and right-eye images, which can be separated by a patterned polarizer. The patterned polarizer can be divided into left- and right-eye polarizers on LCD. In fact, it comprises horizontal stripes along x axis, while the odd number stripes refer to left-eye polarizer on LCD and the even number ones refer to right-eye polarizer on LCD as Fig. 2(a) . As to stereoscopic displays, left-eye images should be blocked by right-eye glasses, and right-eye images should be blocked by left-eye glasses. The crosstalk ratio is defined as [13]:
For example in Fig. 2(a), the unwanted image for left eye means the right-eye image passes through left-eye glasses; and the correct image for left eye means the left-eye image passes through left-eye glasses. In Fig. 2, the patterned polarizer on LCD refers to the combination of an in-cell polarizer, in-cell patterned retarders and biaxial waveplates in Fig. 1. We specifically discuss two situations of 3D crosstalk ratios as shown in Fig. 2(a) and 2(b). Figure 2(a) illustrates that the light normally passes through the patterned polarizer on LCD and glasses, both parts are at normal incidence (θ = 0°), we call it “normal view” for 3D display. Although in Fig. 2(a) unwanted image seems “oblique”, the viewing distance is long enough to assume unwanted image is at normal incidence. In this situation, the change in crosstalk ratio is depending on the rotational angle φ of the glasses with respect to x axis. The condition φ = 0° means viewer’s two eyes have an equal height with respect to the ground while watching LCD screen. Figure 2(b) illustrates the light obliquely passes through the patterned polarizer on LCD, but normally passes through the left-eye and right-eye glasses, we call this “oblique view” for 3D display. In order to simplify the discussion shown in Fig. 2(b), we fix the angle at φ = 0°, which is the most suitable posture for viewer’s head. So the change in crosstalk ratio only depends on polar angle θ and azimuthal angle ψ. The light propagation vector is denoted by k, which is perpendicular to the glasses all the time in our discussion.
Fig. 2 Two situations result in the change of crosstalk. (a) “Normal view” of 3D display. Light normally passes through the patterned polarizer on LCD and glasses, crosstalk depends on rotational angle φ. (b) “Oblique view” of 3D display. Light obliquely passes through the patterned polarizer on LCD, but normally passes through the glasses. The crosstalk ratio depends on polar angle θ and azimuthal angle ψ.
In this paper, the conventional polarizer is assumed with 0.999 extinction ratio, whereas the in-cell polarizer is 0.99. Here the extinction ratio is defined as the luminance ratio of the bright state over the bright and dark states. White LEDs are applied in backlight illumination. In order to exclude the crosstalk caused by the differences of 3D image content, we assume both left-eye and right-eye images have the same white light intensity and spectrum profile. The in-cell patterned retarder is made of Merck RMS-001 reactive liquid crystal and the biaxial retardation waveplate is made of PC film. PC film is relatively firm and stable compared with other polymer films. The dispersion effects of reactive LC and PC films are considered in all simulations and the measured data is shown in Fig. 3 . It shows that these two materials have similar normalized dispersion curves. At 550 nm wavelength, nx = 1.6, ny = nz = 1.5 are assumed for reactive LC; whereas nx = 1.59, ny = 1.58 for PC film. The refractive index nz for biaxial PC film is determined by its Nz factor, where Nz = (nx – nz) / (nx – ny). Other LCD components including glass substrate, are all assumed with refractive index n = 1.5. And in the air, refractive index is n = 1.
Two-step polymerization method described in [7] is the primary design consideration to be compatible with the existing fabrication techniques of LCD industry. First UV exposure produces λ/2 phase difference and second exposure produces null. Hence half- and null-phase patterned waveplate is employed for the in-cell retarder device.
In this paper, the Matlab code is applied for calculating the polarization state and crosstalk ratio. The design and simulation of retarders and biaxial layers is based on the analytical expressions described in [14,15]. Small birefringence approximation [16] is employed in order to simplify the simulation procedure. We have compared our simulation models with the results obtained from 1Dimos software; both are consistent with each other. In addition, 1Dimos cannot simulate the situation in Fig. 2(b), and that is why we use the self-developed Matlab codes in this study.
