## 2 Switchable Color Filter Barrier for Autostereoscopic Display Design
### Two View Mode  
The display design shown in Figure 3 is carried out in Figure 4 for the two-view mode. The interleaving pattern and the overlaid filter barrier are illustrated for a display with six subpixels per subpixel group and two switching stages. The arrangements correspond to the time-sequential steps of operation in an autostereoscopic single-user display. The contents of left view (1) and right view (2) are dedicated to the available subpixels within subpixel-groups \(VP\). As illustrated in Figure 4, through the color barriers, the left content is visible to one eye. The other eye sees the right content. Subpixels covered by the blanked filter stripes are used for mixing of the content. As sign for mixing is an \(x\) used. If the user moves his/her head, mixing ratios and positions of mixed subpixels change depending on the user position. This is effectuates by a tracking signal. The switching stages effect a horizontal offset of three subpixels between the interleaving patterns. The configuration of the filter barriers can be freely selected without changing the basic structure of the display. Thus, additional switching stages will be generated with other filter assignments to control the width of the stereo zone or the value of the optical crosstalk. The interleaving pattern and the frame rate of the display or the readout frequency of the image memory have to be adapted to the respective configuration. This can be adapted precise in the \(X\)-\(Z\) direction to the eye position of the observer. An accurate redistribution of the image content is required. For this purpose, the bordering subpixels \(I_{1\text{X2}}\) and \(I_{2\text{X1}}\) located between the left \(I_{1}\) and right \(I_{2}\) image content are interpolated proportionally in dependence of the displacement value \(I_{s}\) according to the Equations (4) and (5). The offset value \(I_{s}\) is a floating point number. The fractional part of the offset value determines the interpolation ratio [20]. Furthermore, other approaches for a redistribution of brightness intensities of the views are possible [21]. \[I_{1\text{X2}}=I_{1}\cdot\left(I_{s}-\lfloor I_{s}\rfloor\right)+I_{2}\cdot \left(1-\left(I_{s}-\lfloor I_{s}\rfloor\right)\right) \tag{4}\]  
\[I_{2\text{X1}}=I_{2}\cdot\left(I_{s}-\lfloor I_{s}\rfloor\right)+I_{1}\cdot \left(1-\left(I_{s}-\lfloor I_{s}\rfloor\right)\right) \tag{5}\]  
The emission characteristic of this display design was tested in a ray-tracing simulation developed for wavelength-selective 3D displays. Narrowband filters and no refractive optics are used. The simulation software could be limited to the determination of the radiation behavior from the superposition in the three core wavelengths. Modeling of the subpixels, their matrix and the color filter barrier is based on geometrical optics and a Lambertian radiator approximation of higher order [7]. The luminance profiles and, thus, the emission properties of each stereo channel are position dependent. Their determination depends on the special design (geometry and color) of the filter barrier  
Figure 4: **Left side**: wavelength-selective filter barrier in two switching stages \(t_{1}\) and \(t_{2}\)**: **Right side**: the corresponding interleaving of the image contents of the left view (1) and the right view (2) and its mixes (1\(X\)2 and 2\(X\)1). and the necessary content distribution [18]. The luminance profiles for a single-user display shown in Figure 5 are the result of such simulation. They correspond to an idealized description of color filters, which have an optimal transmission characteristic. Only light of the corresponding wavelengths will pass the filter barrier. At first, the display matrix is modeled with rectangular subpixels without a gap. In combination with the vertically-oriented filter barrier, a nearly rectangular gradient of intensity results on the imaging plane, only similar to lenticular lens grids. Therefore, separation of the left and right image content is improved. The increase in crosstalk at larger viewing angles remains moderate.