## 2 Methodology of DLR Measurements
### High PRF of DLR Technology  
The early research on DLR technology mainly focuses on laser pulses having a low PRF and a few joules of energy to pursue high energy with a nanosecond pulse width. In 2002, Electro Optic Systems in Australia published a report on DLR technology at the 13 th International Laser Ranging Conference in Washington. The report briefly introduced the research progress and measurement results of DLR technology and showed that the ranging of 15-cm space debris located at a slant range of 1250 km could be realized by the Mount Stromlo Satellite Laser Ranging station equipped with a 76-cm telescope and 532-nm nanosecond laser [8]. SHAO has actively targeted the development of international DLR technology for a satellite laser ranging (SLR) system using a receiving telescope with an aperture of 60 cm. This development allowed the laser ranging of space debris to a distance of 900 km using a high-power laser system with a PRF of 20 Hz, an average power of 40 W (at a wavelength of 532 nm), a pulse width of 40 ns in 2008, and the ranging precision at approximately 1 m [11]. The above laser generator operated in lamp pump mode with double beam synthesis and had poor beam quality and a short continuous working time. Therefore, in 2008, SHAO improved the laser ranging control system by introducing a large power laser system with high stability, a PRF of 10 Hz, an average power of 10 W (at a wavelength of 532 nm), and a pulse width of 10 ns. In 2009 and 2010, SHAO successfully conducted DLR for a rocket body and disjunction Iridium satellites at a measuring distance exceeding 1200 km, resulting in a ranging precision of 80-100 cm. In 2011, with support from the Chinese Academy of Sciences, SHAO improved the laser ranging system by upgrading the 10 W laser to a 30 W laser and conducted measurements up to 1800 km with an RCS of 3.4 m\({}^{2}\), achieving a detection success rate of more than 50% [11]. Additionally, Yunnan Astronomical Observatory of the Chinese Academy of Sciences developed a laser ranging system with a telescope having an aperture of 1.2 m and a laser having a single pulse energy of 4.5 J at a PRF of 10 Hz and obtained successfully laser echo data of space debris [12]. (1) The 200 Hz PRF DLR  
Equation (3) shows that, for a constant number of laser echo detections, increasing the PRF of a laser can significantly reduce the laser pulse energy. Since 2013, SHAO has developed a high-power nanosecond laser system with a PRF of 200 Hz, single-pulse energy of 300 mJ, and average power of 60 W. The laser structure is shown in Figure 1. The main specifications of the laser system are a wavelength of 532 nm, a pulse width of \(\sim\)10 ns, beam pointing stability of \(\sim\)45 \(\upmu\)rad, and beam quality (M\({}^{2}\)) of \(\sim\)3. The laser measurement of debris was performed by updating the range gate generator, a data acquisition unit, and data process software of the DLR system. Figure 2 shows the observation results of the DLR system at SHAO for hundreds of laps of DLR data. The x-axis and y-axis are the measured distance and the elevation of the observation, respectively. It is seen that the farthest measured distance is nearly 3000 km. The RCS is equivalent to 0.26 m\({}^{2}\) at a distance of 1000 km. (2) The 1 kHz PRF DLR  
In 2015, Graz Station in Austria used a 532 nm laser with a PRF of 1 kHz, a pulse width of 10 ns, and single-pulse energy of 25 mJ and a telescope with a receiving aperture of 50 cm to realize DLR for an orbit height of 3000 km and a minimum area of 0.3 m\({}^{2}\)[9]. SHAO also updated a picosecond laser system adopting a dual-pulse mode, power of 4.2 W, a wavelength of 532 nm, single pulse energy of 2.1 mJ, and PRF of 1 kHz. The RCS of the measured target was 2 to 12 m\({}^{2}\) and the ranging precision was at a sub-decimeter level [15].