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<head>I. INTRODUCTION<lb/></head>
<p>Payloads in deep-space missions are continually increasing<lb/> the amount of information collected during their lifetimes. The<lb/> result is that bigger and bigger amounts of data need to be<lb/> transmitted back to Earth, and current radiofrequency (RF)<lb/> technology has reached a bottleneck, limiting the scientific<lb/> outcome of current missions and threatening the development<lb/> of future manned missions. To solve this, optical frequencies<lb/> have been studied and applied <ref type="biblio">[1]</ref> to increase the bandwidth<lb/> and to reduce the volume, mass and power needs at the same<lb/> time. One of the main advantages of shorter wavelengths is the<lb/> narrow divergence of the laser beams. For example, a<lb/> communication link from Mars would allow a reduction of the<lb/> footprint reaching the Earth from ~1000 in RF to ~0.1 of the<lb/> Earth diameter using optical wavelengths.<lb/> </p>
<p>A natural need of a Free-Space Optical Communication<lb/> (FSOC) link, especially from deep-space, is the use of a ground<lb/> terminal, i.e., a telescope, with a big aperture to overcome the<lb/> very low power received. Nevertheless, unlike conventional<lb/> astronomical telescopes, in FSOC there is no need to obtain<lb/> images, thus the requirements are not so strong in terms of<lb/> optical quality. This is one of the reasons to study the use of<lb/> other kind of telescopes. This paper completes an initial<lb/> proposal from the authors about the use of IACTs (Imaging<lb/> Atmospheric Cherenkov Telescopes) as optical ground<lb/> terminals in deep-space FSOC <ref type="biblio">[2]</ref>.<lb/></p>
<head>II. PROBLEM AND SOLUTION PROCEDURE<lb/></head>
<p>Cherenkov radiation is produced in the atmosphere when a<lb/> cosmic ray or a gamma ray interacts with the molecules of the<lb/> atmospheric upper layers. As a result, visible photons are<lb/> produced, and IACTs are designed to detect them in the ground<lb/> using a big reflective surface. These telescopes observe the<lb/> atmosphere at a height of ~10 km, where on average the<lb/> Cherenkov radiation is produced. The Cherenkov Telescope<lb/> Array (CTA) is a 200 M€ international collaboration involving<lb/> 31 countries to build over a hundred of big segmented<lb/> telescopes (<ref type="figure">fig. 1</ref>) in the next years, deployed in two<lb/></p>
<figure>Fig. 1. Artistic illustration of the Cherenkov Telescope Array [3].<lb/> </figure>
<figure>Fig. 2. Diagram of the three types of different<lb/> CTA telescopes [3].<lb/></figure>
<p>observatories, one in each Earth's hemisphere to allow full<lb/> coverage of the sky <ref type="biblio">[3]</ref>. Recently, the CTA Resource Board<lb/> decided to host CTA-South in the ESO Paranal grounds<lb/> (Chile), and CTA-North in Roque de los Muchachos<lb/> Observatory (La Palma, Spain) <ref type="biblio">[4]</ref>. Several telescope<lb/> prototypes have already been tested and the final telescopes<lb/> will be built in the next few years with the goal of being fully<lb/> operational in 2020.<lb/></p>
<p>The<lb/> CTA<lb/> observatory<lb/> will<lb/> consist of about 100<lb/> telescopes on the<lb/> southern site and<lb/> about 20 telescopes<lb/> on the northern site.<lb/> In each observatory,<lb/> there will be three<lb/> types of different<lb/> telescopes (<ref type="figure">fig. 2</ref>):<lb/></p>
<item>• SST (Small Size Telescopes): with 6-m diameter and<lb/> 10º field of view (FoV). A pool of dozens of them,<lb/> separated by at least 70 m, is projected, thus a massive<lb/> production will be carried out.<lb/> </item>
<item>• MST (Medium Size Telescopes): with 12-m diameter<lb/> and 6º to 8º FoV. Tens of them with 100-m spacing are<lb/> foreseen, being the most similar to current IACTs.<lb/> </item>
