# TRC-Based High-Precision Spot Position Detection in Inter-Satellite Laser Communication
## 5 Experiment  
The experimental optical platform is shown in Figure 7. The platform used a tunable semiconductor laser with a wavelength of 1550 nm and an output power of 120 \(\upmu\)W. The frequency of the modulation signal is 125 kHz. The laser is emitted from the collimator, passes through the attenuation glass, enters the lens, and finally illuminates the QD target surface. The power of the incident light beam is 1.39-13.73 nW. The QD with target radius of 1 mm and a gap width of 0.01 mm is placed on a three-dimensional stage, so that the position of the spot on the QD target surface can be adjusted. Furthermore, QD can be moved back and forth to adjust the size of the incident spot. Two displacement meters are placed on each side of the translation stage, which can measure the displacement of the QD in the x-axis direction and the y-axis direction. The ADC model used in the platform is AD9653 whose sampling frequency is 100 MHz and output data width is 16 bits. The data length used in the experiment is 8000 points. Utilizing the high-speed sampling capability of ADC and the parallel computing capability of FPGA can better meet the real-time requirements of the ATP system and avoid the interference caused by spacecraft dynamics and jitter. Figure 8 shows the pure noise signal and its power spectral density output by the detector used in the experiment under the condition of no incident light irradiation. It can be seen from the figure that, after removing the DC component, the power spectral density of the noise is approximately evenly distributed over the entire frequency band. Figure 9 shows the coordinate curve and error curve obtained by TRC method under different spot radius when QD output SNR = -7.66 dB. In Figure 9a, \(\upomega\) is the spot radius, the abscissa \(X\) is the real  
Figure 8: The output noise of the QD and its power spectral density (PSD). Figure 7: The experiment platform. coordinate value of the light spot, and the ordinate \(x_{0}\) is the calculated coordinate value. In Figure 9b, \(\delta_{x}\) is the absolute error of the calculated coordinate. Taking x coordinates as an example, the absolute error is denoted as:  
\[\delta_{x}\ =\ \frac{x_{0}-X}{D} \tag{25}\]  
where \(D\) is the focal length of the system. It can be seen that all three coordinate curves change in an \"S\" shape, which is affected by spot radius, QD's target size and gap width. However, the detection curve of the TRC method still maintain good linearity and the absolute errors are all limited in 0.0176 mrad in the coordinate interval (\(-0.2\) mrad, 0.2 mrad). This means that the performance of the TRC algorithm has high stability under different spot radius conditions, so the detection results of the TRC method can be relatively easily corrected for the non-linearity by interpolating, fitting and other methods. In order to avoid the influence of QD's non-linearity, this paper selects the data in the (\(-0.1\) mm, 0.1 mm) coordinate interval to calculate various detection errors. When the spot radius \(\omega\) = 0.53 mm and \(\omega\) = 0.71 mm respectively, Figures 10 and 11 show the detection curves under different SNR conditions. It can be seen that the detection result of the TRC method can also present a smoother curve when the SNR is as low as \(-17.86\) dB, and the absolute error fluctuation is suppressed within 0.0238 mrad. This shows that the TRC method can effectively suppress noise and improve the detection accuracy of the spot position. Figure 10: When \(\omega\) = 0.71 mm, detection results of TRC method under different SNR conditions. **(a)** The Calculated coordinate curve; **(b)** Absolute error. Figure 9: When SNR = \(-7.66\) dB, detection results of TRC method under different spot radius. **(a)** The Calculated coordinate curve; **(b)** Absolute error. In contrast, under the same conditions, we also used the direct FFT method and the Kalman filter method to detect the spot position.