# Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display
## 2 Materials and Methods
### Microparticle Manipulation through Light Structures Created by a LCoS Display
By using the light cone shown in Figure 3, the particle cannot fall into the light cone because of its upper surface also offers  
Figure 3: The light trapping scheme based on the split-lens configuration: (**a**) Continuous split-lens configuration; (**b**) Light cone structure created by the LCoS generated continuous split-lens. photophoretic forces that bounces the particle away before entering into the light cone central space. This is demonstrated in Figure 4a. Therefore, we have to open the light cone structure from the upper section to allow particles entering its central area. Note that to open the light cone means removing light from the upper section. This is practically reliable just by properly multiplying an angular sector to the continuous split-lens phase distribution to be sent at the LCoS display. The angular sector presents a constant phase value and therefore, light illuminating this section on the LCoS display is not being modulated according to the split-lens scheme. Under this scenario, an opening is obtained in the light cone (see Figure 4b). Once the particle enters the light cone through the upper opening, we close the light cone from the top once again, by simply removing the added angular sector and recovering the original split-lens phase distribution. After this process, the microparticle is located into the light cone (see Figure 4c). Nevertheless, we still face one major problem as even though the particle is kept steady in the vertical direction, it is still not stable within the horizontal direction, as it can escape from the light cone front side (i.e., from the light circle plane, see Figure 4c). Thus, this section has to be closed to prevent particles from escaping. This is achieved by multiplexing a regular lens together with the continuous split-lens scheme. By choosing a focal length, for the regular lens, shorter than the distance between the LCoS and the light ring plane, light modulated by the regular lens acts as an stopper at the cone opened side (see effect of the regular lens represented by red light in Figure 4d). At this moment, a more sophisticated light structure, demonstrated as an optical bottle architecture, is realized within the combination of these two diffractive elements (regular lens and continuous split-lens). Under this scenario, the particle inside the light cone is now stably trapped within the new optical bottle as both sides are sealed. This optical bottle structure is demonstrated in Figure 4d. Last but not least, by simultaneously adjusting the focal lengths for both light structures, the whole optical bottle structure can be spatially moved along the axial direction. By doing this, the trapped microparticle is dragged by the light system, and the spatially manipulation of microparticles is efficiently realized. Figure 4: Sketch of the proposed microparticle trapping method: (**a**) Microparticle being bounced when encountering a closed light cone; (**b**) Microparticle entering the light cone with its upper section opened; (**c**) Microparticle escaping from the light cone thorough the unsealed section; (**d**) Microparticle trapped in the sealed light capsule structure.