<item>• LST (Large Size Telescopes): with 24-m diameter and<lb/> 4º to 5º FoV, 100-m spacing and around 4 units in each<lb/> observatory. The first prototype of this kind is<lb/> currently under construction in La Palma, Spain.<lb/></item>
<p>The authors of this paper presented the original idea of<lb/> using IACT telescopes for deep-space FSOC in a previous<lb/> paper <ref type="biblio">[2]</ref>. The motivations were explored back then: the big<lb/> apertures of the telescopes, their native operation as an array,<lb/> their low costs due to their relaxed requirements, the ideal<lb/> sky-related conditions, the fast tracking of the telescopes, a<lb/> suitable communications network infrastructure, etc. Now, the<lb/> proposal is studied in more depth and extended to CTA<lb/> telescopes. Data on the telescope designs has been taken from<lb/> those planned under current CTA consideration.<lb/></p>
<p>In the next sections, a deep insight into the main differences<lb/> of gamma-ray and communication telescopes will be carried<lb/> out, focusing on the telescopes from the CTA project.<lb/> Originally, this proposal is aimed to the direct reutilization of<lb/> one or more CTA telescopes for their exclusive use as<lb/> communication receivers. However, a different approach could<lb/> also be taken into consideration, i.e. the shared operation for<lb/> astronomy and communications. The direct reutilization of<lb/> CTA telescopes, with minor modifications, is proposed,<lb/> although a brief discussion on possible improvements to<lb/> optimize their performance for FSOC will be made.<lb/></p>
<p>In this study, reflectance/transmittance measurements were<lb/> performed using a Lambda 900 spectrometer by Perkin Elmer.<lb/> OSLO (Optics Software for Layout and Optimization) software<lb/> from Lambda Research was used for the optical models and<lb/> simulations, allowing the computation of optical performance<lb/> of the telescopes. MODTRAN (MODerate resolution<lb/> atmospheric TRANsmission) software from Spectral Sciences<lb/> was used as the standard tool to retrieve atmospheric<lb/> transmission and sky radiance, in order to compute received<lb/> noise in simulations at different scenarios. Matlab from<lb/> MathWorks was used for the rest of computations. Lastly, the<lb/> recommendations from Optical Link Study Group (OLSG), a<lb/> subcommittee of the Interagency Operations Advisory Group<lb/> (IOAG), co-chaired by ESA and NASA and in charge of the<lb/> international standardization of FSOC, were followed in the<lb/> simulations.<lb/></p>
<head>III. RESULTS AND DISCUSSION<lb/></head>
<p>In order to fulfill the requirements of FSOC, some IACTs<lb/> items must be carefully studied. The reflectivity of the mirrors<lb/> at the desired wavelength, the different position of the image<lb/> plane and the focal plane, the pointing and tracking of the<lb/> telescope gimbal, and a brief discussion of the optimization of<lb/> the detector size were already made in <ref type="biblio">[2]</ref>. Hereafter, updates<lb/> on the reflectivity and focusing with new CTA solutions as<lb/> well as FoV limitations for the SNR (Signal to Noise Ratio) in<lb/> this kind of telescopes will be explored. After that, a number of<lb/> telescope simulations will be performed to validate their proper<lb/> operation for FSOC. With these results, a summary of the link<lb/> budgets that can be achieved for different scenarios will be<lb/> made, concluding with a brief analysis of the costs.<lb/></p>
<head>A. Mirrors of CTA telescopes<lb/></head>
