## 2 Methodology of DLR Measurements
### Low Noise and High Efficient Laser Echo Detection  
For the detection of laser signals of cooperative targets with laser reflectors, a single-photon avalanche diode (SPAD) detector with single-photon sensitivity, timing accuracy of 30-50 ps, a chip diameter of 200 \(\upmu\)m, and a quantum detection efficiency of 20% is widely used at laser ranging stations [20]. The photon detector has a relatively high level of dark noise. In the high-repetition-rate working mode, the dark noise reaches approximately 100 kHz. Combined with the effect of background noise, the detector noise reaches a level of hundreds of kilohertz, which may trigger the avalanche process and cause false detection. Figure 4: Mode of laser emission and reception alternation for laser ranging at an ultra-high PRF. A wide range gate and low noise level of laser detection are required to handle the large-ranging error coming from poor accuracy of debris orbit prediction. The avalanche photodiode (APD) detector technology with a low level of dark noise, high efficiency (>40%), and high sensitivity have been developed [21]. Additionally, a large chip is required to ensure that the detector has a sufficient optical receiving field of view. The APD detector in the Geiger mode operation works at a voltage higher than the breakdown voltage to realize sufficient gain, after the photons are absorbed, the detector can quickly avalanche output to meet the requirements of single-photon detection and realize higher detection efficiency and sensitivity, as shown in Figure 6.  
SHAO developed a low-noise, highly efficient single-photon detector for DLR measurements. The main specifications of the detector are a diameter of the photosensitive surface of 500 \(\upmu\)m, dark noise of approximately is less than 1 kHz at a PRF of 1 kHz, detection efficiency exceeding 40% at a wavelength of 532 nm, and detection accuracy of approximately 500 ps. Figure 5: Laser ranging of the Sentinel 3B satellite at a PRF of 100 kHz. Figure 6: Principle of the avalanche photodiode detector for DLR measurements. The laser echo and noise signal of the APD and SPAD detectors were compared for the laser tracking of satellites using the same system parameters. Table 1 shows that the APD detector outperforms the SPAD detector in terms of detection efficiency and noise signal. The APD detector is thus suitable for the detection of weak laser echo signals from debris targets. The superconducting nanowire single-photon detector (SNSPD) has become the most competitive detector among detectors developed in past decades. It has excellent performance, such as a wide spectral response range, ultra-high detection efficiency, extremely low dark count rate, and little time jitter. The SNSPD is expected to provide breakthroughs in space target detection capabilities and help to improve the search capabilities and acquisition speed for space targets. Since 2015, SHAO has cooperated with the Shanghai Institute of Microsystem and Information Technology to develop the first SNSPD for high-precision laser ranging [22]. This detector has a photosensitive surface diameter of 100 \(\upmu\)m, the detection efficiency was up to 60% with a bias current of 28 uA as shown in Figure 7b, the dark noise (DCR) was less than 10 Hz, and also the time jitter was 68 ps, as shown in Figure 7b. The laser echo signals received in the 200-\(\upmu\)m-diameter core of the fiber are focused on the SNSPD by an aspheric lens. A five-dimensional tunable fiber-coupled aspheric lens realizes the highly efficient coupling of light to the narrow 200-\(\upmu\)m-diameter core under the highly dynamic circumstances of the telescope. Figure 8 illustrates the experimental configuration of the efficient coupling and application of the SNSPD in laser ranging. SHAO applied the SNSPD detector to the centimeter-level-precision laser ranging of satellites and sub-decimeter-level-precision laser ranging of debris targets.