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Hypertemporal photometric measurement of spaceborne mirrors specular reflectivity for Laser Time Transfer link model
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ScienceDirect Advances in Space Research 64 (2019) 957–963 www.elsevier.com/locate/asr
Hypertemporal photometric measurement of spaceborne mirrors specular reflectivity for Laser Time Transfer link model Daniel Kucharski a,b,⇑, Georg Kirchner c, Toshimichi Otsubo d, Hiroo Kunimori e, Moriba K. Jah b, Franz Koidl c, James C. Bennett f,a, Hyung-Chul Lim g, Peiyuan Wang c, Michael Steindorfer c, Krzysztof Sos´nica h a
Space Environment Research Centre, SERC, Canberra, Australia b The University of Texas at Austin, USA c Space Research Institute, Austrian Academy of Sciences, Graz, Austria d Hitotsubashi University, Tokyo, Japan e National Institute of Information and Communications Technology, Tokyo, Japan f EOS Space Systems Pty Ltd, Queanbeyan, Australia g Korea Astronomy and Space Science Institute, Daejeon, Republic of Korea h Wrocław University of Environmental and Life Sciences, Wrocław, Poland Received 27 March 2019; received in revised form 14 May 2019; accepted 16 May 2019 Available online 28 May 2019
Abstract The hypertemporal light curves of the sunlit Ajisai satellite allow for reflectivity measurement of the individual on-board mirror panels. The photon counting technology developed at Graz Satellite Laser Ranging (SLR) station makes it possible to distinguish between the solar flux diffused and specularly reflected off the spinning Ajisai. The flux intensities measured at 10 kHz sampling rate during the period from Oct. 2015 until Jan. 2018 are analyzed through the spacecraft micro-model link budget equation and indicate reflectivity of the 149 mirrors of between 82.3% and 88.2% with the mean value of 85.3% and the RMS of 1.2%. It is predicted that this high specular reflectivity of the satellite will allow for the establishment of a laser link between the distant ground locations with the individual mirrors acting as a zero-latency, passive optical relay. Simulations of the laser link between the Matera (Italy) and Graz (Austria) SLR systems via spaceborne mirror reflections indicate that such a channel can be operated at mean signal strength of 3.46 photoelectrons per laser pulse. The predicted mean number of the laser link intervals per pass is 874.6 with a mean interval duration of 9.15 ms. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Ajisai; Single photon counter; Hypertemporal photometry; Laser time transfer
1. Introduction 1.1. Laser Time Transfer via satellites The Laser Time Transfer (LTT) technique allows for synchronization of the remote, ultra-stable clocks based
⇑ Corresponding author.
E-mail address: [email protected] (D. Kucharski). https://doi.org/10.1016/j.asr.2019.05.030 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
on the exchange of laser pulses between the timing systems. The LTT employs the principles of Satellite Laser Ranging (SLR) that transmits short laser pulses to a satellite in an Earth orbit where a small portion of the laser energy is detected onboard the relay spacecraft and another portion is retro-reflected back to the ground receiver system for the high-precision epoch recording. The Time Transfer by Laser Link (T2L2) transponder onboard Jason-2 satellite (altitude of 1336 km) has been
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developed by Centre National d’Etudes Spatiales and Observatoire de la Coˆte d’Azur (Samain et al., 2008). The mission successfully operated from June 2008 until April 2018 and allowed for the time transfer between the remote SLR systems at the accuracy level below 100 ps (LaasBourez et al., 2015; Exertier et al., 2014; Samain et al., 2015). The ground-to-space and ground-to-ground clock synchronization experiments made it possible to characterize the behavior of the timing systems of the International Laser Ranging Service (ILRS) network (Pearlman et al., 2002). Exertier et al. (2017) used the T2L2 direct timing measurements for the time bias determination of 24 participating SLR systems with a ns accuracy and found that the time biases can evolve rapidly and randomly being correlated to the various events at the laser stations. It is worth mentioning that the time biases at the ls level lead to the mm-scale effects on the geodetic products (station positioning, precise orbit determination) (Exertier et al., 2017) thus the ILRS recommends the Laser Ranging stations to be synchronized at ±100 ns level with Coordinated Universal Time (UTC). The current generation of the LTT technology exploits the spaceborne transponders for the detection and time stamping of the incoming laser pulses. In this configuration the time synchronization between two ground stations involves the operation of three clocks that deliver triplets of timing variables consisting of the laser fire and the onboard detection epoch times as well as the time of flight of the laser pulse between the SLR station and the transponder. As a consequence the accuracy of the ground-to-ground time synchronization depends on the operator’s capability to calibrate and monitor the transponder’s internal delays and drifts (Samain et al., 2014). A significant improvement in the time transfer accuracy can be achieved by implementing the LTT concept proposed by Kunimori et al. (1992) and later reviewed by Otsubo et al. (2006) that envisages the exchange of ultrashort laser pulses between the ground clocks via specular reflections off the geodetic satellite Ajisai as if the onboard mirror array is a zero-delay, passive optical transponder. This scenario eliminates the space clock from the time transfer equation by establishing a direct, optical link between the remote ground timing systems. The improvement in the LTT accuracy would enhance performance of the existing reference systems in space geodesy (Schreiber and Kodet, 2018; Exertier et al., 2018), astronomy, space navigation and the fundamental physics by providing a global time-reference platform at the picosecond accuracy level of synchronization. 1.2. Attitude dynamics of Ajisai The geodetic satellite Ajisai (NORAD 16908) was launched on August 12, 1986 and the mission is operated by the Japan Aerospace Exploration Agency (JAXA). The satellite was launched into a quasi-circular orbit of