<p>The first item to be explored is the performance of the<lb/> mirrors at FSOC wavelength. Several techniques are being<lb/> proposed for manufacturing CTA segments of primary mirrors.<lb/> Due to the foreseen massive production, the spherical mirror<lb/> profiles and the moderate optical quality required, most<lb/> techniques are based on replica to minimize costs<lb/> (~2000 €/m 2 ), where glass is conformed using a molding based<lb/> on a honeycomb structure <ref type="biblio">[5]</ref>, but the curvature radius that this<lb/> technique can achieve is too low for most SST and probably so<lb/> for MST as well. Thus, more traditional polishing techniques<lb/> with diamond in aluminum (~2500 €/m 2 ) will be also<lb/> examined. Finally, to avoid degradation in aluminum layers<lb/> and increase reflectivity, interference dielectric multilayer<lb/> designs are also under study <ref type="biblio">[6]</ref>. In these mirrors, the<lb/> reflectivity can be adjusted in narrow spectral bands. The main<lb/> question to be solved is whether the mirrors can be directly<lb/> used in FSOC wavelength (1550 nm), provided that they are<lb/> designed for Cherenkov radiation band (visible light).<lb/></p>
<figure>Fig. 3. Measured reflectance of the mirrors types considered for CTA.<lb/></figure>
<p>Reflectance measurements have been carried out over<lb/> different mirrors currently intended to be used in CTA <ref type="biblio">[2]</ref>.<lb/> These measurements showed that the reflectance at FSOC<lb/> wavelengths is even higher than in the Cherenkov region for<lb/> current IACT mirrors, reaching over 90% at 1550 nm. <ref type="figure">Fig. 3<lb/></ref> shows the measured reflectance of several replica-based<lb/> samples supplied by the CTA consortium: AR100 is made up<lb/> of an aluminum layer and a quartz coating (Al+SiO2), DH100<lb/> is based on an aluminum layer with dielectric multilayer<lb/> coating (SiO2+HfO2+SiO2), and DD040 is a pure dielectric<lb/> multilayer mirror. AR100 reaches 94.9% at 1550 nm (around<lb/> 85% for Cherenkov range), and DH100 reaches 93.0% (88.8%<lb/> at Cherenkov range). The remarkable interference effect of<lb/> DD040 reaches a 98.8% at Cherenkov wavelengths, although a<lb/> poor 7.3% at 1550 nm. In principle, this could be a problem,<lb/> since this technique is only starting to be spread. However,<lb/> pure dielectric mirrors can be tuned to maximize their<lb/> reflectance in a different wavelength during the manufacture<lb/> process with no additional cost <ref type="biblio">[7]</ref>. Furthermore, mirrors of this<lb/> kind were installed in Hess telescope (28-m IACT located in<lb/> Namibia) in 2012 showing a nearly 100% reflectance at<lb/> 1550 nm, although for reasons not related to communications.<lb/></p>
<head>B. Focusing an IACT<lb/></head>
<p>In <ref type="biblio">[2]</ref>, the required detector position displacement ε in<lb/> order to focus at infinity (as a FSOC receiver) instead of at a<lb/> point 10 km high in the atmosphere (as IACTs are designed to<lb/> operate, in order to detect the Cherenkov radiation), was<lb/> studied for the MAGIC (Major Atmospheric Gamma Imaging<lb/> Cherenkov Telescope) telescope. The same equations of <ref type="biblio">[2]</ref>,<lb/> applied to CTA, give ε values ranging from 1.4 cm (SST) to 9<lb/> cm (LST) (see <ref type="table">table I</ref>). In the case of MAGIC II, the camera<lb/> can be shifted as far as 30 cm in real operations for focusing<lb/> and maintenance <ref type="biblio">[8]</ref>, so this is a normal feature in IACTs.<lb/> Furthermore, when adapting an IACT as a FSOC receiver, the<lb/> big and heavy cameras should be replaced by a simpler system<lb/> based on a single photodetector, leaving enough space to<lb/> allocate any optical setup with no significant constraints.<lb/></p>
<head>C. Field of View and Background Noise<lb/></head>
