## 4 Simulations and Experiments
### Experiments  
The experimental setup for testing the performance of alignment tolerance is shown in Figure 9.  
A fiber-delivered separated modulated laser was implemented by a single-frequency laser source with 780 nm wavelength (Sacher Lasertechnik Group TEC 500) and two acousto-optic modulators (AA Opto Electronic MT80). After transferring to the optical reading head, these beams diffracted at a custom-tailored 1 \(\upmu\)m grating. The grating, assembling to a 6-DOF stage, could be adjusted to generate different types of errors. Autocollimators (Moeller-Wedel ELOMAT 3000) were equipped to monitor the rotation angles, while the translational stand-off displacements were displayed by a homemade laser interferometer. Besides, it is worth emphasizing that the rotational center was located near the center of these beams. Finally, the measurement beam was delivered to the photodetector (FEMTO Messtechnik GmbH HCA-S-200M-SI) and spectrally analyzed with a spectrum analyzer (ADVANTEST R3131A). Since the experiment only focused on the measurement beam, the reference beam was not detected. The aperture of the photodiode was larger than the beam so that only the work-off of the beams were considered. As mentioned above, the parallelism of beams was adjusted by the kinematic mounts to exclude the assembling error. Figure 8: The relationship between the normalized intensity and pitch angle with different structure parameters. (**a**) Rotation arms are changed. (**b**) Lengths of the diffracted beams are changed. (**c**) Beam diameters are changed. A comparison of the proposed reading-head structure and a larger structure built with independent optical components were deployed in the experiments and are depicted in Figure 10. The plots from the former are colored red and those from the latter are blue. Since it is not clear enough to compare two sets of plots, curves were fitted to describe their trends. The type of the fitted curves was selected as the sum of two Gaussian functions, which also fits the curves in the simulation shown in Figure 8 well. Considering the fluctuation of spectrum peaks and the amplitude differences of the assembled and independently built structures, Figure 10 selects the apex of the fitted curve as the origin and uses the amplitude loss as the standard for measuring the misalignment tolerance. Both in the simulations and experiments, the pitch angle leads to the most severe work-off distances and amplitude loss; the yaw angle causes a less severe deterioration, and the roll angle has the slightest effect, which proves that the work-off distance is one of the major factors of the amplitude loss. Compared with the  
Figure 10: Experimental curves showing the relationships between the misalignment errors and amplitude loss of the interfering signal. (**a**) Roll angle. (**b**) Yaw angle. (**c**) Pitch angle. (**d**) Stand-off error. All four figures share the same legend as the first figure. Figure 9: Experimental setup for testing the performance of alignment tolerance. red curve and the blue one in Figure 10a-c, it is proved that the shorter the diffracted beams are, the stronger the tolerances to rotational angles are, which is also consistent with the simulation in Figure 8. It provides an available approach to improve the alignment tolerance, that is, reducing the size of the reading-head and the length of the diffracted beams. However, keeping large enough clear apertures while reducing the size and the beam lengths requires elaborate designs on the optical configurations. Besides, the stand-off error remains as Figure 10d depicts. As for the specific criteria of alignment tolerance, it is determined by the dynamic range of the photodetector, the ratio of the largest and smallest amplitudes can be acquired. Taking the Keysight receivers as instances, the dynamic ranges range from 6:1 to 25:1, depending on the AC/DC ratio [16].