altitude 1490 km and inclination of 50° with the scientific objective defined to be the accurate position determination of fiducial points on the Japanese Islands (Hashimoto et al., 2012). More than 90% of the Ajisai spherical body (diameter of 2.15 m) is covered with the 120 reflector assembly panels that host 1436 corner cube reflectors (CCRs) for SLR and 318 mirrors for satellite direction and spin measurements (Sasaki and Hashimoto, 1987). SLR determines the distance between the ground stations and the satellites by measuring the time-of-flight of the laser pulses that are transmitted towards an orbiting target and retro-reflected back to the ground detection system. The range measurements to the geodetic satellites are used for precise orbit determination, the study of tectonic plate motion, Earth orientation and rotation parameters, as well as determination of the gravity field and the geocenter position (Moore and Wang, 2003; Pearlman et al., 2019; Sengoku, 1998). The convex mirrors of Ajisai are curved at a radius of 8.55 m (±0.15 m) and have a surface area of up to 393 cm2 each. The external aluminum surface is coated with a silicon oxide protective layer that maintains the high reflective efficiency. The mirrors are arranged in the form of 14 rings and their body-fixed orientation is such that the ground observer can detect on average 3-to6 solar reflections per satellite rotation during the sunlit, night-time passes, and only one flash at a time. Ajisai has been launched with an initial spin rate of 40 rpm that stabilizes its inertial orientation. The spin parameters, however, change slowly over time due to the external forces and torques caused mainly by the Earth’s gravitational and magnetic fields and solar irradiation. Long-term analysis reveals that the spin energy of Ajisai dissipates exponentially at a very low rate such that the spin period (currently 2.4 s) doubles every 46.6 years (Otsubo et al., 2000; Kirchner et al., 2007). Additionally, the de-spin rate depends on the amount of solar energy received by the satellite during an orbital revolution (Kucharski et al., 2010). The spin axis remains in the vicinity of the south celestial pole near the coordinates of RA = 88.9°, Dec = 88.85° (J2000) and experiences precession and nutation with the periods of 35.6 years and 116.5 days respectively due to the Earth’s gravity acting on the dynamical oblateness of the satellite (Kucharski et al., 2016).
2. Optical link via spaceborne mirror 2.1. Solar link budget Solar energy reflected off the spinning Ajisai towards the Earth propagates through the atmospheric layers where it attenuates due to absorption by ozone, water vapor, and carbon dioxide as well as being scattered by air molecules, water and dust particles. A ground tracking telescope located within the reflection footprint can collect a fraction of the flash energy and measure the intensity of the
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incoming solar flux Uq (photoelectron counts per second) predicted by: Uq ¼ GR gR
k1 X
gq ðkÞUS ðkÞAD gD gA ðkÞ
ð1Þ
k¼k0
where the photodetector response is integrated over the spectral bandwidth from k0 to k1 at Dk ¼ 1 nm steps with the wavelength dependent quantum efficiency gq ðkÞ. The effective aperture area of the detection telescope is AD ¼ pa2 1 b2 =a2 with a and b being the radii of the primary and secondary mirrors and gD - the overall efficiency of the detection system. The intensity of the solar flux arriving at the satellite (before reflection) at wavelength k is: 2 k R0 US ðkÞ ¼ EðkÞDk ð2Þ hc R1 where h is Planck’s constant, c is the velocity of light in vacuum. The extraterrestrial solar spectral irradiance EðkÞ defined by the reference profile ASTM G173-03 (Fig. 1) is given at the distance of R0 ¼ 1 AU and has to be scaled to the actual Sun - satellite distance R1 according to the inverse-square law. The incident photon flux interacts with the surface elements of the satellite such that a fraction of the flux is absorbed, specularly reflected, and diffused with the corresponding coefficients related through the equation a þ q þ d ¼ 1. The specular reflection from a convex mirror occurs at the efficiency of gR ¼ qM with the on-axis reflector gain defined as a ratio of the mirror XM and reflection footprint XF solid angles: GR ¼ GM;q ¼
XM XF
ð3Þ
The diffuse reflection occurs at the efficiency gR of dM and dP for the mirrors ðM Þ and CCR panels ðP Þ respectively, with the total gain of the Lambertian diffusion being the integrated optical response of the n exposed surface elements of solid angle X: GR ¼ Gd ¼
n X Xi cos bi cos ci p i¼1
ð4Þ
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The incident angles between the surface element normal vector and the directions to the Sun and the ground observer are represented by b and c respectively and must be lower than 90° in order for the element to contribute to the observed reflection. The wavelength dependent atmospheric transmittance gA over the satellite - station slant range can be defined as: ht gA ðk; V ; ht Þ ¼ exp ratm ðk; V Þhscale sechzen exp hscale ð5Þ where ratm ðk; V Þ is the sea level atmospheric attenuation coefficient at wavelength k and visibility V (Weichel, 1990), ht is the altitude of the ground telescope above sea level, hscale ¼ 1:2 km is a scale height, and hzen is the zenith angle of the satellite. 2.2. Laser link budget A laser link between the ground tracking systems realized via specular reflection off an Ajisai mirror can be modeled by the uplink and downlink budget equations. The transmitted laser pulse energy at the satellite ES is given by (Degnan, 1993): E S ¼ E P gT
GT gAT 4pR2T
ð6Þ
where EP is the laser pulse energy, gT is the transmit optics efficiency and gAT is the atmospheric transmittance over the slant range RT from the ground system to the satellite. The transmitter gain GT of the pulsed laser that produces quasigaussian spatial and temporal profiles is defined by the expression: " # 2 8 hP GT ¼ 2 exp 2 ð7Þ hT hT where hT is the far field divergence half-angle between the beam center and the 1=e2 intensity point and hP is the beam pointing error. The mean number of photoelectrons npe per laser pulse recorded by the ground detection system is given by the downlink equation: k npe ¼ gq ES ð8Þ GM;q qM AD gD gAD hc where gq is the quantum efficiency of the receiver detector at the laser wavelength k and gAD is the atmospheric transmittance over the reflection path. 3. Hypertemporal photometry 3.1. Ajisai light curves
Fig. 1. The solar spectral irradiance (at 1 nm step), atmospheric transmittance at the zenith, and the s-SPAD FAST photodetector quantum efficiency at wavelengths of 780–900 nm.
