# Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite

^{*}

## Abstract

**:**

## 1. Introduction

^{−10}~10

^{−11}order.

## 2. TLTT Link Budget

#### 2.1. Link Budget Equation for TLTT

^{2}[8]. Therefore, we need to take into account these two characteristics in the link budget equation to realize the TLTT technique using the Ajisai satellite.

#### 2.1.1. Free Space Loss and Atmospheric Effects for TLTT

#### 2.1.2. Effective Cross Section of Ajisai’s Mirror for TLTT

**N**) of the reflective convex mirror of the Ajisai satellite is coincident with the phase vector (

**P**), which is defined as the product of two vectors pointing to the transmitting (${R}_{t}$) and receiving (${R}_{r}$) ground stations with respect to the satellite, as shown in Figure 1.

#### 2.2. Minimum Required Laser Energy for TLTT

## 3. Simulation Results

#### 3.1. Simulation Parameters

#### 3.1.1. Characteristics of Ajisai for TLTT

^{2}at maximum and 8.35~8.70 m, respectively. These mirrors are placed in 14 rings on the surface of the Ajisai satellite with 2.15 m diameter; the latitude angle of each mirror on the 8.5 m radius sphere is maintained on the surface of Ajisai satellite to reduce the actual radius to 1.08 m. The allocation of convex mirrors on Ajisai was designed to provide solar reflection to the ground observer at 3 times per rotation period by installing three mirrors in the same ring to have an identical latitude angle [7,10]. The key satellite parameters used for TLTT simulation are listed in Table 1.

#### 3.1.2. Parameters of SLR Stations in the Target Network

#### 3.2. Results

#### 3.2.1. Effects of Geometric Configuration

^{2}during the simulation period, with phase angle of 0.83~40.02 degrees for the three geometric combination cases. In the simulation, the minimum value of the effective cross section is in the range of 93.9% to 99.9% when compared to the peak value in each configuration. The cross section has less influence on the laser link budget than does the geometric effect resulting from the free space loss and atmospheric transmission.

