# Optical Interference Suppression Based on LCD-Filtering
## 2 Fundamentals and Experimental Set-Up
### LCD Transmissivity  
Using an LCD as an optical beamforming filter, we restrict ourselves to the two LCD pixel states \"transmissive\" and \"opaque\". For \(s=0\), the LCD pixels are transmissive with transmission coefficient \(\eta_{0}\left(\lambda,\vartheta\right)\) while for \(s=1\) only a small fraction \(\eta_{1}\left(\lambda,\vartheta\right)\) of the incoming light arrives at the detector. Thus, we can fully model the transmissivity as  
\[\eta\left(\lambda,\vartheta\right)=\eta_{0}\left(\lambda,\vartheta\right)+s \cdot\left(\eta_{1}\left(\lambda,\vartheta\right)-\eta_{0}\left(\lambda, \vartheta\right)\right). \tag{6}\]  
The selected transmission coefficient depends on the wavelength \(\lambda\) and the angle \(\vartheta\) of the incoming light rays.  
Generally speaking, LCDs are highly-optimized commercial products and are undergoing a continuous development owing to their commercial importance. Nowadays, almost all LCDs are offered as colored screens with integrated backlight. High-performance gray-scale screens are typically available as application-specific products only. Furthermore, datasheets usually specify the contrast ratio but not the transmissivity in transparent state, and thus we decided to base our research on measurements conducted on a large-area liquid-crystal (LC) cell.  
These measurements were carried out by targeting a narrow light beam on the LC cell and measuring the received power for \(s\in\left\{0,1\right\}\) using a Si-PD of type FDS 100 from Thorlabs Inc. (Newton, NJ, USA), connected to a Keithley 2450 source-measurement unit (SMU). The LC cell is of size \(60\,\mathrm{mm}\times 90\,\mathrm{mm}\) and is advertised as a low-cost optical shutter e.g., used in auto-darkening welding helmets. As a light source, an LED Engin LZC-03 MD07 module comprising four different LED colors with spectral distribution shown in Figure 3 is used. The measurement results in Figure 2 are obtained by normalizing the received powers for the LC cell states \"on\" and \"off\" by the received power without the LC cell in the optical path. Since the orientation of the LCD has a comparatively low impact on the measurement results, we specified the transmissivity values by averaging the measurement results in respect to the LC cell rotation. In order to enable an analytic evaluation, the LC transmissivity has been approximated for the 454 nm LED as  
\[\eta_{0}\left(\vartheta\right)=0.297\cdot\cos\left(0.81\cdot\vartheta\right) \tag{7}\]  
and  
\[\eta_{1}\left(\vartheta\right)=1.0001-\cos\left(0.071\cdot\vartheta\right). \tag{8}\]  
As shown in Figure 2, this approximation is very close to the measurement results for incident angles \(\vartheta\leq 60^{\circ}\).  
The measurements in Figure 3 are obtained using a BTS 256-EF spectrometer by Gigahertz-Optik (Turkenfeld, Germany). In case of the LC transmissivity, relative measurements are performed using sunlight. Notably, the wavelength-dependent transmissivity variation of the LC cell is moderate in the range from 400 nm to 750 nm. Below 400 nm, the LC cell strongly attenuates the receive signal, and above 750 nm the LC cell is transparent for the optical signals. To avoid infrared interference leaking into the LC cell, a combination with an infrared blocking filter is an apparent solution.  
Figure 3: Spectral measurement results for the LC cell and the four different LEDs.  
Figure 2: Transmissivity of the LC cell.