3. Conventional wide-view patterned circular polarizers
As shown in Fig. 4 , the patterned polarizer on LCD consists of an in-cell polarizer, an in-cell patterned retarder inside the LCD panel and one piece of out-cell quarter waveplate attached outside the LCD glass. The patterned polarizer on LCD can be divided into left- and right-eye polarizers on LCD. The left-eye polarizer on LCD and the corresponding right-eye polarizer on glasses form a pair of crossed circular polarizers, while the right-eye polarizer on LCD and the corresponding left-eye polarizer on glasses form the other pair of crossed circular polarizers. Both pairs eliminate the unwanted images for normal incidence. As to oblique view of 3D images, light has different incident angles to the glasses and the patterned polarizer on LCD, so the oblique compensations are separately designed for them.
Fig. 4 Configuration of single-wavelength wide-view patterned polarizer for in-cell stereoscopic display and corresponding polarizers on glasses.
We define ψm as the angle between the transmittance axis of glasses polarizer or the slow axis of retarder and the transmittance axis of the in-cell polarizer. In Fig. 4, the transmittance axis of in-cell polarizer is at ψm = 0°. To investigate the off-axis property of the in-cell polarizer, the polarization state represented by Stokes vector is calculated through Muller matrix method. The Muller matrix of a linear absorptive polarizer is given by [15]
For oblique incidence, the angle Φ is determined by [14]where ψm = 0° and 90° are the angles of transmittance axes of in-cell polarizer and polarizers on glasses, respectively. And the angle θ0 can be calculated by Snell’s law 1 × sin θ = 1.5 × sin θ0. The angles θ and ψ represent incident polar and azimuthal angles respectively. In this case, the refractive index of in-cell polarizer is approximated to 1.5 considering small birefringence approximation [16].The slow axis of in-cell patterned retarder for right-eye is at ψm = 45°, whereas in-cell retarder for left eye is an isotropic medium. The slow axis of out-cell QWP (quarter waveplate) is at ψm = 135°, so for left-eye and right-eye images, they become left-hand and right-hand circular polarized light, respectively. Moreover, biaxial out-cell retarder not only is a QWP but also compensate the in-cell patterned retarder for oblique incidence. In fact, biaxial compensation must be simultaneously optimized for both left-eye and right-eye polarizers on LCD. To investigate the biaxial phenomenon, we utilize Muller matrix method. The Muller matrix of a retarder or waveplate can be calculated by [15]
The term Γ is the phase retardation value. And for oblique incidence, the angle 2Φ can be determined by [14]with and . And ψm is the angle of slow axis in the x-y plane with respect to in-cell polarizer. In the coordination of oblique incident light, the refractive index difference between slow and fast axes can be derived bywhere and respectively refer to the refractive indices of slow and fast axes for off-axis light. So the retardation value of oblique incidence is given bywhere λ is the wavelength and d is the thickness of the waveplate. For normal incidence, Eq. (6) becomes and retardation value in Eq. (7) simply becomes . Also cos2Φ and sin2Φ can be expressed in terms of Eq. (5) and (6): Thus combining Eq. (7), (8) and (9) into Eq. (4), we can obtain the Muller matrix formulation of the retarder for off-axis light.The polarization state can be represented by Stokes parameter, in which S3 = 1 denotes left-hand circular polarization and S3 = –1 gives the right-hand circular polarization. For Nz = 0.5, the biaxial film will have nearly unchanged slow-axis orientation for off-axis light due to its self-compensated property [17]. In order to maintain the absolute value of S3 as high as 1 for the light emerged from both left- and right-eye polarizer on LCD, we start the parameter Nz <0.5 of the out-cell QWP to compensate both biaxial film itself and the in-cell retarders. By exhausted search, we obtain that the best result is Nz = 0 for the out-cell QWP. In this case, if the Nz >0 or <0 for the out-cell QWP, the absolute value of S3 for the light emerged from either left- or right-eye polarizer on LCD will be lower than 0.9156. In fact, Nz = 0 means nx = nz = 1.59, so it is a uniaxial film with only two different refractive indices. As to the in-cell retarder, its Nz factor inherently remains 1 for the uniaxial property. Figure 5(a) and 5(b) show the comparisons of parameters S3 for the light emerged from the uniaxial and the biaxial out-cell waveplates at polar angle θ = 60° and centered at 550 nm in wavelength. In Fig. 5(a), dash line represents the out-cell QWP adopting a uniaxial film with Nz = 1 and solid line denotes the out-cell QWP adopting a biaxial film with Nz = 0 (actually it is a uniaxial film since nx = nz = 1.59) for the left-eye polarizer on LCD depicted in Fig. 4. The minimum values of dash and solid lines are both S3 = 0.9156 located at ψ = 52°, 232° and ψ = 128°, 308°, respectively. There is no improvement in biaxial film compensation for the left-eye image. However, in Fig. 5(b), the maximum value of dash line is S3 = –0.5259 at ψ = 130°, 310°, while solid line is S3 = –0.9156 at ψ = 128°, 308°, which is effectively enhanced by biaxial film.