<p>In <ref type="biblio">[2]</ref>, a discussion about the relation between the FoV and<lb/> the SNR was made for MAGIC-II telescope. A deeper<lb/> discussion needs to be made regarding the concepts of SNR,<lb/> FoV and their relation with the optical resolution of the CTA<lb/> telescopes. The optical resolution is characterized by the Point<lb/> Spread Function (PSF), which determines the spatial<lb/> distribution of the radiation received from a point source at<lb/> infinity, i.e., the radiation coming from a space probe received<lb/> at the focal plane of the telescope. The FoV θFOV is the angular<lb/> spread in the object plane projected on the image plane of the<lb/> telescope. It is also a function of the detector size (in this work,<lb/> a circular shape is assumed), given by eq. (1).<lb/></p>
<formula>θFOV = 2arctan(d/2f)<lb/> (1)<lb/> </formula>
<p>d being the diameter of the detector, and f the focal length of<lb/> the telescope. The multi-pixel camera (made up by up to 2500<lb/> photomultiplier tubes in the case of LST) designed for CTA<lb/> telescopes should be replaced by a simpler system based on a<lb/> single photodetector, with an important reduction in the<lb/> detector size, and therefore in the FOV.<lb/></p>
<p>Cherenkov telescopes operate during dark nights only.<lb/> However, FSOC telescopes must support also daylight<lb/> operation. In this case, the sunlight, which is the main source of<lb/> background radiation due to the scattering caused by<lb/> atmospheric gases (Rayleigh) and particles (Mie), reaches the<lb/> detector as a noisy signal, hence with a decrease in the SNR. In<lb/> this work, a worst case for each link scenario will be studied,<lb/> and this spurious light will lead to a detected noise power N S.<lb/> According to eq. (2), this power depends on the sky radiance<lb/> L(λ,θ,ϕ) (which in turn depends on wavelength λ, zenith angle<lb/> θ, and the angle ϕ between the telescope, the target and the<lb/> Sun), the receiver's aperture area Ar, the two-dimensional FoV<lb/> angle ΩFOV, and the spectral bandwidth of the signal ∆λ.<lb/></p>
<formula>NS = L(λ,θ,φ)·Ar·ΩFOV·Δλ<lb/> (2)<lb/></formula>
<p>In terms of two-dimensional space (one-dimensional<lb/> angle), eq. (2) can be translated to eq. (3), with Dr being the<lb/> aperture diameter of the telescope.<lb/> </p>
<formula>NS = L(λ,θ,φ)·(π/4·Dr· θFOV) 2 ·Δλ<lb/> (3)<lb/></formula>
<p>The parameter that allows more control in this kind of link<lb/> design (using an already-built telescope) is the detector area d,<lb/> which has a strong relation with the optical resolution of the<lb/> telescope. If d is bigger than the PSF, then too much noise will<lb/> reach the detector, decaying the SNR. If d is smaller than the<lb/> PSF, then many signal photons will be lost, which must be<lb/> avoided in links as strongly limited by the received signal<lb/> power as deep-space ones. Therefore, the detector size d will<lb/> determine the performance of the link, and ideally it should<lb/> match the size of the PSF, which in turn should be as small as<lb/> possible to minimize the FoV, thus the background noise,<lb/> maximizing the SNR.<lb/></p>
<p>In IACTs, the PSF is mainly limited by telescope<lb/> aberrations, which prevail over turbulence and diffraction<lb/> effects. The PSF of MAGIC II was simulated by the authors to<lb/> have a diameter of 31.7 mm <ref type="biblio">[2]</ref>, which agrees well with<lb/> experimental measurements <ref type="biblio">[9]</ref>. As this IACT has an aperture<lb/> diameter of 17 m, its diffraction limit is in the order of tens of<lb/> nm, five orders of magnitude below that value. The PSF<lb/> affected by turbulence has been computed to be around<lb/> 7.5 µrad for the worst case of 70º zenith angle at 1550 nm, over<lb/> 3 orders of magnitude below the PSF. The MAGIC FoV for a<lb/> single pixel is around 2 mrad, two orders of magnitude over<lb/></p>
<table>TABLE I. DETECTOR DISPLACEMENT ε IN IACTS FOR FSOC OPERATION.<lb/> Telescope<lb/> Diameter<lb/> D (m)<lb/> f/D<lb/> Focal length<lb/> f (m)<lb/> ε (cm)<lb/> MAGIC<lb/> 17<lb/> 1<lb/> 17<lb/> 2.9<lb/> CTA-SST<lb/> 6<lb/> 0.5<lb/> 12<lb/> 1.4<lb/> CTA-MST<lb/> 12<lb/> 1 / 0.75<lb/> 16<lb/> 2.5<lb/> CTA-LST<lb/> 24<lb/> 1.25<lb/> 30<lb/> 9<lb/></table>
