# Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display
## 3 Results
### LCoS Display Self-Calibration
#### 3.1.1 Phase-Voltage Calibration  
In this section, the method described in Section 2.1.1, is experimentally implemented and tested to determine the phase-voltage relation of the LCoS display. The sketch shown in Figure 1 is experimentally implemented and shown in Figure 6. We use a polarized He-Ne laser with the wavelength of 632.8 nm as the illumination. Later, light is expanded and collimated through the combination of a microscope objective (MO), a pinhole and a convergent lens. Note that the combination of such three elements not  
Figure 5: LCoS display based double-sideband filter IL holographic system.  
only makes light expansion feasible, but also they guarantee light filtering. A half-waveplate (HWP) combined with a linear polarizer (LP) is used to control the intensity of light illuminating the LCoS. In addition, the direction of LP is selected to ensure an LCoS display performance in the phase-only regime (i.e., the polarization direction is parallel to the LC director direction). Once the input light is properly modulated, the PLUTO-LCoS display (distributed by HOLOEYE) is aligned with its surface strictly perpendicular to the input beam (see the zoomed figure at the right bottom corner of Figure 6). Here, the LCoS display presents a 1920 \(\times\) 1080 resolution with the pixel size as 8 \(\upmu\)m, and it has the filling factor as 87%. Finally, the collimated light entering the LCoS display is modulated by the digital two split-lens configuration (see Figure 1a) and the corresponding fringes-like interference pattern is obtained at the CCD camera, with the help of the beam splitter (B-S) and the mirror placed after the LCoS.  
Once the system set-up is determined, the two split-lens configuration is addressed to the LCoS display. The focal length of the addressed split-lens is set to 350 mm and the separation distance as 0.4 mm. Later, the two split-lens scheme is addressed for different values of the constant phase \(\phi(V)\), so that the interferometry pattern is modified (see Section 2.1). To realize the whole gray level range calibration, we drive different voltages (phases) by the means of changing the gray level from 0 to 255 with the step of 8. Therefore, 33 different interferometry patterns are obtained in the CCD with each pattern relates one phase value (voltage) to its corresponding gray level. As stated in Section 2.1, from this collection of interference patterns, the phase-voltage look-up table can be retrieved [22]. The obtained experimental curve, representing the phase as the function of the gray level, is shown in Figure 7. Each data in the curve given in Figure 7 is obtained by repeating the experiment for one hundred times, hence we also calculate the corresponding standard deviations, which are presented as the error bars in red. From Figure 7, we see that the phase-gray level curve demonstrates a nearly linear distributed tendency and the error bar values along the whole distribution are small. What is more, the phase values after the calculation is ranging from 0 to \(\sim\)6.28 radians, which is suitable for phase-only applications.  
Figure 6: LCoS self-calibration implementation.  
Figure 7: Phase-gray level curve measured using the split-lens separation distance as 0.4 mm.