A.

Effective Aperture

The effective aperture diameter is the main driver of the telescope cost. The search for an inexpensive solution maintaining the required performance leads to different configurations, as explained in section I. To start evaluating the option of a single large aperture, a first reference is the last generation of astronomical telescopes. On the one hand we have a generation of general purpose 8-10m telescopes as VLT, Subaru, Gemini, LBT, Keck and GTC. These telescopes have reached collecting areas from 40 to 100m² on a single mount with a very good optical quality in several arcmin FOV, which avoids degrading the atmospheric quality of the best sites in the world. However, all these telescopes have complex wavefront control systems and their cost is higher than 100M€. On the other hand, the Hobby-Ebberly and SALT telescopes have been developed providing collecting areas of approximately 80m² with a cost below 50M€. This cost saving comes from the very specific purpose, spectroscopy survey, that permits an extremely simple mount and optics design whose validity for deep space optical communications has to be evaluated, considering the fact that the declination travel range could be limited to the ecliptic.

In the most inexpensive range are the MAGIC telescopes in the Observatory Roque de Los Muchachos (ORM) in La Palma, which reach ~240m² collecting area with less than 10M€ cost. This reduced cost is mainly derived from the very relaxed optical performances required for their specific use to detect Cherenkov light, achieving a 1.8arcmin full width half maximum (FWHM) Point Spread Function (PSF). Despite the large OGS has to operate also during bad seeing conditions, not requiring the excellent image quality of the general purpose 8-10m class telescopes, the MAGIC optical quality is too poor requiring a large FOV that does not allow to reject background properly.

The main design driver for a large aperture OGS with certain optical quality is the already mentioned SEP angle, down to 7°, needed to maintain contact with the deep-space satellite (probe) during the maximum possible time. The required day and night operation also pushes to consider solar telescopes as a reference for the large OGS design. The next generation of solar telescopes with optical apertures of 4m, includes the Daniel K. Inouye Solar Telescope (DKIST, USA) and the European Solar Telescope (EST, Europe). These telescopes are designed to point directly to the Sun, so that the solar radiation comes from small angles with respect the optical axis, always illuminating the telescope in the same symmetrical way, and it is easy to safely include specific systems to reject the unused Sun light. However, the thermal problem becomes an issue more difficult to be solved in the large OGS that is going to be unevenly radiated by the Sun in different parts of the telescope structure and in all these conditions the telescope performance shall be granted. In this changing situation, the shadowing produced by a dome can simplify the thermal and safety problems, but implies the investment in a classical dome to protect the telescope, discarding the open air (cheaper) operation. These solar changing conditions are not only a problem for a large OGS, but also for the other configurations.

Telescope arrays provide a convenient way to expand effective aperture size without suffering significant additional performance degradation. This performance degradation can be described by a combination loss parameter that incorporates the effects of tracking and synchronization errors, as well as the additional corresponding losses. Results shown later have been obtained taking into account that the margin of error for the tracking estimation increases as the aperture diameter of the individual element decreases. The adaptation of existing RF antennas to optical communications also supposes an attractive alternative to reduce costs. The main shortcoming is that the FOV for this approach is much larger than for the standard telescopes, leading to high noise background during day-time operation.

B.

Receiver and Telescope Field Of View

Diffraction-limited operation is not required for optical communications, and as first approach wavefront control technologies (active optics, adaptive optics), that can reduce the FOV required by the receiver to catch all the satellite photons, will not be considered. The receiver FOV then is closely related to the blur circle size. Blur size is determined by different factors, including the atmospheric and dome seeing, the gravitational sag of the primary mirror, and the surface quality, as well as other mechanical and thermal effects of the system. In general, the FOV for detection should be designed to operate in an atmospheric seeing-limited regime. In this case, the FOV is related to the seeing FWHM, so that FOV≈1.52·FWHM to encircle 80% of signal energy. Since typical seeing values for telescope sites reach 20-25 μrad for low pointing elevations, FOV should be limited to roughly 30-38 μrad. If the other factors were not compensated (e.g., the contribution of surface roughness or gravity sag can amount to values as high as 100 μrad), the blur size could be in the range of 200 μrad. The telescope FOV is, on the other hand, limited by acquisition. Acquisition probabilities of ~99% are achieved for 3σ values of full angular pointing errors.

C.

Configurations Comparison

The performance of different configuration approaches (i.e., single telescope, telescope array, and modified RF antenna) is compared in Fig. 1. Here we can observe that telescope array can provide similar results to the single-telescope solution, whereas the modified RF antenna reaches the 100 Mbps requirement at 1 AU for very large effective aperture diameter. The cost for the modified RF antenna should be nevertheless considerably lower. Therefore, the cost analysis and the possibility of future expansion become critical factors to determine the optimum solution. One key aspect in the analysis is the distribution of both signal and background photons collected by the receiver at the focal plane [8][9]. In the case of telescope arrays, the performance can be increased at lower cost than for large apertures by using adaptive optics correction. The optimization of modified RF antennas is attained by adjusting the detection FOV (optimum FOV for the scenario in Fig.1 is obtained when encircling 75% of signal energy, whereas 99.9% is covered by the full detection FOV) [10]. Note that results shown in Fig. 1 include a 3-dB communication margin, and have been computed using the values provided in Table 1 and Table 2 (note also that the peak-to-average power ratio, i.e., the value of M, has been changed to improve performance).