The Graz SLR station (Austria) operates multiple optical techniques for satellite observations. The high repetition rate 532-nm laser system allows for mm-accuracy range measurements to satellites and space debris equipped
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with CCRs, while the high power laser is used for ranging to the non-cooperative objects. The complex photon counting system developed for the quantum communication experiments (Liao et al., 2018) is also used to measure light curves of sunlit satellites at wavelengths from 780 nm to 900 nm. The incoming solar photons are detected by the Single-Photon Avalanche Diode (s-SPAD FAST) and converted into an electronic signal that is processed and time stamped in UTC by the Field Programmable Gate Array (FPGA). The acquired data is then converted into a light curve at a 10 kHz sampling rate for further analysis. A short sample of Ajisai light curve is presented in Fig. 2: the low-intensity flux Ud is recorded when only diffusely reflected light arrives at the telescope, while the highintensity flux Uflash consists of a specular glint of sunlight from a single mirror element towards the ground station. The rising and falling edges of the mirror reflection define the timing boundaries of the flash with the central plateau corresponding to the situation when the detection system remains within the ground footprint of the solar reflection. The central epoch time of the flash is determined with the time-derivative of the recorder flux intensity and occurs when the negative slope of the trend crosses the zero level. The observed brightness of Ajisai is a function of multiple variables including the reflective properties of the satellite surface elements but also the parameters of the photon counting system. The observed photon count rate UObs is obtained by correcting the recorded flux URec for the system pulse-pair resolution t ¼ 1 ls (the time it takes for a single event to be processed, time stamped and recorded) and the noise constant of e which consists of the detector dark noise and the site ambient light pollution: UObs ¼
URec e 1 URec t
3.2. Satellite model The light curve analysis is performed with the satellite simulation model where the position and orientation of the surface elements are expressed in a right-handed Cartesian, satellite-centered and -fixed Body Coordinate System (BCS) with the þZ BCS axis pointing towards the top of the sphere and the X BCS and Y BCS defining the body’s equatorial plane. The conversion of a satellite-centered vector r from the Inertial Coordinate System, ICS (J2000) to the satellite-fixed BCS rBCS ¼ RrICS can be realized with the transformation matrix R defined as: p p ð10Þ R ¼ R2 ðxP ÞR1 ðy P ÞR3 ðcÞR1 d R3 þ a 2 2 where R1 , R2 and R3 are the standard rotation matrices about the x, y and z-axis respectively, in a right-handed Cartesian coordinate system. The satellite inertial orientation is represented by right ascension a and declination d, while c is the body rotational angle about the spin axis. The pole coordinates xP and y P describe the relative position of the spin axis with respect to the satellite body axis þZ BCS and can be neglected here due to the fact that the Ajisai passive nutation damper minimizes the pole deviation to a level better than 0.1°. The phase angle p between the satellite centered vectors towards the light source S and the ground telescope T is SþT bisected by the phase vector P ¼ jSþT as presented in j Fig. 3. The inclination angle i ¼ arccosðP N Þ between the phase vector P and the central normal N of the convex mirror (Fig. 3b) must be lower than the angular size of the mirror in order for specular reflection towards the ground telescope T to occur.
ð9Þ 3.3. Specular and diffuse reflection flux During an example pass of Ajisai observed by Graz on April 4, 2016, 540 pairs of strong flashes Uflash (5–8 ms in duration) and the preceding diffuse reflection Ud
Fig. 2. A short sample of Ajisai light curve. (a) The low-intensity flux Ud is produced by diffused reflection off the satellite surface while the strong flux Uflash represents a solar glint from a mirror panel. (b) The central epoch of the flash is determined by the time derivative of the recorded flux intensity.
Fig. 3. The satellite model. The X ; Y ; Z axes represent Body Coordinate System BCS. (a) S: vector towards the Sun, T: vector towards the ground observing telescope, P: phase vector, p: phase angle. (b) The significant vectors in relation to the central normal ðN Þ of the convex mirror; the phase ðpÞ and the inclination ðiÞ angles are indicated.
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(10 ms bin) have been identified as explained in Fig. 2. Since more than 90% of the satellite surface is covered with the mirrors (M) and CCR panels (P ) it is assumed that only reflections from those elements contribute to the observed signal, such that the intensity of the Ajisai diffuse flux is Ud ¼ UM;d þ UP ;d and the intensity of the mirror specular reflection is UM;q ¼ Uflash Ud . The selected diffuse and specular signal pairs occur within a very short time interval of 30 ms (300 photometric samples) during which the detection system properties, the atmospheric transmission, and the diffuse reflectivity of the satellite are assumed to remain stable. The comparison of the observed flux intensities (a mean flux value per time bin) with the link budget predictions is presented in Fig. 4; the generally good agreement between the observed and predicted trends might well be disturbed by the locally inaccurate representation of the atmospheric transmission that can be azimuth-dependent (higher dust concentration in the city direction, higher water vapor at the forest side, scattered clouds for examples). Within the short time slot of 30 ms, the ratio of the observed flux intensities W ¼ Ud =UM;q is proportional to the ratio of the realized reflection gains W ¼ ðGM;d dM þ GP ;d dP Þ=GM;q qM and allows for the mirror specular reflectivity coefficient qM to be obtained from: qM ¼
GM;d ð1 aM Þ þ GP ;d dP GM;d þ GM;q W
ð11Þ
where the mirror absorptivity is aM ¼ 0:04 and the CCR panel diffusion coefficient is dP ¼ 0:80. We have collected hypertemporal light curves of Ajisai during the period from Oct. 2015 until Jan. 2018 and selected the good quality, continuous passes for the mirror reflectivity analysis. Fig. 5a presents the solar flash statistics of 149 observed mirrors grouped by the ring they form on the array: C0 - is the central (equatorial) ring of the
Fig. 4. Ajisai photometric pass measured on April 4, 2016. (a) Observed and simulated flux intensities: specular UM;q and diffuse Ud . (b) The configuration of the angles during the pass.