Fig. 5 Comparisons of Stokes parameters S3 at θ = 60° with different azimuthal angles. The dash line represents using a uniaxial out-cell QWP with Nz = 1, whereas solid line represents using a biaxial out-cell QWP with Nz = 0. (a) Left-eye polarizer on LCD; and (b) Right-eye polarizer on LCD of Fig. 4.
We examine the polarization states at fixed θ = 60° with different azimuthal angles from ψ = 0° to 360°. Here we define R = S3 at 650 nm wavelength, G = S3 at 550 nm and B = S3 at 450 nm. For the light emerged from the left-eye circular polarizer on LCD, the minimum values are R = 0.8604, G = 0.9156 and B = 0.6816. For the light emerged from the right-eye circular polarizer on LCD, the maximum values are R = –0.8604, G = –0.9156 and B = –0.6816. Because the system of Fig. 4 is not a broadband patterned polarizer, it is hard to maintain the blue and red spectra as circular polarized light at normal and oblique incidence.
The crosstalk ratio is determined by Eq. (1). Compared to the luminance of correct image, the small luminance fluctuation of unwanted image will change crosstalk ratio dramatically. In this regard, the luminance of unwanted image dominates the crosstalk ratio. Figures 6 and 7 show the iso-crosstalk contour simulations, while the condition is depicted in Fig. 2(b) as the “oblique view” of 3D display. In Figs. 6 and 7, (a) refer to the “left-eye” crosstalk ratios, and (b) refer to the “right eye” ones. As shown in Fig. 6, without biaxial compensation, at polar angle θ = 60°, the maximum crosstalk ratio happens at around ψ = 130°, 310° in Fig. 6(a), which is highly related to S3 data in Fig. 5(b). And the maximum crosstalk ratio happens at around ψ = 52°, 232° in Fig. 6(b), which is highly related to S3 data in Fig. 5(a). In Fig. 7, with biaxial QWP, the maximum crosstalk ratio happens at around ψ = 128°, 308° both in (a) and (b). The data meet the previous results as shown in Fig. 5 with almost the same azimuthal angles. Comparing Fig. 7(b) with Fig. 6(b), the crosstalk ratio did not change obviously because the Stokes parameter S3 is little modified for oblique incidence as in Fig. 5(a), and the improvement depicted in Fig. 5(b) is correct image in this case. However, the right-eye crosstalk ratio decreases sharply from more than 0.1 to 0.05 at θ = 60° in the comparison of Fig. 6 and 7 (a). Before compensation in Fig. 6, the maximum values at θ = 60° are 0.26 in (a) and 0.066 in (b); at θ = 40°, the maximum are 0.076 in (a) and 0.015 in (b). By biaxial compensation in Fig. 7, the maximum value at θ = 60° is 0.058 for both left eye and right eye with 77.7% improvement; at θ = 40°, the maximum is 0.0114 for both left eye and right eye with 85% improvement.
