# Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display
## 3 Results
### LCoS Display Self-Calibration
#### 3.1.2 Surface Homogeneity Calibration  
The surface homogeneity calibration shares the same experimental set-up given in Figure 6, and it is achieved just by changing the phase pattern addressed to the LCoS display. In this case, the Shack-Hartmann configuration is addressed (see Section 2.1.2). In particular, we generate a 4 \(\times\) 2 micro-lens pattern in which each micro-lens scheme occupies 400 \(\times\) 400 LCoS pixels. Therefore, the whole micro-lens scheme presents an LCoS display dimension as 1600 \(\times\) 800 pixels. The phase distribution of such scheme is given in Figure 8a and the corresponding spot-array received at the focal plane is given as Figure 8b. Note that such eight micro-lenses pattern cannot cover the whole LCoS surface, not to mention so few focal points cannot guarantee a precise surface integration [31]. Therefore, we dynamically displace the generated micro-lens pattern along the whole LCoS screen both in \(x\) and \(y\) directions. In both directions, this is implemented for 8 times with a step of 50 pixels. Finally, by recording the 8 focal points within each step (64 displacements in total) we can construct a full image with 512 intensity spots in the CCD (see Figure 8c). Once the final spot array image is obtained, we implement a 38 \(\times\) 38 reference grid to analyze the spot deviations from their corresponding centers.  
As detailed in Section 2.1.2, by calculating the deviations of light dots in the final spot array image (i.e., image in Figure 8c) from a reference pattern, the final LCoS surface can be reconstructed. Obtained results are given in radian units in Figure 9a, where a quadratic profile is clearly observed. This quadratic deformation is normally introduced by the lateral mechanical stress applied on the screen during the fabrication process, when the LC surface is stuck to the bottom structures of the LCoS display. To describe the quadratic profile of the LCoS display quantitatively, we studied the pixel-value cross section of a horizontal line in Figure 9a (from the middle pixel of the surface left edge to the middle pixel of the surface right edge). The corresponding peak-to-valley (PV) value of such line is 28.01 radians. To compensate such quadratic deviation, we implement a further step by adding the inverse phase distribution of Figure 9a to the LCoS display. Under this scenario, we repeated the LCoS surface measurement, once again by using the same self-addressed S-H scheme. Ideally, the screen profile after such compensation should be flat. In reality, the measured compensated surface profile after correction is given in Figure 9b, where we can easily find the quadratic error is almost eliminated, and the obtained surface is smoother. In particular, the surface PV (for the same pixels line previously stated) after correction is decreased to just 1.28 radians.  
Figure 8: (**a**) Phase distribution sent to the LCoS display to generate the 4 \(\times\) 2 diffractive micro-lens; (**b**) the intensity spot array at the focal plane obtained by illuminating the 4 \(\times\) 2 diffractive micro-lens with collimated light; and (**c**) the final 512 intensity spots image obtained by performing micro-lens array displacements.