Fig. 1.

Achievable data rate as a function of effective aperture diameter for single telescope (single), telescope array (array) and modified RF antenna (antenna) configurations assuming a code efficiency of –0.97 dB. The encircled dot has been obtained using the approach from [8][9]. SR in the open-diamond curve label denotes Strehl Ratio (adaptive optics correction).

A.

Adaptive Optics

The need of an Adaptive Optics (AO) system in a Large Aperture OGS mainly depends on the specific deep-space mission. As a reference, a basic configuration of a 1-meter telescope, observing in 1064 nm, pointing at zenith, with a turbulence coherence length of r₀=10 cm at 550 nm, will deliver a performance of Strehl ratio=0.02. Several deep-space mission scenarios considered for the OGS, like coupling the received signal to a single mode fiber for optical preamplification, require a Strehl ratio of at least S=0.3, which can only be achieved correcting the wavefront by means of an AO system.

Assuming some standard parameters for the AO system, the complexity to achieve S=0.3 can be analyzed. Using a Shack-Hartmann Wavefront Sensor (WFS), with 1 kHz frame rate, 2 frames close-loop delay (from detector readout to deformable mirror positioning) and Fried geometry, we can estimate the WFS subaperture size on sky and therefore the number of degrees of freedom required. With an r₀= 10 cm at 550 nm, the maximum WFS subaperture size to comply with S=0.3 is shown in Table 3.

Table 3.

WFS subaperture size on sky to comply with S=0.3 for different wavelengths and elevations

As can be seen, a realistic subaperture around 30 cm will not reach S=0.3 in a wide range of elevations. For low elevation, 15-cm subaperture will still comply at 1550 nm but not at 1064 nm. It has to be emphasized that using an r₀=10 cm at 550 nm is a conservative choice for a good astronomical site, considering that it is equivalent to a seeing of 1.14”. Statistics of several years give a seeing better than 1” at ORM (La Palma) 85% of the year [11]; similar statistical values have been published for Teide Observatory (Tenerife) [12]. This means almost every clear night the AO requirement can be complied in all the operational elevation range with 15-cm subapertures at 1550 nm. This is equivalent to having 7×7 degrees of freedom in a 1m telescope (commercially available systems), or 67×67 in a 10m telescope (in the limit of the present technology).

In addition to the complexity, we have to face the fact that to compensate atmospheric turbulence the Tracking System (tip-tilt compensation) and the AO system (high order compensation) require an intense light source (Guide Star - GS) in the field of view (FOV) close to the target satellite to be used as a reference to measure the wavefront error. Ideally, in the case of optical communications, the reference should be the satellite transmitter, but this implies the use of part of the downlink communication signal for AO, being not possible in all the cases. If we analyze different scenarios, the baseline reference star changes.

For Moon and L2 the downlink communication signal is bright enough to use part of it for the tracking and AO system. For Mars and Jupiter, where we are in a “photon-starved” regime, photons of the communication signal will not be available for the tracking system nor for the AO system. Using the planet as a “extended reference source” could be possible if the angular separation with the satellite is not more than a few arcseconds, but if the separation is much larger than the isoplanatic angle, an artificial laser guide star (LGS) is required. The use of LGS relaxes the required amount of light of the reference for any mission, even though a Natural GS is still needed in the FOV for tip-tilt correction. There are two main effects that affect the performance of AO systems using LGSs: the cone effect and the residual tip-tilt jitter.

The cone effect is due to the finite altitude of the LGS, which is generated in the mesosphere emitting a spherical wavefront that does not pass through all the turbulence the satellite light is crossing. The cone effect induces a systematic degraded correction and thus limits the improvement of the image quality. It becomes more significant for shorter wavelengths, for larger telescopes and for high altitude seeing.

If a LGS is used, the NGS for tip-tilt correction may be faint and far off-axis. The residual error of the tip-tilt correction with the NGS is called tip-tilt jitter and depends on θ_NGS, the angular separation with respect to the axis. Simulations have been carried out for the two sets of deep-space scenarios of interest, to evaluate the expected performance. The results are shown in Table 4.

Table 4.

RMS error in a LGS system due to tip-tilt jitter and cone effect, and relative performance with respect the Strehl ratio using a NGS (i. e. satellite light) as AO reference, SNGS

We can conclude that the cone effect is a systematic and relatively small error, and that the main error introduced by a LGS system is due to the tip-tilt jitter if the NGS off-axis angle becomes large. The additional degradation in Strehl ratio due to the use of a LGS-based AO system in the large aperture OGS can be tolerated within the error budget, for a NGS up to 60” off-axis and 1550 nm, if the requirement is to achieve a total Strehl ratio of 30%. An additional important conclusion is that receiving at 1550 nm is an advantage from AO performance (or AO simplicity) point of view, for NGS and LGS systems.