Fig. 6 Iso-crosstalk ratio contour simulations of single-wavelength patterned polarizer by a uniaxial out-cell film for in-cell structure. (a) Left-eye & (b) right-eye crosstalk of Fig. 4.
Fig. 7 Iso-crosstalk ratio contour simulations of single-wavelength patterned polarizer by a biaxial out-cell film for in-cell structure. (a) Left-eye and (b) right-eye crosstalk of Fig. 4.
The polarizers on glasses and on LCD are separated by an air. 3D glasses are put on viewer’s head and randomly oriented, so it’s hard to maintain normal incident light to glasses all the time. Therefore, Nz = 0.5 is determined for all of the retarders on glasses since it has a nearly unchanged slow-axis orientation for off-axis illumination. Due to its self-compensated property [17], the oblique incidence into the polarizers on glasses is similar to the performance of normal incidence.
4. Broadband wide-view patterned circular polarizers (type A, three layers)
As shown in Fig. 8 , two sheets of in-cell patterned retarders are employed for broadband circular polarized 3D display. A similar structure has been proposed by photo-alignment to produce broadband patterned retarder [18], which required sophisticated fabrication technique. The right-eye polarizer on LCD has an in-cell polarizer, an in-cell HWP (half waveplate) with slow axis at 22.5° and a QWP with slow axis at 90°; whereas the left-eye polarizer on LCD has an in-cell polarizer, an in-cell HWP with slow axis at –22.5° and a QWP at 90°. Again, the left-eye polarizer on LCD and the corresponding right-eye polarizer on glasses form a pair of crossed circular polarizers, and so do the right-eye polarizer on LCD and the corresponding left-eye polarizer on glasses. This structure produces broadband left-hand and right-hand circular polarized light, and satisfies the equation [19]:
Fig. 8 Configuration of broadband wide-view patterned polarizer (type A) for in-cell stereoscopic display and corresponding polarizers on glasses.
Figure 9 shows the loci of Stokes parameters (S1, S2, S3) for the light emerged from both left-eye (a) and right-eye polarizers on LCD (b). Spectrum properties are examined by 450 nm (blue line), 550 nm (green line) and 650 nm (red line) in wavelength. Here R, G and B denote S3 at 650 nm, 550 nm and 450 nm wavelengths, respectively. For left-eye image in (a), {R = 0.994, G = 1, B = 0.9852} represents broadband left-hand circular polarized state at normal incidence. For right-eye image in (b), {R = –0.994, G = –1, B = –0.9852} represents broadband right-hand circular polarized state at normal incidence. The reason for choosing (22.5°, 90°) and (–22.5°, –90°) angular pair instead of (15°, 75°) and (–15°, –75°) is because it only needs a single out-cell QWP without patterning and slow axis at ψm = –90° can be regarded as ψm = 90°.
Fig. 9 Loci of Stokes parameters with R = S3 at 650 nm wavelength, G = S3 at 550 nm and B = S3 at 450 nm at normal incidence for the light emerged from (a) Left-eye polarizer on LCD; and (b) Right-eye polarizer on LCD in Fig. 8.
Figure 10 shows the optimization of biaxial compensation at polar angle θ = 60° and centered at 550 nm in wavelength. In Fig. 10, the parameter S3 of the light emerged from the out-cell QWP is optimized by biaxial compensation with Nz = 0.1 for both polarizers on LCD depicted in Fig. 8. In Fig. 10(a), the minimum value of dash line is S3 = 0.7244 at ψ = 168°, 348°, while that of solid line is S3 = 0.9195 at ψ = 65°, 245°. Figure 10(b), the maximum value of dash line is S3 = –0.7244 at ψ = 12°, 192°, while that of solid line is S3 = –0.9195 at ψ = 115°, 295°, which is effectively enhanced by biaxial film.