#### 3.2.2. Optimal Laser Energy

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Kirchner, D. Two-Way Time Transfer via Communication Satellites. Proc. IEEE
**1991**, 79, 983–990. [Google Scholar] [CrossRef] - Freelance, P.; Veillet, C. Operation and data analysis in the LASSO experiment. Metrologia
**1995**, 32, 27–33. [Google Scholar] [CrossRef] - Fridelance, P.; Samain, E.; Veillet, C. T2L2—Time Transfer by Laser Link: A New Optical Time Transfer Generation. Exp. Astron.
**1997**, 7, 191–207. [Google Scholar] [CrossRef] - Vrancken, P. Characterization of T2L2 (Time Transfer by Laser Link) on the Jason 2 Ocean Altimetry Satellite and Micrometric Laser Ranging. Ph.D. Thesis, Université de Nice, Sophia-Antipolis, Nice, France, 2008. [Google Scholar]
- Samain, E.; Weick, J.; Vrancken, P.; Para, F.; Albanese, D.; Paris, J.; Torre, J.-M.; Zhao, C.; Guillemot, P.; Petitbon, I. Time transfer by laser link—The T2L2 experiment on Jason-2 and further experiments. Int. J. Mod. Phys. D
**2008**, 17, 1043–1054. [Google Scholar] [CrossRef] [Green Version] - Samain, E.; Vrancken, P.; Guillemot, P.; Fridelance, P.; Exertier, P. Time transfer by laser link (T2L2): Characterization and calibration of the flight instrument. Metrologia
**2014**, 51, 503–515. [Google Scholar] [CrossRef] [Green Version] - Sasaki, M.; Hashimoto, H. Launch and Observation Program of the Experimental Geodetic Satellite of Japan. IEEE Trans. Geosci. Remote Sens.
**1987**, GE-25, 526–533. [Google Scholar] [CrossRef] - Kunimori, H.; Takahashi, F.; Itabe, T.; Yamamoto, A. Laser ranging application to time transfer using geodetic satellite and to other Japanese space programs. In Proceedings of the 8th international Workshop on Laser Ranging Instrumentation, Annapolis, MD, USA, 18–22 May 1992; pp. I-34–I-42. [Google Scholar]
- Kucharski, D.; Kirchner, G.; Otsubo, T.; Kunimori, H.; Jah, M.K.; Koidl, F.; Bennett, J.C.; Lim, H.; Wang, P.; Steindorfer, M.; et al. Hypertemporal photometric measurement of spaceborne mirrors specular reflectivity for Laser Time Transfer link model. Adv. Space Res.
**2019**, 64, 957–963. [Google Scholar] [CrossRef] - Otsubo, T.; Kunimori, H.; Gotoh, T. New Application for Khz Laser Ranging: Time Transfer Via Ajisai. In Proceedings of the 15th international Workshop on Laser Ranging, Canberra, Australia, 15–20 October 2006; pp. 420–424. [Google Scholar]
- Degnan, J.J. Millimeter Accuracy Satellite Laser Ranging: A Review. In Contributions of Space Geodesy to Geodynamics: Technology; Smith, D.E., Turcotte, D.L., Eds.; AGU: Washington, DC, USA, 1993; Volume 25, pp. 133–162. [Google Scholar]
- Lim, H.; Seo, Y.; Na, J.; Bang, S.; Lee, J.; Cho, J.; Park, J.H.; Park, J. Tracking Capability Analysis of ARGO-M Satellite Laser Ranging System for STSAT-2 and KOMPSAT-5. J. Astron. Space Sci.
**2010**, 27, 245–252. [Google Scholar] [CrossRef] [Green Version] - Kucharski, D.; Kirchner, G.; Otsubo, T.; Lim, H.; Bennett, J.; Koidl, F.; Kim, Y.; Hwang, J. Confirmation of gravitationally induced attitude drift of spinning satellite Ajisai with Graz high repetition rate SLR data. Adv. Space Res.
**2016**, 57, 983–990. [Google Scholar] [CrossRef] - Kucharski, D.; Kirchner, G.; Otsubo, T.; Koidl, F. The impact of solar irradiation on Ajisai’s spin period measured by the Graz 2 kHz SLR system. IEEE Trans. Geosci. Remote Sens.
**2010**, 48, 1629–1633. [Google Scholar] [CrossRef] - Hattori, A.; Otsubo, T. Time-varying solar radiation pressure on Ajisai in comparison with LAGEOS satellite. Adv. Space Res.
**2019**, 63, 63–72. [Google Scholar] [CrossRef] - Otsubo, T.; Amagai, J.; Kunimori, H.; Elphick, M. Spin motion of the Ajisai satellite derived from spectral analysis of laser ranging data. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 1417–1424. [Google Scholar] [CrossRef] - Kirchner, G.; Hausleitner, W.; Crisrea, E. Ajisai spin parameter determination using Graz kilohertz satellite laser ranging data. IEEE Trans. Geosci. Remote Sens.
**2007**, 45, 201–205. [Google Scholar] [CrossRef] - International Laser Ranging Service. Available online: https://ilrs.gsfc.nasa.gov/network/stations/index.html (accessed on 2 April 2021).
- Vallado, D.; Crawford, P. SGP4 Orbit Determination. In Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, Honolulu, HI, USA, 18-21 August 2008; p. AIAA-2008-6770. [Google Scholar] [CrossRef]
- CelesTrak: Current NORAD Two-Line Element Sets. Available online: https://www.celestrak.com/NORAD/elements (accessed on 29 March 2021).
- International Earth Rotation and Reference System Service. Available online: https://www.iers.org/IERS/EN/Science/EarthRotation/EOP.html (accessed on 29 March 2021).
- Zhang, Z.; Yang, F.; Zhang, H.; Wu, Z.; Chen, J.; Li, P.; Meng, W. The use of laser ranging to measure space debris. Res. Astron. Astrophys.
**2012**, 12, 212–218. [Google Scholar] [CrossRef] [Green Version] - Kirchner, G.; Koidl, F.; Friederich, F.; Buske, I.; Völker, U.; Riede, W. Laser measurements to space debris from Graz SLR station. Adv. Space Res.
**2013**, 51, 21–24. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Ajisai satellite (courtesy of JAXA) and (

**b**) phase angle model of Ajisai’s convex mirror.

**Figure 2.**Target ground network for TLTT implementation with three combination cases between laser transmitting station (Sejong) and receiving stations on the google maps.

**Figure 3.**Ratio of geometric term to peak value including free space loss, atmospheric attenuation and cirrus cloud transmission in TLTT link budget. (

**a**) Sejong−Geochang, (

**b**) Sejong−Beijing and (

**c**) Sejong−Koganei.

**Figure 4.**Ratio of geometric effects including free space loss and atmospheric transmission in TLTT link budget with respect to ordinary SLR observation. (

**a**) Sejong−Geochang, (

**b**) Sejong−Beijing and (

**c**) Sejong−Koganei.

**Figure 5.**Ratio of geometric term in TLTT link budget to peak value including free loss, atmospheric transmission and effective cross section in time domain. (

**a**) Sejong−Geochang and (

**b**) Sejong−Koganei.

**Figure 6.**Time series of (

**a**) detection probability and (

**b**) minimum laser energy corresponding to threshold of detection probability.

**Figure 7.**Number of TLTT paths and total TLTT passage times to enable TLTT link in terms of transmitting laser energy.

