# High-Precision Single-Photon Laser Time Transfer with Temperature Drift Post-Compensation
## 2 Temperature Drift Experiment Setup  
The laser time transfer system is a process of laser-pulse detection and epoch recording both on board a satellite and at an on-the-ground station. Due to the effects listed above, we focused on the space segment of the system. The experiment system of space segment contains a laser, a single-photon avalanche detector (SPAD) and a timing system (see Figure 1). A short-pulsed semiconductor laser at 709 nm with a pulse width of 70 ps was used as the light source. It was triggered by a two-channel signal generator and synchronized with the gate signal to the SPAD. The gate signal is used to set the SPAD into its sensitive mode. The first detected signal of the SPAD will reset it as unsensitive again. The repetition rate of the entire experiment was set to 10 kHz. The laser beam was collimated by a telescope system composed of two lenses marked as L1 and L2. An aperture was placed at the focus of the two lenses for spatial filtering. After attenuation, the laser beam was coupled into a multi-mode fiber (2 m long) by a lens with a focal length of 50 mm. The fiber output was coupled to the SPAD active area. The number of incident photons could be adjusted consecutively by adjusting the continuous attenuator or changing the distance between the SPAD and the output head of the multi-mode fiber.  
In this experiment, the SPAD detector was operated in an active quenching and gating mode. A detection chip with a 25-\(\upmu\)m-diameter active area (K14 series) was used [16]. It was produced by Czech Technical University and has been used in the onboard LTT instrument on the Chinese Beidou Navigation system [2]. A single-shot precision of 150 ps was achieved with this application. Thanks to the high-speed comparator and faster Resistor-Capacitance (RC) circuit, with the same chip, our SPAD detector achieved a single-shot precision better than 30 ps. We set a bias voltage of 2 V above the SPAD's breakdown voltage to get a detection efficiency of approximately 30% at 709 nm. An event timer (ET) with a precision of 8 ps and resolution of 13 ps was used to record the propagation delay changes of the entire transfer chain. A multi-channel temperature recorder (TR) (NAPUI TR230X) based on thermocouple was used to record the temperature changes over time with a precision of 0.1 \({}^{\circ}\)C. A thermocouple was set on the bottom of the SPAD near the optical platform representing the room temperature. At first, two data sets were recorded simultaneously: propagation delay as a function of time (by ET) and temperature as a function of time (by TR). Then, all the collected data were processed. A curve of propagation delay as a function of temperature was obtained, the fitting equation was calculated and then the temperature compensation function was established. Finally, the variation of original propagation delay results was obtained using the compensation function.  
The laboratory temperature was changed to simulate the temperature variations in the space environment. The initial room temperature of 22 \({}^{\circ}\)C was slowly increased by 2-3 degrees per day, and data were collected for 7 days till 34 \({}^{\circ}\)C. In the data processing, we used a \"2.2 \(\times\) \(\sigma\)\" editing procedure to extract the useful signal [17]. Furthermore, we analyzed the whole system temperature drift and time stability in terms of TDEV. Usually, original data record length should be at least 3 times of the average time, which are used to analyze time stability [10]. Considering the actual measurement time and the upload transfer speed of ET in this test, we chose 10 kHz as the laser frequency and a 10% counting rate, which corresponds to an incident light intensity of 0.3 photon/pulse. This setup simulated the in-space operation.