Fig. 10 Comparisons of Stokes parameters S3 at θ = 60° with different azimuthal angle. The dash line represents using a uniaxial out-cell QWP with Nz = 1, whereas solid line represents using a biaxial out-cell QWP with Nz = 0.1. (a) Left-eye polarizer on LCD. (b) Right-eye polarizer on LCD of Fig. 8.
We examine the polarization states at fixed θ = 60° with different azimuthal angles from ψ = 0° to 360°. Here R, G and B denote S3 at 650, 550 and 450 nm in wavelength respectively. For the light emerged from the left-eye polarizer on LCD, the minimum values are R = 0.9313, G = 0.9195 and B = 0.7416. For the one emerged from the right-eye polarizer on LCD, the maximum values are R = –0.9313, G = –0.9195 and B = –0.7416. Because Fig. 8 is a broadband circular polarized system, blue and red lights have better circular polarization states at oblique incidence compared to the ones emerged from the system of Fig. 4.
Figure 11 shows the iso-crosstalk ratio contour simulations, while the condition is depicted in Fig. 2(b). Here we only show the optimized results for the case using the biaxial out-cell QWP with Nz = 0.1. In Fig. 11, (a) refers to the “left-eye” crosstalk ratio and (b) refers to the “right-eye” one. By employing the biaxial out-cell QWP at polar angle θ = 60°, the maximum crosstalk ratio happens at around ψ = 115°, 295° in Fig. 13(a) , which is highly related to S3 solid line in Fig. 10(b). And in Fig. 11(b), the maximum value happens at around ψ = 65°, 245°, highly related to S3 solid line in Fig. 10(a). At polar angle less than θ = 60°, the crosstalk ratio is less than 0.05 for most cases and for both left-eye and right-eye systems. The maximum value at θ = 60° is 0.065 for both left eye and right eye. At θ = 40°, the maximum is 0.0125 for both left eye and right eye.
Fig. 11 Iso-crosstalk ratio contour simulations of broadband patterned polarizer by a biaxial out-cell film for in-cell structure. (a) Left-eye and (b) right-eye crosstalk of Fig. 8.
Fig. 13 Loci of Stokes parameters with R = S3 at 650 nm wavelength, G = S3 at 550 nm and B = S3 at 450 nm at normal incidence. (a) Left-eye polarizer on LCD. (b) Right-eye polarizer on LCD in Fig. 12.
5. Broadband wide-view patterned circular polarizers (type B, four layers)
As shown in Fig. 12 , two pieces of in-cell patterned retarders are employed for broadband circular polarized 3D display. As to left-eye polarizer on LCD, an out-cell HWP with slow axis at 15° and an out-cell QWP with slow axis at 75° contribute to a right-hand circular polarized light. As to right-eye polarizer on LCD, the 1st in-cell HWP with slow axis at –22.5° and the 2nd in-cell HWP with slow axis at –67.5° form a broadband linear retarder. Combining the broadband linear retarder to the out-cell HWP with slow axis at 15° and the QWP with slow axis at 75°, left-eye polarizer on LCD will produce almost left-hand circular polarized light. Again, left-eye polarizer on LCD and corresponding right-eye polarizer on glasses form a pair of crossed circular polarizers. As to right-eye glasses retarder, we find that it only required one HWP with slow axis at 15° and a QWP with slow axis at 75° to compensate left-eye polarizer on LCD. The broadband effect of corresponding right-eye polarizer on glasses is discussed in Fig. 16 , which mostly eliminates crosstalk.
Fig. 12 Configuration of broadband wide-view patterned polarizer (type B) for in-cell stereoscopic display and corresponding polarizers on glasses.
Fig. 16 Comparison of crosstalk ratio v.s. angle φ at “normal view of 3D display” for three proposed structures.
Figure 13 shows the loci of Stokes parameters (S1, S2, S3) for the light emerged from the patterned polarizer for both left-eye and right-eye images at normal incidence. R, G and B denote S3 at 650, 550 and 450 nm wavelengths, respectively. For the light emerged from the left-eye polarizer on LCD, {R = –0.9987, G = –1, B = –0.9947} represents broadband right-hand circular polarized state. For the one emerged from the right-eye polarizer on LCD, {R = 0.9979, G = 1, B = 0.9914} represents broadband left-hand circular polarized state at normal incidence. These results show better circular-polarized performance than “type A” in Fig. 9 do.
