## 5 Assembly  
The nominal optical layout has perfectly matched paths, but constructing an interferometer without path mis-match is difficult. In the process of assembly, the precise position of the beam is first measured, so that the position of the optical element can be adjusted by the beam position. The measurement of the beam requires a CQP (Calibrated Quadrant-photodiode Pair) device (Figure 4) [20]. The CQP is an auxiliary measuring equipment, which consists of a BS, two reflectors, and two quadrant photodiodes (QPDs). The measurement principle of the CQP is to determine the unique straight line through two QPDs. If a beam passes through the centers of the two QPDs, a particular set of position parameters exists with the CQP, i.e. the incident point and the directional vector of the beam are constant in value in the CQP reference coordinate system. After calibrated [20], the position parameters under the reference coordinate system is known and can be converted to the global coordinate system by means of Coordinate Measuring Machine (CMM). Because of the measurement precision of CMM (1.5 \(\upmu\)m + 1 \(\upmu\)m/m) and the fitting error of parameters, the measurement precision of the position parameters under the global coordinate system is \(\pm\)5 \(\upmu\)m, \(\pm\)30 \(\upmu\)rad. Figure 4: CQP (Calibrated Quadrant-photodiode Pair) prototype and assembly process diagram. The use process of CQP is: first, the global and reference coordinate system of the system are established using the CMM (Coordinate Measuring Machine); Next, the CQP is aligned with the beam (the number shown on the two quadrant photodiodes is 0), and the position of the beam within the reference coordinate system is determined according to the known positional parameters; Finally, the position parameters of beam is converted to the global coordinate system by a coordinate transformation. Figure 3: Comparison of surface of optical components between (left) before and (right) after polishing. The unit of pix is 0.2 mm, and wave denotes wavelength (\(\uplambda\) = 632.8 nm). Although the edge collapse causes an increase in the PV (Peak to valley) value, the bonding effect is not affected in this case. (**a**) The surface of optical component before polishing; (**b**) The surface of optical component after polishing. In the alignment process (Figure 5), the FCPS of the interference system acts as a light source to provide a stable and collimated Gaussian beam, which is directed into the starting position of the interferometer. Because of influences from pre-assembly and measurement errors, the beams may show large deviations once the components are directly positioned in their geometric model positions. The specific operation procedure for the FCPS assembly is the following: (a) First, the CQP pose is adjusted using the hexapod platform to ensure the beam passes through the center of the two QPDs. (b) Second, with the aid of the CQP, the absolute position of the beam in the global coordinate system is read by the CMM. (c) Finally, the position of the FCPS is adjusted iteratively until the exiting light reaches the desired position. Then, the location of the BS and BC are determined in the same way. After curing the optical element, the deviation of the position parameters between the theoretical beam and the measured beam (the absolute deviation of the beam itself) of the two interference positions under the global coordinate system is re-measured using the CMM with CQP. The results show that compared to theoretical position at the PDa, the position and angle (directional vector sum of \"in-plane\" and \"out-of-plane\") of deviation of the two beams are 3 \(\upmu\)m, 18 \(\upmu\)rad and 9 \(\upmu\)m, 42 \(\upmu\)rad, respectively; the corresponding result for the deviation at the PDb is 5 \(\upmu\)m, 30 \(\upmu\)rad and 10 \(\upmu\)m, 45 \(\upmu\)rad, respectively. Finally, PDa and PDb are fixed in suitable positions so that the energy of the two interference beams on the PD is not clipped.