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Fig. 5. The observation statistics for the selected 149 mirrors located on the rings: D1 (the first ring below the body’s equator), C0 (central ring), U1 - U6 (the upper rings). (a) The number of solar flashes collected. (b) The determined specular coefficient of the mirrors.
satellite body, D1 - the first ring down from the body equator, U1 to U6: the upper rings. The stable orientation of Ajisai in inertial space determines that the rings C0, U1, and U2 will cause most flashing towards the terrestrial latitude of the Graz SLR station. The specular coefficient of the observed mirrors is determined and varies from 82.3% to 88.2% (mean 85.3%, RMS 1.2%) (Fig. 5b). 4. Laser link via individual mirrors of Ajisai In order to predict the efficiency of the laser link via Ajisai mirrors, we have selected two SLR systems from Matera (Italy) and Graz (Austria) as transmitter and receiver stations (Table 1) with a distance of 719 km between the locations. The laser link simulation covers the full year of 2019 with the satellite position predicted by the SGP4 propagator and the mirror inertial attitude given by the Ajisai spin models (Kucharski et al., 2010, 2016). The phase vector P for the laser link is defined as a product of two satellite centered vectors pointing towards the transmitting T and the detecting D ground systems: TþD P ¼ jTþD . The common view (CV) situation occurs when j the inclination angle i (Fig. 3b) is smaller than the angular size of the convex mirror and allows for a transmitted laser pulse to be specularly reflected in the direction of the detection system. In the simulation scenario, it is assumed that the fire time of the transmitted laser pulses (EP = 100 mJ, k = 532 nm, hT = 500 ) is synchronized with the predicted epoch time of the CV events and only one laser pulse per CV interval is fired. The clear atmosphere model is used with the sea level visibility of V ¼ 15 km and no cirrus clouds present. The mirror reflection efficiency is qM ¼ 0:85, and the quantum efficiency of the receiving Graz C-SPAD detector is gq ¼ 0:2. A total of 716 night passes have been identified with the satellite simultaneously observed by the Matera and Graz SLR systems at the one way atmospheric transmission gA varying from 0.54 to 0.81 (mean 0.71). The predicted mean
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Table 1 Transmitting and receiving system parameters. Name
Matera SLR, transmitter
Graz SLR, receiver
Agency DOMES number Latitude Longitude Elevation,ht Minimum satellite tracking elevation angle above the local horizon Transmit laser parameters
Italian Space Agency, ASI 12734S008 40.6486° N 16.7046° E 537 m 20° EP ¼ 100 mJ k ¼ 532 nm hT ¼ 5 arcsec 3 arcsec gT ¼ 0:6 –
Austrian Academy of Sciences 11001S002 47.0678° N 15.4942° E 495 m 20° –
Pointing error, hP Optics efficiency Effective area of the telescope receive aperture, AD
number of the CV intervals per pass is 874.6 with a mean interval duration of 9.15 ms. The laser link budget statistics per CV interval in relation to the satellite elevation angle above the local horizon is presented in Fig. 6 and indicates that the link between the distant SLR systems via Ajisai reflections can be established at an average signal strength of npe ¼ 3:46 photoelectrons per CV interval (Fig. 6b). The longest CV intervals up to 15.6 ms - can occur when Ajisai is observed by Graz at elevation angles between 60° and 80° and the phase vector P remains on the mirrors from the ring U6. The investigated laser link scenario is not limited to the SLR systems operating at the 100 mJ energy levels. The transmitted laser energy per pulse can be lowered if the other components of the link budget equation are properly adjusted in order to keep the strength of the received signal at the detectable levels. The LTT via spaceborne mirrors is the common view mode concept and the necessity for the strict geometrical configuration between the space mirror and the ground stations makes it difficult to execute. Even though the Ajisai spin models provide highly accurate spin axis and rate predictions, the rotational phase of the satellite (and thus the occurrence of the CV intervals) is nearly impossible to predict at the sub-degree level on the pass-to-
3 arcsec gD ¼ 0:5 0:1826 m2
pass basis due to the thermal nano-torques that perturb the spin dynamics along the orbit. A promising solution to this problem that we propose for further investigation is a software algorithm that operates in the background of the kHz SLR system and performs a near real-time analysis of the high rate laser range data for the satellite spin determination. After the rotational phase of Ajisai is found (<1 min procedure) the UTC epochs of the CV intervals for the remaining arc of the pass can be predicted and distributed via the Internet in order to update the laser pulse transmit times and the gating of the detection system so that the laser link between the SLR stations can be technically established. 5. Conclusions The accurate attitude models of Ajisai allow for the hypertemporal light curves to be processed in the way that characterizes the reflective properties of the spaceborne spinning mirrors. The link budget analysis of the diffused and specularly reflected solar flux gives the mirror mean reflectivity coefficient of qM ¼ 85:3%, and indicates no significant decrease of the surface reflective quality despite the long duration of the mission. The measured optical properties of Ajisai surface elements can improve the determination of the satellite solar radiation pressure coefficient as demonstrated by Hattori and Otsubo (2019). The simulation study indicates that the CV intervals between the distant SLR systems occur frequently and can be used to establish an LTT link via individual mirrors of Ajisai at an average signal strength of 3.46 photoelectrons per laser pulse on the basis of the SLR system parameters at Matera and Graz. Acknowledgements
Fig. 6. The CV statistics of the laser link budget simulation with respect to the satellite elevation angle above the local horizon of the transmitting (Matera) and receiving (Graz) systems. (a) CV interval duration. (b) The mean number of photons recorded at the receiving station.
This research is supported by the Cooperative Research Centre for Space Environment Management, SERC Limited, through the Australian Government’s Cooperative Research Centre Programme.