Figure 14 shows the optimization results of biaxial compensation at polar angle θ = 60° and centered at 550 nm in wavelength. In Fig. 14, the parameter S3 of the light emerged from the out-cell QWP is optimized by a biaxial HWP with Nz = 0.4 and a QWP with Nz = 0.15 depicted in Fig. 12. Figure 14(a) shows the maximum values of dash line is S3 = –0.8269 at ψ = 179°, 359°, while that of solid line is S3 = –0.9157 at ψ = 45°, 225°. Figure 14(b), the minimum value of dash line is S3 = 0.3790 at ψ = 164°, 344°, while that of solid line is S3 = 0.9055 at ψ = 104°, 284°. Both are effectively enhanced by biaxial film.
Fig. 14 Comparisons of Stokes parameters S3 at θ = 60° with different azimuthal angles. The dash line represents using a uniaxial out-cell QWP and a HWP with Nz = 1, whereas solid line represents using a biaxial out-cell HWP with Nz = 0.4 and a QWP with Nz = 0.15. (a) Left-eye polarizer on LCD. (b) Right-eye polarizer on LCD of Fig. 12.
We examine the polarization states at fixed θ = 60° with different azimuthal angles from ψ = 0° to 360°. Here R, G and B mean S3 at 650, 550 and 450 nm wavelengths, respectively. For the light emerged from the left-eye circular polarizer, the maximum values are R = –0.9029, G = –0.9157 and B = –0.9057. For the one emerged from the right-eye circular polarizer, the minimum values are R = 0.9011, G = 0.9055 and B = 0.7507. Compared to the light emerged from the patterned polarizer described in Fig. 4, it shows that blue and red lights have better circular polarization states at oblique incidence.
Figure 15 shows the iso-crosstalk ratio contour simulations, while the condition is depicted in Fig. 2(b). In Fig. 15, (a) refers to the “left-eye” crosstalk ratio and (b) refers to the “right-eye” one. Here we only show the optimized results corresponding to the solid line in Fig. 14(a) and 14(b). By employing a biaxial out-cell QWP and considering at polar angle θ = 60°, the maximum crosstalk ratio happens at around ψ = 104°, 284° in Fig. 15(a), which is highly related to S3 solid line in Fig. 14(b). And in Fig. 15(b), the local maximum happens at around ψ = 45°, 225°, highly related to S3 solid line in Fig. 14(a). At polar angle less than θ = 60°, the crosstalk ratio is almost less than 0.03 for both left-eye and right-eye systems. The maximum values at θ = 60° are 0.034 for left eye and 0.035 for right eye. Meanwhile, the region of crosstalk ratio less than 0.01 completely covers the entire θ = 40° viewing cone. The maximum values at θ = 40° are 0.0077 for left eye and 0.0082 for right eye.
Fig. 15 Iso-crosstalk ratio contour simulations of broadband patterned polarizer by biaxial out-cell films for in-cell structure. (a) Left-eye and (b) right-eye crosstalk of Fig. 12.
Comparing Fig. 15 with Fig. 11, at θ = 60° cone angle, the crosstalk ratio has nearly dropped from 0.05 to 0.03. As the result, the design of “type B” has not only better broadband performance for “3D normal view” but also better wide-view performance for “3D oblique view”.
