# Phase Alignment of an Array Optical Telescope System Using Balanced Detection
## 4 Results and Discussion  
On the basis of the above discussion on the subject scheme and simulation theory, we will analyze and interpret the simulation experimental results, including the power size, demodulation signal, and the result feedback of the eye diagram. In the first step, the two optical signals received at the receiving end were kept free of other relative phases except for the one-bit phase difference generated by modulation and the \(\pi\) phase difference generated by detection. That is when the transmission process does not affect the two optical signals. In the second step, phase interference was added to the transmission section to simulate the phase difference caused by the optical axis tilt. Additionally, the results of the simulation were recorded and analyzed. Thirdly, according to the relationship between the voltage signal received by the oscilloscope and the phase difference between the two optical signals, the electrical signal feedback module was designed to correct the phase difference. In this simulation, the bit error analyzer was used as a visual tool to evaluate the communication quality of the system. We obtained Q factors and eye diagrams as follows. As shown in Figures 8 and 9, ideally, the eye pattern was symmetrical and wide open with the upper and lower eyelids both thin. Therefore, there was a high noise capacity limit, small jitter, a bit error rate of 0, and a large Q factor reaching 369.391 to obtain excellent signal quality. When there was a phase difference of \(\pi\)/2, the eye-opening was significantly smaller, even zero, the upper and lower eyelids were wider, the jitter was increased, the bit error rate was one, the Q factor was zero, the communication quality was significantly decreased, and the communication could not be completed. After the phase compensation, the eye-opening was significantly larger, the upper and lower eyelids were thinner, the jitter was reduced, and the bit error rate was 3.42 \(\times\) 10\({}^{-35}\), which was 10\({}^{29}\) orders of magnitude less than that when it was not adjusted. It can communicate normally, the Q factor was increased to 12.66, and the communication quality was significantly improved. The power values of the three cases were recorded. Under ideal conditions, the power was 2.75 mW. Additionally, the power decreased to 3.30 \(\times\) 10\({}^{-6}\) W, when the phase difference of \(\pi\)/2 was added. It increased to 2.62 mW after phase correction, and the power was significantly increased. Figure 8: Communication quality without phase difference in the transmission of two optical signals: (**a**) Q factor without phase difference; (**b**) BER without phase difference. The waveforms of the three cases and the waveforms of the modulation end are recorded as follows:  
As shown in Figures 10 and 11, when there was no phase difference, the demodulation waveform and modulation waveform was consistent. When the phase difference reached \(\pi/2\), the waveform was very messy. The waveform shape was improved when the phase was corrected. Figure 11: Demodulation waveform: (**a**) Demodulation waveform with \(\pi/2\) phase difference; (**b**) Demodulation waveform after phase compensation. Figure 9: Communication quality with the phase difference in the transmission of two optical signals: (**a**) Q factors with the phase difference; (**b**) BER with the phase difference. The analysis of various phase perturbations was carried out as follow, and the obtained power values were used to solve the relative phase error values. Feedback compensation was then carried out to meet the requirements of phase consistency, leaving the combined signal's power values essentially unchanged and the BER optimized. Power comparison diagrams before and after phase difference correction are shown in Figure 12. It is intuitively obvious that, before the phase difference correction, the power size gradually shrunk as the phase difference increased.