# Method to Measure Light Spot Position in Beacon-Less Inter-Satellite Communication System
## 5 Experiment  
The experiment platform is shown in Figure 4. The experiment system used two modulated 1550 nm wavelength lasers, one as received light and another as reflected light. The QD has an active radius of 1 mm with a gap width of 0.01 mm and was mounted on a three-dimensional micro-displacement motion stage. We used a Gaussian beam with a spot diameter of 0.51 mm to improve the detection accuracy [6].  
Before the experiment, we placed the probe of the optical power meter on the focus of the focusing lens, turned on the received laser and turned off the reflected laser. This way we could measure the light intensity of the received laser. By repeating the same process, the intensity of the reflected laser can be measured. The intensity of the two lights was 0.14 nW and 12.84 nW, respectively.  
One of the optical fiber collimator was mounted on a displacement motion stage; thus, the received light spot could be moved across the surface of the QD when the reflected laser was turned on. The calculated x coordinate curves of CCR are shown in Figure 5a,c as the yellow curves. The same procedure was repeated when the reflected laser was turned off and the calculated x coordinate curves are shown in Figure 5a,c as the blue curves.  
We also used the Fast Fourier Transform (FFT) method and NCR method to calculate the spot position when the reflected laser was turned on, and their calculated x coordinate curves are shown in Figure 5a,c as the red and green curves, respectively.  
Furthermore, the absolute errors are calculated and shown in Figure 5b,d. Taking x coordinates as an example, the absolute error is denoted as:  
\[\delta_{x}=\frac{x_{0}-X}{R} \tag{22}\]  
where \(x_{0}\) is the calculated \(x\) coordinate, \(X\) is the real \(x\) coordinate, and \(R\) is the focal length of the system.  
As can be seen from Figure 5, when the two lights differ in intensity by 91.7 times, the calculated curves of CCR method is almost the same as that without reflected light. In contrast, the FFT method and NCR method cannot detect the light spot position when reflected light was turned on.  
Figure 4: The experimental platform.  
Moreover, we used maximum error and root-mean-square error to compare the performance of CCR method at different \(f_{2}\) frequency points. Maximum error is defined as:  
\[\delta_{\text{max}}=\max_{i}(|\delta_{x\!i}|) \tag{23}\]  
Moreover, root-mean-square error is defined as:  
\[\delta_{RMSE}=\sqrt{\sum_{i=1}^{N}\delta_{xi}^{2}/N} \tag{24}\]  
The performance of QD is influenced by its own target surface size and gap size, the x coordinates curve presents obvious non-linearity [8]. To avoid the impact of the non-linearity of QD, the calculated x coordinates in interval [-0.1, 0.1] with good linearity were selected to calculate the two kinds of errors. The results are shown in Table 1.  
Figure 5: The calculated x coordinate curves and absolute errors. (**a**) The calculated x coordinate curves when \(f_{2}\) = 200 kHz; (**b**) the absolute errors when \(f_{2}\) = 200 kHz; (**c**) the calculated x coordinate curves when \(f_{2}\) = 300 kHz; (**d**) the absolute errors when \(f_{2}\) = 300 kHz.  
As shown in Table 1, the CCR method has high detection accuracy, with the maximum error below 0.026 mrad and the root-mean-square error as low as 0.012 mrad. Moreover, its detection accuracy is almost unaffected by the change of \(f_{2}\). When the modulation frequencies \(f_{2}\) changed from 200 kHz to 300 kHz, the root-mean-square error increased only 0.002 mrad.