<p>usual values in FSOC receiver. CTA telescopes need to be<lb/> characterized with their optical resolution to quantify this<lb/> limitation when applied to a communication link, as well as to<lb/> analyze possible PSF improvements to optimize their operation<lb/> to FSOC. Next section will be devoted to this characterization.<lb/></p>
<head>D. CTA telescopes simulations<lb/></head>
<p>Telescopes with lower focal ratios (f/D) have stronger<lb/> geometrical aberrations <ref type="biblio">[10]</ref>, which is the case for CTA<lb/> telescopes. Furthermore, the use of spherical optics to reduce<lb/> costs in the mirror manufacture, worsen the aberration<lb/> behavior. For these reasons, ray-tracing simulations of CTA<lb/> telescopes have been carried out to obtain their performance in<lb/> terms of optical resolution. IACTs are designed to have a wide<lb/> FoV, as they need to observe wide sections of the sky.<lb/> Conversely, in FSOC, once the telescope is pointed towards the<lb/> spacecraft, the radiation of interest will be received only in<lb/> axis, hence FoV can be greatly reduced to maximize the SNR.<lb/></p>
<p>CTA telescopes have been simulated in OSLO (see<lb/> example of (<ref type="figure">fig. 4</ref>) modelling their respective geometries and<lb/> hexagonal spherical segments, each with its curvature radius<lb/> according to its position in the primary mirror profile. In this<lb/> study, aperture profiles are taken as they were designed for<lb/> CTA: LST parabolic <ref type="biblio">[11]</ref>, MST <ref type="biblio">[12]</ref> and SST <ref type="biblio">[13]<lb/></ref> Davies-Cotton (MST-DC and SST-DC) <ref type="biblio">[14]</ref>, and MST and<lb/> SST Schwarzschild-Couder (MST-SC and SST-SC) <ref type="biblio">[15]</ref>. The<lb/> latter one has two variations: the British-French GATE<lb/> (GAmma-ray Telescope Elements): SST-SC GATE <ref type="biblio">[16-17]</ref>;<lb/> and the Italian ASTRI (Astrofisica con Specchi a Tecnologia<lb/> Replicante Italiana): SST-SC ASTRI <ref type="biblio">[18-19]</ref>.<lb/></p>
<p>As a first step, after computing the OSLO simulation<lb/> assuming ideal mirrors, the following spot diagram radii were<lb/> obtained for the segments of each telescope: 57.3 µm for SST-<lb/>DC, 25.7 µm for MST-DC and 16.4 µm for LST (close to their<lb/> diffraction limits, being 11.9 µm, 22 µm and 30.9 µm,<lb/> respectively). Then, the final profiles were created by<lb/> assembling all the segments according to the shape of each<lb/> telescope. For each mirror (e.g. LST is made up by 198<lb/> different segments), it is necessary to compute its 3D position,<lb/> its curvature radii and its tip/tilt angles: the 3D position of each<lb/> mirror can be calculated according to each telescope profile,<lb/> indicated in the previous paragraph; the curvature radii are<lb/> calculated as an average value of the maximum and minimum<lb/> values of the telescope profile in each segment; and as for the<lb/> tip/tilt angles, initial values were calculated as a first approach<lb/> using simple trigonometry.<lb/></p>
<p>The obtained spot diagrams were asymmetrical and needed<lb/> to be optimized ((<ref type="figure">fig. 5(a)</ref>). An iterative method for all the<lb/> tip/tilt angles was applied to get an optimized and symmetrical<lb/> spot diagram (<ref type="figure">fig. 5(b)</ref>). A damped least-squares method<lb/> applied to an error function defined by the diameter of the PSF<lb/> was applied in OSLO using its optimization capabilities. This<lb/> is as realistic as using the actual tip/tilt actuators currently used<lb/> in each IACTs to locally correct the alignment of each<lb/> segment. The movements needed to perform this optimization<lb/> were all below the actual capabilities of the Active Mirror<lb/> Control (AMC) systems projected for CTA telescopes.<lb/></p>