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ScienceDirect Advances in Space Research 64 (2019) 957–963 www.elsevier.com/locate/asr
Hypertemporal photometric measurement of spaceborne mirrors specular reflectivity for Laser Time Transfer link model Daniel Kucharski a,b,⇑, Georg Kirchner c, Toshimichi Otsubo d, Hiroo Kunimori e, Moriba K. Jah b, Franz Koidl c, James C. Bennett f,a, Hyung-Chul Lim g, Peiyuan Wang c, Michael Steindorfer c, Krzysztof Sos´nica h a
Space Environment Research Centre, SERC, Canberra, Australia b The University of Texas at Austin, USA c Space Research Institute, Austrian Academy of Sciences, Graz, Austria d Hitotsubashi University, Tokyo, Japan e National Institute of Information and Communications Technology, Tokyo, Japan f EOS Space Systems Pty Ltd, Queanbeyan, Australia g Korea Astronomy and Space Science Institute, Daejeon, Republic of Korea h Wrocław University of Environmental and Life Sciences, Wrocław, Poland Received 27 March 2019; received in revised form 14 May 2019; accepted 16 May 2019 Available online 28 May 2019
Abstract The hypertemporal light curves of the sunlit Ajisai satellite allow for reflectivity measurement of the individual on-board mirror panels. The photon counting technology developed at Graz Satellite Laser Ranging (SLR) station makes it possible to distinguish between the solar flux diffused and specularly reflected off the spinning Ajisai. The flux intensities measured at 10 kHz sampling rate during the period from Oct. 2015 until Jan. 2018 are analyzed through the spacecraft micro-model link budget equation and indicate reflectivity of the 149 mirrors of between 82.3% and 88.2% with the mean value of 85.3% and the RMS of 1.2%. It is predicted that this high specular reflectivity of the satellite will allow for the establishment of a laser link between the distant ground locations with the individual mirrors acting as a zero-latency, passive optical relay. Simulations of the laser link between the Matera (Italy) and Graz (Austria) SLR systems via spaceborne mirror reflections indicate that such a channel can be operated at mean signal strength of 3.46 photoelectrons per laser pulse. The predicted mean number of the laser link intervals per pass is 874.6 with a mean interval duration of 9.15 ms. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Ajisai; Single photon counter; Hypertemporal photometry; Laser time transfer
1. Introduction 1.1. Laser Time Transfer via satellites The Laser Time Transfer (LTT) technique allows for synchronization of the remote, ultra-stable clocks based
⇑ Corresponding author.
E-mail address: [email protected] (D. Kucharski). https://doi.org/10.1016/j.asr.2019.05.030 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
on the exchange of laser pulses between the timing systems. The LTT employs the principles of Satellite Laser Ranging (SLR) that transmits short laser pulses to a satellite in an Earth orbit where a small portion of the laser energy is detected onboard the relay spacecraft and another portion is retro-reflected back to the ground receiver system for the high-precision epoch recording. The Time Transfer by Laser Link (T2L2) transponder onboard Jason-2 satellite (altitude of 1336 km) has been
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developed by Centre National d’Etudes Spatiales and Observatoire de la Coˆte d’Azur (Samain et al., 2008). The mission successfully operated from June 2008 until April 2018 and allowed for the time transfer between the remote SLR systems at the accuracy level below 100 ps (LaasBourez et al., 2015; Exertier et al., 2014; Samain et al., 2015). The ground-to-space and ground-to-ground clock synchronization experiments made it possible to characterize the behavior of the timing systems of the International Laser Ranging Service (ILRS) network (Pearlman et al., 2002). Exertier et al. (2017) used the T2L2 direct timing measurements for the time bias determination of 24 participating SLR systems with a ns accuracy and found that the time biases can evolve rapidly and randomly being correlated to the various events at the laser stations. It is worth mentioning that the time biases at the ls level lead to the mm-scale effects on the geodetic products (station positioning, precise orbit determination) (Exertier et al., 2017) thus the ILRS recommends the Laser Ranging stations to be synchronized at ±100 ns level with Coordinated Universal Time (UTC). The current generation of the LTT technology exploits the spaceborne transponders for the detection and time stamping of the incoming laser pulses. In this configuration the time synchronization between two ground stations involves the operation of three clocks that deliver triplets of timing variables consisting of the laser fire and the onboard detection epoch times as well as the time of flight of the laser pulse between the SLR station and the transponder. As a consequence the accuracy of the ground-to-ground time synchronization depends on the operator’s capability to calibrate and monitor the transponder’s internal delays and drifts (Samain et al., 2014). A significant improvement in the time transfer accuracy can be achieved by implementing the LTT concept proposed by Kunimori et al. (1992) and later reviewed by Otsubo et al. (2006) that envisages the exchange of ultrashort laser pulses between the ground clocks via specular reflections off the geodetic satellite Ajisai as if the onboard mirror array is a zero-delay, passive optical transponder. This scenario eliminates the space clock from the time transfer equation by establishing a direct, optical link between the remote ground timing systems. The improvement in the LTT accuracy would enhance performance of the existing reference systems in space geodesy (Schreiber and Kodet, 2018; Exertier et al., 2018), astronomy, space navigation and the fundamental physics by providing a global time-reference platform at the picosecond accuracy level of synchronization. 1.2. Attitude dynamics of Ajisai The geodetic satellite Ajisai (NORAD 16908) was launched on August 12, 1986 and the mission is operated by the Japan Aerospace Exploration Agency (JAXA). The satellite was launched into a quasi-circular orbit of
