# Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display
## 3 Results
### LCoS Display Based Inline Holographic System  
In this section, we present the experimental implementation to achieve the IL holographic imaging using the LCoS display (see Section 2.3 and Figure 5). The experimental implementation is shown in Figure 13. We use as illumination a 633 nm wavelength linear polarized laser with the output power as 17 mW. The laser is then spatially filtered and later collimated by a convergent lens L1 (focal length as 250 mm). The object to be studied is placed to a distance after L1. Then, we insert a second convergent lens with a focal length of 300 mm (L2, see Figure 13). The function of L2 is twofold: one the one hand, it images a plane of the object space (we label it as object plane \(P\)) into the CCD1 and CCD2 camera planes (the object plane was situated at 690 mm before L2); on the other hand, the Fourier spectrum of the object is set at the focal plane of L2, where the LCoS display is set. Note that this configuration accomplishes the scheme shown in Figure 5.  
As the LCoS used (distributed by HOLOYE) works into a reflective configuration, a system of beam-splitters (B-S1 and B-S2 in Figure 13) are used to properly imaging the object to CCD1 and CCD2. What is more, the obtained images at the CCDs are filtered according to the double-sideband filter explained in Section 2.3. This is experimentally achieved thanks to combination of the LCoS display with two linear polarizers (LP1 and LP2 in Figure 13), which are placed in front of the CCD1 and CCD2 cameras, respectively. As CCD cameras we used two Basler CCDs (KAI-1020) which guarantee the resolution of 1 MP with the frame rate as 60 fps. Note that for a better vision, the optical elements before the second convergent lens (i.e., the laser, the primary convergent lens and the spatial filter) are ignored in Figure 13.  
By computational processing the images recorded by CCD1 and CCD2, according to the mathematical formulation described in Section 2.3, holographic images of objects can be retrieved without the degradation associated to ghost images. In particular, we implemented two objects for the measurement at the same time: a reticle and a thin glass plate. In the case of the thin glass plate, it is covered with microparticles with sizes of \(\sim\)100 \(\upmu\)m. The reticle is located 50 mm before the \(P\) plane (i.e., 740 mm before L2) and the thin glass plate with microparticles is implemented closer to L2, 50 mm behind the \(P\) plane (i.e., 640 mm before L2). In this way we can prove how we simultaneously image the reticle and the microparticles, which are at different axial planes. Moreover, the thin glass plate is hinged to a rotation mechanism from which we can provide the dynamic potential of the method. Figure 12: Microparticle trapping and spatial manipulation: (**a**) the original trapped particle; (**b**) new axial position of the trapped particle when displacing the light capsule structure. By applying the method explained in Section 2.3 we can reconstruct the complex amplitude at the object plane \(P\). From this information, reticle and thin glass plate can be also retrieved by properly applying the Rayleigh-Sommerfeld diffraction method (Equation (6)) [38; 39]. In particular, by taking into account the magnification introduced by L2, the reticle plane is reconstructed by setting the reconstruction position of \(z=-30\) mm to the object plane \(P\) (note \(P\) is set at \(z=0\)). Results are given in Figure 14a, where the image of the reticle is clearly distinguished but the microparticles are defocused (see Figure 14a). Afterwards, by changing the reconstruction position to \(z=+31\) mm, we focus the microparticles plane (microparticles on the thin glass plate) but the reticle at this time is defocused (see Figure 14b). Such pattern shifting demonstrates the feasibility of using the IL holography system to realize the object imaging at different axial positions. Finally, we rotated as well the thin glass plate from which we observed the microparticle dynamic rotation.