## 4 Multi-Beam Array Generation and Optical Alignment Experiment
### Optical Alignment  
As it is discussed in Section 3, the captured image is sensitive to the position of the CCD camera. After loading a single OAP phase, the in-focus image (Figure 15a) and defocus image Figure 15b of the light spot could be observed as well as that with coma Figure 15c. This means the position and orientation of the CCD could be adjusted according to the captured image in the optical system to align it to the optical axis. Figure 14: (**a**) OAP array phase and (**b**) its light spots with different focal lengths. No. 1 and 3 are set with the focal length of \(f_{1}\), while No. 2 and 4 are set with \(f_{2}\). Figure 13: The light spots array from (**a**) OAP array specimen and (**b**) OAP array phase on the LCoS-SLM. The accuracy of the spots array in the horizontal direction is at the pixel level, depending on the CCD pixel size. In the experiment, the CCD is produced by AVT Company (Advanced Video Technology, Alabama, USA) at \(2448\times 2050\) resolution with a pixel size of \(3.45\)\(\upmu\)m. Its accuracy in the vertical direction (optical axis direction) is at the sub-millimeter level, which is enough for primary optical alignment. In particular, if the focus spot is projected to a plane mirror surface, an interference pattern could be observed by the interferometer camera, which would offer extra adjustment reference by nulling the interference pattern, and this would improve the alignment accuracy. In the multi-beam array system, the focus light spots produced by LCoS-SLM can be used to implement the alignment of the optical device to the optical axis at the designed position and orientation as well. The rotation adjustment is an important part of optical alignment. An example is shown in Figure 16. A \(2\times 2\) array of light spots array with the same focal length of 500 mm is generated to aid the alignment. Figure 16a shows the misalignment image, and Figure 16b presents the in-focus image after the adjustment. The CCD camera is rotated by \(17^{\circ}\) relative to the optical axis. No. 2 and 3 light spots change from the defocus state to the in-focus state, and all four light spots reach nearly the same intensity and shape. The light spots array captured by the CCD show more reference and information than an OAP light spot, and the adjustment of rotation angle is much accurate. Otherwise, the defocused image or coma image could only offer a simple adjustment tendency. In the meantime, the adjustment in the horizontal direction is made, which can be easier to be achieved by moving the four light spots to the preset position in the CCD image. Other optical components could be aligned to the optical axis as well as the CCD camera used in the experiment. The experiment verifies the multiple-beam OAP array can be used to aid the optical alignment procedure. On the other side, with the help of the interferometer, the alignment job could be done precisely in the actual measurement process. When the spots array is projected to the reference plan part of the measured sample, the reflected light and interference pattern should be observed by the interferometer camera. By nulling the interference pattern array synchronously, the misalignment could be removed. Figure 17a presents the left two light spots of the \(2\times 2\) array that are defocused; thus, their interference pattern shows an obvious spherical aberration fringe. After nulling that fringe, all spots are focused in Figure 17b, which means that the measured sample was aligned with the optical path, and it is proper to do the next surface measurement process. It is very useful to observe the image of the spot array with an interferometer and to align the light path. If there is a shift or tilt in the path, the shift of the spot and the change in the spot shape on one side will be observed. At the same time, using the phase measurement function, the phase of the light spots array can be obtained. In the defocused state, a phase pattern similar to a spherical wave could be observed.