altitude 1490 km and inclination of 50° with the scientific objective defined to be the accurate position determination of fiducial points on the Japanese Islands (Hashimoto et al., 2012). More than 90% of the Ajisai spherical body (diameter of 2.15 m) is covered with the 120 reflector assembly panels that host 1436 corner cube reflectors (CCRs) for SLR and 318 mirrors for satellite direction and spin measurements (Sasaki and Hashimoto, 1987). SLR determines the distance between the ground stations and the satellites by measuring the time-of-flight of the laser pulses that are transmitted towards an orbiting target and retro-reflected back to the ground detection system. The range measurements to the geodetic satellites are used for precise orbit determination, the study of tectonic plate motion, Earth orientation and rotation parameters, as well as determination of the gravity field and the geocenter position (Moore and Wang, 2003; Pearlman et al., 2019; Sengoku, 1998). The convex mirrors of Ajisai are curved at a radius of 8.55 m (±0.15 m) and have a surface area of up to 393 cm2 each. The external aluminum surface is coated with a silicon oxide protective layer that maintains the high reflective efficiency. The mirrors are arranged in the form of 14 rings and their body-fixed orientation is such that the ground observer can detect on average 3-to6 solar reflections per satellite rotation during the sunlit, night-time passes, and only one flash at a time. Ajisai has been launched with an initial spin rate of 40 rpm that stabilizes its inertial orientation. The spin parameters, however, change slowly over time due to the external forces and torques caused mainly by the Earth’s gravitational and magnetic fields and solar irradiation. Long-term analysis reveals that the spin energy of Ajisai dissipates exponentially at a very low rate such that the spin period (currently 2.4 s) doubles every 46.6 years (Otsubo et al., 2000; Kirchner et al., 2007). Additionally, the de-spin rate depends on the amount of solar energy received by the satellite during an orbital revolution (Kucharski et al., 2010). The spin axis remains in the vicinity of the south celestial pole near the coordinates of RA = 88.9°, Dec = 88.85° (J2000) and experiences precession and nutation with the periods of 35.6 years and 116.5 days respectively due to the Earth’s gravity acting on the dynamical oblateness of the satellite (Kucharski et al., 2016).
2. Optical link via spaceborne mirror 2.1. Solar link budget Solar energy reflected off the spinning Ajisai towards the Earth propagates through the atmospheric layers where it attenuates due to absorption by ozone, water vapor, and carbon dioxide as well as being scattered by air molecules, water and dust particles. A ground tracking telescope located within the reflection footprint can collect a fraction of the flash energy and measure the intensity of the
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incoming solar flux Uq (photoelectron counts per second) predicted by: Uq ¼ GR gR
k1 X
gq ðkÞUS ðkÞAD gD gA ðkÞ
ð1Þ
k¼k0
where the photodetector response is integrated over the spectral bandwidth from k0 to k1 at Dk ¼ 1 nm steps with the wavelength dependent quantum efficiency gq ðkÞ. The effective aperture area of the detection telescope is AD ¼ pa2 1 b2 =a2 with a and b being the radii of the primary and secondary mirrors and gD - the overall efficiency of the detection system. The intensity of the solar flux arriving at the satellite (before reflection) at wavelength k is: 2 k R0 US ðkÞ ¼ EðkÞDk ð2Þ hc R1 where h is Planck’s constant, c is the velocity of light in vacuum. The extraterrestrial solar spectral irradiance EðkÞ defined by the reference profile ASTM G173-03 (Fig. 1) is given at the distance of R0 ¼ 1 AU and has to be scaled to the actual Sun - satellite distance R1 according to the inverse-square law. The incident photon flux interacts with the surface elements of the satellite such that a fraction of the flux is absorbed, specularly reflected, and diffused with the corresponding coefficients related through the equation a þ q þ d ¼ 1. The specular reflection from a convex mirror occurs at the efficiency of gR ¼ qM with the on-axis reflector gain defined as a ratio of the mirror XM and reflection footprint XF solid angles: GR ¼ GM;q ¼
XM XF
ð3Þ
The diffuse reflection occurs at the efficiency gR of dM and dP for the mirrors ðM Þ and CCR panels ðP Þ respectively, with the total gain of the Lambertian diffusion being the integrated optical response of the n exposed surface elements of solid angle X: GR ¼ Gd ¼
n X Xi cos bi cos ci p i¼1
ð4Þ
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The incident angles between the surface element normal vector and the directions to the Sun and the ground observer are represented by b and c respectively and must be lower than 90° in order for the element to contribute to the observed reflection. The wavelength dependent atmospheric transmittance gA over the satellite - station slant range can be defined as: ht gA ðk; V ; ht Þ ¼ exp ratm ðk; V Þhscale sechzen exp hscale ð5Þ where ratm ðk; V Þ is the sea level atmospheric attenuation coefficient at wavelength k and visibility V (Weichel, 1990), ht is the altitude of the ground telescope above sea level, hscale ¼ 1:2 km is a scale height, and hzen is the zenith angle of the satellite. 2.2. Laser link budget A laser link between the ground tracking systems realized via specular reflection off an Ajisai mirror can be modeled by the uplink and downlink budget equations. The transmitted laser pulse energy at the satellite ES is given by (Degnan, 1993): E S ¼ E P gT
GT gAT 4pR2T
ð6Þ
where EP is the laser pulse energy, gT is the transmit optics efficiency and gAT is the atmospheric transmittance over the slant range RT from the ground system to the satellite. The transmitter gain GT of the pulsed laser that produces quasigaussian spatial and temporal profiles is defined by the expression: " # 2 8 hP GT ¼ 2 exp 2 ð7Þ hT hT where hT is the far field divergence half-angle between the beam center and the 1=e2 intensity point and hP is the beam pointing error. The mean number of photoelectrons npe per laser pulse recorded by the ground detection system is given by the downlink equation: k npe ¼ gq ES ð8Þ GM;q qM AD gD gAD hc where gq is the quantum efficiency of the receiver detector at the laser wavelength k and gAD is the atmospheric transmittance over the reflection path. 3. Hypertemporal photometry 3.1. Ajisai light curves
Fig. 1. The solar spectral irradiance (at 1 nm step), atmospheric transmittance at the zenith, and the s-SPAD FAST photodetector quantum efficiency at wavelengths of 780–900 nm.