**Figure 9.**Ratio of detecting probability to threshold value for receiving one photoelectron from Ajisai’s reflective mirror in satellite elevation space. (

**a**) Sejong−Geochang, (

**b**) Sejong−Beijing and (

**c**) Sejong−Koganei.

Number of mirrors | 318 pieces |

Curvature of mirrors | 8.35~8.7 m (8.5 m for simulation) |

Reflectivity | 0.85~0.92 (0.85 for simulation) |

Duration of light flash | 5 msec |

Rate of flashing | 1.25 Hz (2 Hz at initial) |

Spin rate | 25 rpm (40 rpm at initial) |

**Table 2.**Parameters of 4 SLR stations in the target network [18].

Parameters | Sejong | Geochang | Beijing | Koganei | ||
---|---|---|---|---|---|---|

Laser | λ | Wavelength | 532 nm | 532 nm | 532 nm | 532 nm |

${E}_{t}$ | Pulse energy | 2.5 mJ | 15 mJ | 1 mJ | 50 mJ | |

Pulse width | 50 ps | 9.2 ps | 200 ps | 35 ps | ||

Repetition rate | 1 KHz | 60 Hz | 1 KHz | 20 Hz | ||

Telescope | ${a}_{t}$ | Tx Primary mirror | 0.1 m | 1.0 m | 0.16 m | 1.5 m |

${b}_{t}$ | Tx Secondary mirror | - | 0.25 m | - | ||

${\eta}_{t}$ | Transmit optic efficiency | 92.3% | 75% | 70% | 30% | |

${\theta}_{d}$ | Beam divergence angle | 5~200 arcsec | 8 arcsec | <103 arcsec | 5 arcsec | |

${\theta}_{p}$ | Beam pointing error | <5 arcsec | <4 arcsec | <5 arcsec | <5 arcsec | |

${a}_{r}$ | Rx Primary mirror | 0.4 m | 1.0 m | 0.60 m | 1.5 m | |

${b}_{r}$ | Rx Secondary mirror | 0.1 m | 0.25 m | - | - | |

${\eta}_{r}$ | Receiver optic efficiency | 64.9% | 35% | 70% | 10% | |

Detector | ${\eta}_{q}$ | Quantum efficiency | 20% | 20% | 20% | 15% |

Position | Longitude | 127.3029E | 127.9201E | 115.8920E | 139.489E | |

Latitude | 36.5210N | 35.5902N | 39.6069N | 35.710N | ||

${h}_{t}$ | Altitude | 176.415 m | 934.063 m | 82.300 m | 121.820 m |

**Table 3.**Number of TLTT paths and total TLTT passage times with respect to transmitting laser energy.

Laser Energy | Number of TLTT Paths | Total TLTT Passage Times (min) | ||||
---|---|---|---|---|---|---|

Geochang | Beijing | Koganei | Geochang | Beijing | Koganei | |

2.5 mJ | 0(0%) | 0(0%) | 0(0%) | 0 | 0 | 0 |

5.0 mJ | 48(47%) | 33(33%) | 15(16%) | 238.3 | 104.4 | 26.0 |

10.0 mJ | 61(60%) | 50(50%) | 34(36%) | 359.7 | 232.5 | 131.5 |

25.0 mJ | 86(84%) | 78(79%) | 51(54%) | 561.6 | 433.2 | 278.6 |

50.0 mJ | 96(94%) | 94(95%) | 65(68%) | 732.5 | 618.1 | 400.7 |

Observable | 102 | 99 | 95 | 1163.8 | 930.5 | 837.6 |

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**MDPI and ACS Style**

Park, J.U.; Lim, H.-C.; Sung, K.-P.; Choi, M.
Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite. *Remote Sens.* **2021**, *13*, 3739.
https://doi.org/10.3390/rs13183739

**AMA Style**

Park JU, Lim H-C, Sung K-P, Choi M.
Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite. *Remote Sensing*. 2021; 13(18):3739.
https://doi.org/10.3390/rs13183739

**Chicago/Turabian Style**

Park, Jong Uk, Hyung-Chul Lim, Ki-Pyoung Sung, and Mansoo Choi.
2021. "Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite" *Remote Sensing* 13, no. 18: 3739.
https://doi.org/10.3390/rs13183739