B.

Uplink functionality

The main reasons for having a laser system at the large OGS are to provide a beacon to assist the on-board terminal Pointing, Acquisition and Tracking (PAT), and to provide optical uplink transmission (basically low-rate command capability).

For short-distance scenarios (Moon, L2), a laser for the uplink is commercially available in several technologies, being the required laser power is tens to a hundred W. For long-distance scenarios (Mars, Jupiter), uplink beacons require several kW average power, available in 1030 nm – 1064 nm technologies. This is an additional reason for choosing 1550 nm technology for the downlink, although using 1030 nm – 1064 nm for the uplink has stronger implications concerning laser safety regulations.

Therefore, key requirements for the uplink laser are:

A good reference for specifying uplink beam parameters is the empirical data collected by ESA OGS at Tenerife in optical link campaigns with ARTEMIS satellite [13]. The nominal divergence of the uplink from ESA OGS (at Teide Observatory) to ARTEMIS satellite was variable between 3.6 μrad and 27 μrad, for a laser at 847 nm with M²=2. An uplink widening factor (beam spread) due to the propagation through the atmospheric turbulence was estimated from the additional losses at the satellite receiver. The beam widening was computed applying theoretical models [14], and compared with experimental measurements on the atmospheric Rayleigh scattering and the far field pattern at ARTEMIS [15]. The results were correlated with atmospheric turbulence strength, determining a beam widening factor of 1.2 for a seeing of 0.8”, a typical value of an astronomical site (75% percent of the clear nights at an astronomical site are better than this value [11]), and a widening factor of 1.75 for seeing conditions of 1.45”, equivalent to r₀=8 cm at 500 nm (90% percent of the clear nights at an astronomical site are better than this value [11]).

Photon counting detectors on board require a stable received signal level that the uplink system shall achieve by using aperture diversity to mitigate atmospheric turbulence effects that contribute to scintillation (mainly beam wander [15]). A minimum of four uplink transmitting subapertures shall be used, separated enough to be uncorrelated from the turbulence spatial point of view (namely, separation larger than the typical r₀ at an astronomical site at Tx wavelength, i.e., 22 cm at 1064 nm and 35 cm at 1550 nm). The signal of the different subapertures shall be also delayed enough to avoid interference between them when the beams overlap in the atmosphere. If a Tx-Rx common optical path configuration is used in the large OGS, the n (four) incoherent apertures shall be configured symmetrically around the telescope central obscuration [15]. The possibility of using different optical paths for Tx-Rx demands the consideration of larger divergences (and consequently higher power) since the tip-tilt correction measured in the downlink cannot be applied to the uplink. Nevertheless, due to the large Point Ahead Angles (PAA) involved in deep-space scenarios (up to 600 μrad), the tip-tilt measured in the downlink could not be valid for the uplink. Different Tx-Rx optical paths have on the other hand the advantage of simplifying the post focal optical design, because isolation of both signals is not needed. The size of the transmitting apertures shall cope with the range of laser divergences.

C.

Downlink detectors

The use of a high-power efficiency modulation, PPM, combined with a direct-detection scheme is particularly suitable for deep-space communications since photon efficiency can be traded with bandwidth. As it can be observed in Table 1 and Fig. 1, the PPM channel capacity is better optimized with symbols consisting of a large number of slots (higher M values) in the case of power-starved links or under high background conditions, whereas symbols with a small number of slots (lower M values) are preferred for shot-noise-limited operation. Obviously, saturation of capacity appears at high capacity values due to the limited modulation bandwidth. This detection scheme is, in general, developed using photon-counting detectors.

The main parameters for the design of photon-counting detectors include their detection efficiency, their size (basically, the angular size defined by the FOV for detection), their temporal-handling capabilities (both in terms of bandwidth and timing jitter), their intrinsic dark count rates, and their saturation constraints. Most parameters depend on material and/or device technology. However, specific detection techniques and structures have also been realized to mitigate the limitations imposed using conventional technology (e.g., negative feedback or dividing the device area into multiple pixels to avoid blocking). It is worth noticing that, in principle, the optimum detector size increases with the aperture diameter of the telescope (e.g., due to the change in the focal length) and as the background noise level decreases. A similar behavior is expected when the atmospheric seeing conditions become more severe. These dependences can be used to improve the system performance, taking advantage of adaptive spatial filtering and/or adaptive optics techniques (see, for example, the results shown in Fig. 1) [16]. Required values for the basic photon-counting detector parameters are summarized in Table 5 [6][10][16][17]. Currently, Superconducting Nanowire Single-Photon Detectors (SNSPDs) offer the best approach to develop high-performance photon-counting detectors as those required for deep-space ground receivers. In fact, a successful demonstration using this technology was carried out in the framework of the Lunar Laser Communications Demonstration (LLCD) for links operating at 622 Mbps and high power efficiencies.

Table 5.

Recommended values for some relevant photon-counting detector parameters