The Graz SLR station (Austria) operates multiple optical techniques for satellite observations. The high repetition rate 532-nm laser system allows for mm-accuracy range measurements to satellites and space debris equipped
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with CCRs, while the high power laser is used for ranging to the non-cooperative objects. The complex photon counting system developed for the quantum communication experiments (Liao et al., 2018) is also used to measure light curves of sunlit satellites at wavelengths from 780 nm to 900 nm. The incoming solar photons are detected by the Single-Photon Avalanche Diode (s-SPAD FAST) and converted into an electronic signal that is processed and time stamped in UTC by the Field Programmable Gate Array (FPGA). The acquired data is then converted into a light curve at a 10 kHz sampling rate for further analysis. A short sample of Ajisai light curve is presented in Fig. 2: the low-intensity flux Ud is recorded when only diffusely reflected light arrives at the telescope, while the highintensity flux Uflash consists of a specular glint of sunlight from a single mirror element towards the ground station. The rising and falling edges of the mirror reflection define the timing boundaries of the flash with the central plateau corresponding to the situation when the detection system remains within the ground footprint of the solar reflection. The central epoch time of the flash is determined with the time-derivative of the recorder flux intensity and occurs when the negative slope of the trend crosses the zero level. The observed brightness of Ajisai is a function of multiple variables including the reflective properties of the satellite surface elements but also the parameters of the photon counting system. The observed photon count rate UObs is obtained by correcting the recorded flux URec for the system pulse-pair resolution t ¼ 1 ls (the time it takes for a single event to be processed, time stamped and recorded) and the noise constant of e which consists of the detector dark noise and the site ambient light pollution: UObs ¼
URec e 1 URec t
3.2. Satellite model The light curve analysis is performed with the satellite simulation model where the position and orientation of the surface elements are expressed in a right-handed Cartesian, satellite-centered and -fixed Body Coordinate System (BCS) with the þZ BCS axis pointing towards the top of the sphere and the X BCS and Y BCS defining the body’s equatorial plane. The conversion of a satellite-centered vector r from the Inertial Coordinate System, ICS (J2000) to the satellite-fixed BCS rBCS ¼ RrICS can be realized with the transformation matrix R defined as: p p ð10Þ R ¼ R2 ðxP ÞR1 ðy P ÞR3 ðcÞR1 d R3 þ a 2 2 where R1 , R2 and R3 are the standard rotation matrices about the x, y and z-axis respectively, in a right-handed Cartesian coordinate system. The satellite inertial orientation is represented by right ascension a and declination d, while c is the body rotational angle about the spin axis. The pole coordinates xP and y P describe the relative position of the spin axis with respect to the satellite body axis þZ BCS and can be neglected here due to the fact that the Ajisai passive nutation damper minimizes the pole deviation to a level better than 0.1°. The phase angle p between the satellite centered vectors towards the light source S and the ground telescope T is SþT bisected by the phase vector P ¼ jSþT as presented in j Fig. 3. The inclination angle i ¼ arccosðP N Þ between the phase vector P and the central normal N of the convex mirror (Fig. 3b) must be lower than the angular size of the mirror in order for specular reflection towards the ground telescope T to occur.
ð9Þ 3.3. Specular and diffuse reflection flux During an example pass of Ajisai observed by Graz on April 4, 2016, 540 pairs of strong flashes Uflash (5–8 ms in duration) and the preceding diffuse reflection Ud
Fig. 2. A short sample of Ajisai light curve. (a) The low-intensity flux Ud is produced by diffused reflection off the satellite surface while the strong flux Uflash represents a solar glint from a mirror panel. (b) The central epoch of the flash is determined by the time derivative of the recorded flux intensity.
Fig. 3. The satellite model. The X ; Y ; Z axes represent Body Coordinate System BCS. (a) S: vector towards the Sun, T: vector towards the ground observing telescope, P: phase vector, p: phase angle. (b) The significant vectors in relation to the central normal ðN Þ of the convex mirror; the phase ðpÞ and the inclination ðiÞ angles are indicated.
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(10 ms bin) have been identified as explained in Fig. 2. Since more than 90% of the satellite surface is covered with the mirrors (M) and CCR panels (P ) it is assumed that only reflections from those elements contribute to the observed signal, such that the intensity of the Ajisai diffuse flux is Ud ¼ UM;d þ UP ;d and the intensity of the mirror specular reflection is UM;q ¼ Uflash Ud . The selected diffuse and specular signal pairs occur within a very short time interval of 30 ms (300 photometric samples) during which the detection system properties, the atmospheric transmission, and the diffuse reflectivity of the satellite are assumed to remain stable. The comparison of the observed flux intensities (a mean flux value per time bin) with the link budget predictions is presented in Fig. 4; the generally good agreement between the observed and predicted trends might well be disturbed by the locally inaccurate representation of the atmospheric transmission that can be azimuth-dependent (higher dust concentration in the city direction, higher water vapor at the forest side, scattered clouds for examples). Within the short time slot of 30 ms, the ratio of the observed flux intensities W ¼ Ud =UM;q is proportional to the ratio of the realized reflection gains W ¼ ðGM;d dM þ GP ;d dP Þ=GM;q qM and allows for the mirror specular reflectivity coefficient qM to be obtained from: qM ¼
GM;d ð1 aM Þ þ GP ;d dP GM;d þ GM;q W
ð11Þ
where the mirror absorptivity is aM ¼ 0:04 and the CCR panel diffusion coefficient is dP ¼ 0:80. We have collected hypertemporal light curves of Ajisai during the period from Oct. 2015 until Jan. 2018 and selected the good quality, continuous passes for the mirror reflectivity analysis. Fig. 5a presents the solar flash statistics of 149 observed mirrors grouped by the ring they form on the array: C0 - is the central (equatorial) ring of the
Fig. 4. Ajisai photometric pass measured on April 4, 2016. (a) Observed and simulated flux intensities: specular UM;q and diffuse Ud . (b) The configuration of the angles during the pass.
