## 3 Experiments and Results
### Evaluation of Novel Fast Tunable Interference Color Filter  
The switching times of the electric field-driven reorientation of NLCs are given by Equations (6) and (7), respectively. \[t_{\mathrm{on}}=\frac{\gamma_{1}d^{2}}{\epsilon_{0}|\Delta\epsilon|\left(u^{2 }-u_{\mathrm{th}}^{2}\right)}\text{ with }u_{\mathrm{th}}=\pi\sqrt{\frac{K_{11}}{ \epsilon_{0}|\Delta\epsilon|}} \tag{6}\]  
Figure 12: **Left**: simulated and experimental measured luminance for views 1 and 2; **Right**: crosstalk of green between views 1 and 2, one channel green/one channel black. Figure 13: **Left**: simulated and experimental measured luminance for views 1 and 2; **Right**: crosstalk of green between views 1 and 2, three channels green/three channels black. \[t_{\text{off}}=\frac{\gamma_{1}d^{2}}{(\pi^{2}K_{11})} \tag{7}\]  
Here, \(\gamma_{1}\) is the NLC rotational viscosity, \(d\) is the NLC layer thickness, \(\epsilon_{0}\) is the free space permittivity, \(\Delta\epsilon\) is the anisotropy of the dielectric constant of the NLC, \(K_{11}\) is the NLC splay elastic constant, \(U\) is the applied voltage and \(U_{\text{th}}\) is the NLC threshold voltage. Both \(t_{\text{on}}\) and \(t_{\text{off}}\) are directly proportional to the square of the layer thickness. Accordingly, the Lyot filter stage with the thickest NLC layer limits the switching time of the entire stack. Its usual large thickness leads to relatively long switching times ranging from tens to hundreds of milliseconds. The tunable NLC Fabry-Perot filters have the potential to switch significantly faster. They consist of a single cavity sandwiched between mirrors and electrodes. Their simple structure enables one to minimize the NLC layer thickness and thus to improve the switching time. As shown by Equation (8), a decreasing cavity thickness also results in an increase of the free spectral range (FSR), which stands for the distance between two successive transmission peaks. \[\text{FSR}=\frac{2\text{nd}\;\cos\Theta}{m(m+1)}\text{ with }m=\frac{2\text{nd}\;\cos\Theta}{\lambda} \tag{8}\]  
Here, \(n\) is the refractive index; \(\Theta\) is the angle of incident; \(m\) is the interference order; \(d\) is the cavity thickness; and \(\lambda\) is the resonance wavelength. However, the conventional spacer technologies used for the construction of the reported examples limit the minimum thickness of the NLC layer to about 2 \(\upmu\)m [27]. At this layer thickness, the electro-optical properties of NLCs are still not optimally utilized, and the small FSR limits the applicability in the visible range. Consequently, no example of a fast switchable interference filter for the visible range has yet been reported. In this paper, we present a design concept and three examples of a fast tunable NLC Fabry-Perot interference filter operating in the visible range. It consists of a sub-micrometer-thick NLC layer embedded in a matched filter design. The electro-optical properties of the interference filters were characterized by Vis-spectroscopic and switching time measurements as a function of the applied voltage. The obtained data prove the design concept of the fast tunable color filters. The basic structure of the designed electrically-tunable NLC Fabry-Perot color filters is shown in (Figure 14). The devices were manufactured by assembling two half cells followed by filling the resulting cell gap with an NLC. One of the half cells consists of a glass plate successively coated with ITO, a dielectric mirror and a photo-structured alignment layer [28; 29] and the other one of a glass plate successively coated with ITO, a dielectric mirror and patterned spacer. The key element of the electrically-tunable color filter (Figure 14) is a sub-micrometer-thick NLC layer, which is homogeneously planar orientated by the adjacent alignment layer. The NLC and alignment layer fill the cavity between two dielectric mirrors. In the field-free state, the NLC layer is birefringent.