<p>When using real mirrors, the wavefront will be distorted<lb/> beyond the ideal behavior. The performed OSLO models also<lb/> took this effect into account simulating realistic prototypes of<lb/> CTA mirrors from Japanese Sanko and Italian ASTRI <ref type="biblio">[11, 21]</ref>.<lb/> A series of random surface profiles were generated and<lb/> superimposed over each ideal mirror to simulate this behavior<lb/> (see the realistic model in <ref type="figure">fig. 6(b)</ref>, compared to the ideal<lb/> model in <ref type="figure">fig. 6(a)</ref>). Following similar statistical parameters as<lb/> the experimental measurements from real samples, a different<lb/> random surface was generated for each mirror. After this, more<lb/> realistic spot diagrams were obtained.<lb/></p>
<p>The PSF size obtained with these OSLO simulations were<lb/> as follows: 6.20 cm for LST, 3.42 cm for MST-DC, and 3.43<lb/> cm for SST-DC. Using their respective focal lengths, the FoV<lb/> can be calculated as 2.24, 2.19 and 6.13 mrad, respectively for<lb/> LST, MST-DC and SST-DC. For the SC configurations of<lb/> MST and SST telescopes, not enough information was<lb/> available to perform the OSLO simulations, therefore nominal<lb/> </p>
<figure>(a)<lb/> (b)<lb/> Fig. 6. (a) Wavefront of a LST mirror computed with an ideal model.<lb/> (b) Wavefront computed with a realistic distorted model.<lb/> (a)<lb/> (b)<lb/></figure>
<figure>Fig. 5. (a) Spot diagram for non-optimized LST using ideal mirrors. (b) Spot<lb/> diagram of the optimized telescope model with realistic mirrors.<lb/></figure>
<figure>Fig. 4. Model in OSLO of the CTA-LST telescope.<lb/></figure>
<p>design data were used instead, with FoV under 1 mrad <ref type="biblio">[16-19]</ref>.<lb/> These profiles allow achieving a better PSF due to the use of<lb/> aspheric optics in order to reduce the pixel size, and hence the<lb/> cost and size of the cameras, which can be built using smaller<lb/> photodetectors (APDs instead of PMTs). This design constraint<lb/> will be also an advantage for adapting the telescope to FSOC.<lb/></p>
<head>E. Background noise<lb/></head>
<p>To characterize the link in terms of SNR, the background<lb/> noise power needs to be calculated. Eq. (2) must be solved for<lb/> the worst scenario. The sky radiance L(λ,θ,ϕ) has been<lb/> computed using MODTRAN, the usual reference for<lb/> background noise computation in FSOC link budgets <ref type="biblio">[21]</ref>.<lb/> Following the suggestions from OLSG, the simulations used a<lb/> minimum Sun-Earth-probe angle of 5° and a maximum<lb/> observation zenith angle of 70°. The aerosol model applied was<lb/> a maritime one, with 23-km visibility, taking into account a site<lb/> like La Palma (Spain) for CTA North. Desert aerosol from<lb/> Sahara also reaches Canary Islands, but the altitude of the<lb/> observatory (2390 m) is usually beyond the influence of such<lb/> an air mass.<lb/></p>
<p>As an example, <ref type="figure">fig. 7</ref> shows the MODTRAN simulated sky<lb/> radiance for a solar zenith angle (SZA) of 45°, azimuthal angle<lb/> of 0° and observation zenith angles from 0° to 90°. The highest<lb/> curve is the one with equal observation and solar zenith angles.<lb/> Sweeping the SZA for a wavelength of 1550 nm, the results in<lb/> <ref type="figure">fig. 8</ref> are obtained, after limiting the observation zenith angle<lb/> to 70° and SEP angle to 5°. The average of all the maximum<lb/> sky radiance values has been considered in this work as a worst<lb/> case for daylight operation, giving a result of<lb/> 430 µW/(cm 2 ·srad·µm).<lb/></p>