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Fig. 5. The observation statistics for the selected 149 mirrors located on the rings: D1 (the first ring below the body’s equator), C0 (central ring), U1 - U6 (the upper rings). (a) The number of solar flashes collected. (b) The determined specular coefficient of the mirrors.
satellite body, D1 - the first ring down from the body equator, U1 to U6: the upper rings. The stable orientation of Ajisai in inertial space determines that the rings C0, U1, and U2 will cause most flashing towards the terrestrial latitude of the Graz SLR station. The specular coefficient of the observed mirrors is determined and varies from 82.3% to 88.2% (mean 85.3%, RMS 1.2%) (Fig. 5b). 4. Laser link via individual mirrors of Ajisai In order to predict the efficiency of the laser link via Ajisai mirrors, we have selected two SLR systems from Matera (Italy) and Graz (Austria) as transmitter and receiver stations (Table 1) with a distance of 719 km between the locations. The laser link simulation covers the full year of 2019 with the satellite position predicted by the SGP4 propagator and the mirror inertial attitude given by the Ajisai spin models (Kucharski et al., 2010, 2016). The phase vector P for the laser link is defined as a product of two satellite centered vectors pointing towards the transmitting T and the detecting D ground systems: TþD P ¼ jTþD . The common view (CV) situation occurs when j the inclination angle i (Fig. 3b) is smaller than the angular size of the convex mirror and allows for a transmitted laser pulse to be specularly reflected in the direction of the detection system. In the simulation scenario, it is assumed that the fire time of the transmitted laser pulses (EP = 100 mJ, k = 532 nm, hT = 500 ) is synchronized with the predicted epoch time of the CV events and only one laser pulse per CV interval is fired. The clear atmosphere model is used with the sea level visibility of V ¼ 15 km and no cirrus clouds present. The mirror reflection efficiency is qM ¼ 0:85, and the quantum efficiency of the receiving Graz C-SPAD detector is gq ¼ 0:2. A total of 716 night passes have been identified with the satellite simultaneously observed by the Matera and Graz SLR systems at the one way atmospheric transmission gA varying from 0.54 to 0.81 (mean 0.71). The predicted mean
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Table 1 Transmitting and receiving system parameters. Name
Matera SLR, transmitter
Graz SLR, receiver
Agency DOMES number Latitude Longitude Elevation,ht Minimum satellite tracking elevation angle above the local horizon Transmit laser parameters
Italian Space Agency, ASI 12734S008 40.6486° N 16.7046° E 537 m 20° EP ¼ 100 mJ k ¼ 532 nm hT ¼ 5 arcsec 3 arcsec gT ¼ 0:6 –
Austrian Academy of Sciences 11001S002 47.0678° N 15.4942° E 495 m 20° –
Pointing error, hP Optics efficiency Effective area of the telescope receive aperture, AD
number of the CV intervals per pass is 874.6 with a mean interval duration of 9.15 ms. The laser link budget statistics per CV interval in relation to the satellite elevation angle above the local horizon is presented in Fig. 6 and indicates that the link between the distant SLR systems via Ajisai reflections can be established at an average signal strength of npe ¼ 3:46 photoelectrons per CV interval (Fig. 6b). The longest CV intervals up to 15.6 ms - can occur when Ajisai is observed by Graz at elevation angles between 60° and 80° and the phase vector P remains on the mirrors from the ring U6. The investigated laser link scenario is not limited to the SLR systems operating at the 100 mJ energy levels. The transmitted laser energy per pulse can be lowered if the other components of the link budget equation are properly adjusted in order to keep the strength of the received signal at the detectable levels. The LTT via spaceborne mirrors is the common view mode concept and the necessity for the strict geometrical configuration between the space mirror and the ground stations makes it difficult to execute. Even though the Ajisai spin models provide highly accurate spin axis and rate predictions, the rotational phase of the satellite (and thus the occurrence of the CV intervals) is nearly impossible to predict at the sub-degree level on the pass-to-
3 arcsec gD ¼ 0:5 0:1826 m2
pass basis due to the thermal nano-torques that perturb the spin dynamics along the orbit. A promising solution to this problem that we propose for further investigation is a software algorithm that operates in the background of the kHz SLR system and performs a near real-time analysis of the high rate laser range data for the satellite spin determination. After the rotational phase of Ajisai is found (<1 min procedure) the UTC epochs of the CV intervals for the remaining arc of the pass can be predicted and distributed via the Internet in order to update the laser pulse transmit times and the gating of the detection system so that the laser link between the SLR stations can be technically established. 5. Conclusions The accurate attitude models of Ajisai allow for the hypertemporal light curves to be processed in the way that characterizes the reflective properties of the spaceborne spinning mirrors. The link budget analysis of the diffused and specularly reflected solar flux gives the mirror mean reflectivity coefficient of qM ¼ 85:3%, and indicates no significant decrease of the surface reflective quality despite the long duration of the mission. The measured optical properties of Ajisai surface elements can improve the determination of the satellite solar radiation pressure coefficient as demonstrated by Hattori and Otsubo (2019). The simulation study indicates that the CV intervals between the distant SLR systems occur frequently and can be used to establish an LTT link via individual mirrors of Ajisai at an average signal strength of 3.46 photoelectrons per laser pulse on the basis of the SLR system parameters at Matera and Graz. Acknowledgements
Fig. 6. The CV statistics of the laser link budget simulation with respect to the satellite elevation angle above the local horizon of the transmitting (Matera) and receiving (Graz) systems. (a) CV interval duration. (b) The mean number of photons recorded at the receiving station.
This research is supported by the Cooperative Research Centre for Space Environment Management, SERC Limited, through the Australian Government’s Cooperative Research Centre Programme.
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