# Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite
###### Abstract  
Two-way Laser Time Transfer (TLTT) using the Ajisai satellite has been considered as a more accurate and stable time transfer technique than existing methods; TLTT requires the kHz laser pulses to decrease the systematic restrictions for TLTT realization. However, because of the low energy of the kHz laser pulses as well as the low cross section due to the small size of the Ajisai reflecting mirror, the link budget is an important issue to establish the TLTT link between two ground stations. In this study, the TLTT link budget is investigated to find the optimal laser pulse energy via analysis of geometric effects using 30 days of orbital data of the Ajisai satellite from 29 March 2021 within a ground network consisting of four stations located in three countries. The geometric configuration reduces the TLTT link budget by three orders of magnitude due to free space loss, atmospheric transmission, and effective cross section; then, the pulse energy is required to be much higher than laser ranging to the Ajisai satellite. It is shown from the simulation that a few tens of m] level of pulse energy at the transmitting station is quite enough for TLTT realization. two-way laser time transfer; Ajisai satellite; link budget; geometric configuration; detection probability +
Footnote †: journal: **Publisher’s Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. rigorous data processing, T2L2 showed the capability of time transfer with stability better than 1 picosecond over 1000 s and accuracy of 100 picoseconds [6]. Another approach for LTT is Two-way Laser Time Transfer (TLTT) using the reflective mirrors on satellites such as the Ajisai satellite. The Ajisai satellite is a Japanese geodetic satellite launched in 1986, which is covered with not only corner cube reflectors (CCRs) for laser ranging but also mirror panels for photometric observation. The Ajisai satellite has a long mission life, and its mirrors are made of an alloy of aluminum that has no lifetime limit [7]. The TLTT technique using the Ajisai's reflective mirrors as a two-way zero-delay optical transponder was proposed and initial analysis including configuration, calibration and link budget were provided by [PERSON] et al. [8]. As with the TWSTFT technique, each SLR station transmits a laser pulse to the other station using the reflective mirror on the Ajisai's satellite and measures the firing and arriving time of reflected pulse at both stations with the internal system delays to determine the time difference for the synchronization of atomic clocks with the accuracy of 10\({}^{-10}\)-10\({}^{-11}\) order. However, there are two critical issues to realize this concept using the Ajisai satellite. One is the limited hitting probability at the right time when employing the low repetition rate laser pulse in traditional SLR systems. The individual mirror of the Ajisai was designed to flash three times per rotation (-2 s) and the passage duration time of the reflected mirror, that is, the footprint passage time of the reflection beam of Ajisai's curved mirror at the receiving station, is 5 to 10 milliseconds. Therefore, the repetition rate of the laser pulse is required to be at least 200 Hz, which is a few tens of times faster than that of traditional systems, to hit the mirror at every footprint passage. Another issue is the weak strength of reflected signals due to the very small size of the Ajisai's reflective mirror, and the variation of the effective cross section resulting from the phase angle of the reflective mirror when dealing with signals from two ground stations. [PERSON] et al. [9] simulated the laser link via individual mirrors, based on the Ajisai's spin model, between the Matera (Italy) and Graz (Austria) SLR systems for TLTT, and the result showed an average signal strength of 3.46 photoelectrons at the received station (Graz) when the parameters of laser source (532 nm) at the transmitting station are the high energy level of 100 mJ and low repetition rate of 10 Hz.