We conclude the simulation results of three arrangements below in Table 1 . It compares the minimum absolute values of S3 parameters of light emerged from different designs of patterned polarizer at polar angle θ = 60° with different wavelengths. It also shows the maximum crosstalk ratio at θ = 60° for left or right eye. Meanwhile, we compare the maximum crosstalk ratios at θ = 60° of three arrangements in Fig. 4, 8 and 12 with the one (0.26) in Fig. 6(a), they are 22.3%, 25% and 13.5% relative to 0.26, respectively. Although the arrangement in Fig. 12 can reduce the crosstalk much dramatically, it is the most complex which requires 2 in-cell layers and 2 out-cell layers to perform broadband effect. The arrangement in Fig. 8 can perform broadband effect requiring 2 in-cell layers and 1 out-cell layer. The arrangement in Fig. 4 is the simplest structure but its waveplates are designed for single wavelength. Moreover, we note that at 550 nm wavelength, although the Stokes parameters of G = 0.9195 and –0.9195 for the light emerged from the patterned polarizer in Fig. 8 have better circular polarization states than G = –0.9157 and 0.9055 for the light emerged from that in Fig. 12, the crosstalk ratios in the system of Fig. 12 are much lower than that in Fig. 8. This is because we only consider the polarization states of the light emerged from the patterned polarizers on LCD while discussing S3 parameters. Furthermore, the corresponding polarizers on glasses are at normal incidence, so the loci of polarization states as well as the crosstalk ratios will not the same as that at oblique incidence.
Table 1. Comparisons of S3 parameters of light emerged from different patterned polarizer, and maximum crosstalk ratio calculated for left or right eye at polar angle θ = 60°
6. Comparison of “normal view” of 3D display
Now we compare the performance of “normal view of 3D display” for the three systems illustrated in Fig. 2(a). In order to simplify the discussion, zero crosstalk ratio is designed at φ = 0°, which also means that the viewer’s head didn’t tilt or rotate. As shown in Fig. 16, the left-eye and right-eye systems of the configuration in Fig. 4 have the most severe crosstalk ratio for any φ angle and the maximum crosstalk ratio is 0.01677 at φ = ± 90°. As to the left-eye and right-eye ones of Fig. 8, the maximum crosstalk ratio dramatically drops to 0.003626 at φ = ± 90°. The best performance is the crosstalk ratio of the left-eye and right-eye ones for Fig. 12, where the maximum values are 0.000851 and 0.001093.
The angle φ is not only an indicator of viewer’s head rotation, but also can be applied to rotatable-view devices. For example, some portable media devices such as “iPhone” have both “landscape” and “portrait” modes. When an iPhone device is rotated with 90°, it switches to the appropriate view at the same time. If a 3D image can be applied to transform between landscape and portrait mode, the design of broadband patterned circular polarizer is critical for reducing the crosstalk. If we change the landscape into portrait mode by rotating 90° angle, the crosstalk ratio of “oblique view” will also increase. That is why the design of broadband circular polarizer is important for novel portable devices.
7. Conclusion
We propose three novel designs for wide-view stereoscopic displays. In-cell patterned retarders are made of uniaxial liquid crystal and hence need to be compensated for oblique incidence. In this paper, the biaxial out-cell films with least materials and simple fabrication concepts are employed for off-axis compensation. For each case, the Stokes parameter S3 is optimized by using different Nz factor; while both left-eye and right-eye performances are considered simultaneously. In the results of “oblique view” of 3D display, conventional wide-view design in Fig. 4 shows the maximum crosstalk ratio is 0.058 at θ = 60° and is 0.0114 at θ = 40° for both eyes. And the maximum crosstalk ratio of “type B” is 0.035 at θ = 60° with 39.7% improvement, and is 0.0082 at θ = 40° with 28.1% improvement compared to single-wavelengh wide-view design. At “normal view”, the crosstalk ratio of single-wavelength patterned polarizer in Fig. 4 is up to 0.01677 at φ = ± 90°. Broadband patterned circular polarizers have much lower crosstalk ratios with 0.003626 (type A) and 0.001093 (type B) at φ = ± 90°, which means 78.4% and 93.5% improvements compared to single-wavelengh design, respectively. In conclusion, we demonstrate a methodology for designing broadband wide-view patterned polarizers with much easier fabrication concepts; the results show dramatically enhancements for stereoscopic applications.
Acknowledgements
The authors gratefully acknowledge the financial support by the National Science Council of the Republic of China under projects NSC-99-2221-E-002-140 and NTU under the Aim for Top University Project.
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