Laser Time Transfer (LTT) is the one of the laser applications in space, which allows time synchronization between two remote clocks using a short laser pulse. This technique can provide the high-precision time transfer with accuracy of sub-nanosecond level that is required to enhance performance in astronomy, space geodesy, timekeeping systems and deep space exploration. LTT has been recognized as a more accurate and stable time synchronization technique than other time transfer methods using radio waves, such as the two-way satellite time and frequency transfer (TWSTFT) technique [1
] and GNSS common view observation.
Laser Synchronization from Stationary Orbit (LASSO) was the first experimental project in space for optical time transfer using an artificial satellite. The LASSO instruments package onboard the geostationary MeteoSat-3 satellite was designed to compare the time at two or more laser ranging sites using a one-way up-link laser pulse transmitted from the ground. In 1992, this experiment not only successfully performed inter-continental time transfer between McDonalds (Texas, USA) and Grasse (France) with an accuracy on the order of nanoseconds but also validated the feasibility of the LTT concept [2
The Time Transfer by Laser Link (T2L2) experiment is the follow-on mission to LASSO, and the T2L2 instrument was the one of experimental passengers on the Jason 2 mission, launched in June 2008 [3
]. The T2L2 payload records the arrival time of laser pulses from Satellite Laser Ranging (SLR) stations at the scale of the on-board oscillator and provides these data for time synchronization through post-processing with laser ranging data of the stations. The accuracy of the T2L2 instrument is essential to translate the raw information into time transfer data and to facilitate the calibration process. Through the 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 Kunimori 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
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. Daniel 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.
Even though there are some difficulties to realize this concept, it can provide a more accurate and stable time transfer compared to that of the T2L2 technique because there are no error sources, such as modeling error of onboard time comparison unit and the long-term variation of transponder delay. This approach has received considerable attention as a potential technology to allow very high-precision and accuracy of 100 picoseconds or even better.
The TLTT concept using the Ajisai satellite was re-formulated as a kilohertz (kHz) SLR application by Otsubo et al. [10
]. The high repetition rate of laser pulses based on kHz laser technology provides full capability for the laser pulse to hit the Ajisai’s reflective mirror at the right time, and the event timer at the kHz SLR station can record multiple stop events for TLTT; these were the key problems involved in the TLTT approach using the Ajisai satellite. However, the low signal strength of received photons at the receiving station is still a serious issue for real application.
In general, the repetition rate and the pulse energy of a laser system have a reciprocal relationship. This means that a high repetition rate usually decreases the pulse energy for a fixed average power. The low pulse energy of the kHz laser system makes the expected number of photons less than 1 photon/footprint passage of the Ajisai satellite. To overcome this restriction, several methods to improve system performance were proposed, which include (i) increasing the laser energy, (ii) enhancing the optical efficiency, and (iii) using a modified algorithm allowing a single signal transfer [10
For TLTT realization based on kHz laser technology, there are two critical elements (i.e., geometric configuration and laser pulse energy) to determine the signal strength of received photons. Therefore, the effects of geometric configuration are analyzed in this paper for the TLTT application in terms of the laser link budget, which plays a large role in the variation of the TLTT link budget. Additionally, an analytical approach to find the optimal laser energy for the kHz laser system is investigated based on the threshold of detection probability and the operation concept of the network for TLTT application.
The purpose of this paper is to investigate an analytical approach to finding the optimal laser energy of a transmitting station via analysis of the geometric effects on the TLTT link budget for TLTT implementation using the Ajisai satellite.
The minimum geometric terms of space loss, atmospheric attenuation and cirrus cloud cover in the TLTT link budget have values of 0.055%, 0.075% and 0.077%, respectively, when compared to the peak values of each combination. The peak values can be obtained when the slant range and zenith angle of receiving path are at minimum under the maximum zenith angle of the transmitting path. Another term affected by the geometric configuration is the effective cross section of the Ajisai’s convex mirror, which has a range of 93.9%~99.9% when compared to the peak value of effective cross section at the minimum phase angle of each combination. Consequently, the geometric effects reduce the TLTT link budget by three orders of magnitude when compared to the peak value of the TLTT link budget in the simulation; the cross section effect of the Ajisai’s convex mirror is relatively smaller than other geometric effects coming from free space loss and atmospheric degradation. The reduced value of TLTT link budget increases the required laser energy to receive one photoelectron by the same order at every epoch during the entire TLTT passage time, because the peak value of the TLTT link budget in the target network is close to the critical value for TLTT link establishment.
The chance of establishing a TLTT link can be determined as the ratio between the detection probability and the threshold value = 0.2 for 1 kHz repetition rate of laser pulse and the passage duration time of 5 msec. When employing the original value of laser energy = 2.5 mJ at Sejong SLR station, all the detection probabilities are less than the threshold ratio (i.e., . This means that there is no chance to establish the TLTT link and zero TLTT path in the target network during the simulation period. When the laser energy of the transmitting station increases to = 25 mJ, the ratio of the detection probability improves 3–5 times for each combination, which can be interpreted as the maximum number of photoelectrons to receive at each station; the TLTT paths also increase to 50% of total observable paths during the simulation period.
By increasing the laser energy of the transmitting station from 2.5 mJ to 50 mJ, the number of TLTT paths increases from 0% to 94.1% of the total observable paths; total TLTT passage times gradually increase from 0% to 66.4% of the total passage times for all observable paths in the period of 30 days with 20 degrees cut-off angle. Therefore, using these simulation data, the optimal laser energy of the transmitting station can be selected following the operational concept for TLTT implementation (i.e., frequency of TLTT paths and total TLTT passage times) in the target network.
It was demonstrated that a few tens of mJ level of laser pulse energy at the transmitting station is quite enough for TLTT realization in the target network, and that optimal laser energy can be selected through an analytical approach based on not only the operation concept of the TLTT network but also the threshold of detection probability.