<p>Next step is computing eq. (2) using the previous result. For<lb/> noise power calculations, a spectral band Δλ of 0.01 nm has<lb/> been considered, although new filtering techniques can<lb/> improve this figure in one order of magnitude <ref type="biblio">[22-24]</ref>. For<lb/> receivers, quantum efficiency has been taken as 75%, although<lb/> 90% values have been achieved recently <ref type="biblio">[25]</ref>. Background<lb/> noise NS is therefore estimated as 70.69 nW for the LST as the<lb/> worst case, 18.35 nW for MST-DC and 15.95 nW for SST-DC.<lb/> SC configurations improve these values several orders of<lb/> magnitude, thanks to their better optical resolution, which<lb/> makes it possible to reduce the FoV: the NS for SST-SC ASTRI<lb/> is 0.183 nW, being 0.052 nW for SST-SC GATE, and<lb/> 0.041 nW for MST-SC.<lb/></p>
<p>Night operation is also affected by background noise. In a<lb/> link with another planet, its albedo is the highest contribution.<lb/> For example, background noise power from Mars is computed<lb/> with eq. (2) but using Mars irradiance IM (in W/cm 2 ·µm)<lb/> instead of the radiance L due to the fact that Mars will be<lb/> always included in the receiver's FoV. Eq. (4) was used to<lb/> compute IM <ref type="biblio">[26]</ref>.<lb/></p>
<formula>IM =AM ·(IS/dM-S 2 )·(RM/dM-T)2<lb/> (4)<lb/></formula>
<p>where AM is the 25% Mars albedo, IS = 28.7 mW/(cm 2 ·µm) is<lb/> the solar irradiance at 1 astronomical unit for 1500 nm, dM-S is<lb/> the 1.52366 astronomical units Mars-Sun distance, RM is the<lb/> 3390 km Mars radius, and dM-T is 68.6·10 6 km, Mars-Earth<lb/> distance in Mars opposition scenario, which is the case during<lb/> nighttime. The background power NM by Mars albedo is then<lb/> calculated with the eq. (5), resulting in 445 pW for LST, 120<lb/> pW for MST-DC and 7 pW for SST-DC.<lb/> </p>
<formula>NM =IM ·π (D/2) 2 ·Δλ<lb/> (5)<lb/></formula>
<head>F. Link budgets<lb/></head>
<p>The link budget equation <ref type="biblio">[21]</ref> applied to a downlink as the<lb/> one simulated here is given by eq. (6), being Pr (dBm) the<lb/> power at the receiver, Pt (dBm) the average transmitted power,<lb/> Gt (dB) the transmitter gain, Lt (dB) the internal transmitter<lb/> losses, Ltp (dB) the transmitter pointing losses, Lfs (dB) the<lb/> free-space propagation losses, Latm (dB) the losses by<lb/> atmospheric propagation, Gr (dB) the receiver gain, Lr (dB) the<lb/> internal losses of the receiver and Lrp (dB) the receiver pointing<lb/> losses.<lb/></p>
<formula>Pr = Pt + Gt – Lt – Ltp – Lfs – Latm + Gr – Lr – Lrp<lb/> (6)<lb/></formula>
<figure>Fig. 8. Sky radiance as a function of zenith angle for different SZA angles at<lb/> λ=1550 nm limited to observation zenith angle of 70º and SEP of 5º.<lb/></figure>
<figure>Fig. 7. MODTRAN Sky radiance for a maritime aerosol at La Palma (Spain)<lb/> observatory. SZA 45º, azimuth 0º, observation zenith angles from 0º to 90º.<lb/></figure>
<table>TABLE III. LINK BUDGET AND SNR FOR EACH SCENARIO ASSUMING WORST-CASE BACKGROUND-NOISE LEVELS. IN EACH CASE, THE SIMPLEST TELESCOPE<lb/> ALTERNATIVES WERE PREFERRED (INDICATED IN Gr BETWEEN BRACKETS, AS WELL AS THE NUMBER OF ELEMENTS WHEN USING AN ARRAY OPERATION).<lb/> LEO<lb/> Moon<lb/> Lagrange L1<lb/> Lagrange L2<lb/> Mars opposition<lb/> Mars conjunction<lb/> Pt (dBm)<lb/> 26.99<lb/> 26.99<lb/> 30<lb/> 30<lb/> 36.02<lb/> 36.02<lb/> Lt (dB)<lb/> -3.01<lb/> -4.81<lb/> -4.56<lb/> -4.56<lb/> -5.19<lb/> -5.19<lb/> Gt (dB)<lb/> 104.20<lb/> 106.77<lb/> 108.74<lb/> 108.74<lb/> 112.98<lb/> 112.98<lb/> Lel (dB)<lb/> -260.46<lb/> -309.86<lb/> -324.2<lb/> -324.2<lb/> -354.91<lb/> -370.22<lb/> Latm (dB)<lb/> -2.64<lb/> -1.44<lb/> -2.64<lb/> -2.64<lb/> -0.42<lb/> -0.42<lb/> Gr (dB)<lb/> 135.29 (1×SST-DC) 135.29 (1×SST-DC) 147.36 (1×MST-DC) 135.29 (1×SST-DC) 147.36 (1×MST-DC) 147.36 (3×MST-SC)<lb/> Lr (dB)<lb/> -3.01<lb/> -3.34<lb/> -4.56<lb/> -4.56<lb/> -4.89<lb/> -4.89<lb/> Lrap (dB)<lb/> -0.11<lb/> -0.31<lb/> -0.08<lb/> -0.08<lb/> -0.05<lb/> -0.05<lb/> Pr (dBm)<lb/> -2.75<lb/> -50.72<lb/> -62<lb/> -62<lb/> -69.1<lb/> -78.7<lb/> SNR (dB)<lb/> 45.22<lb/> 3.27<lb/> 7.7<lb/> 25.3<lb/> 6.15<lb/> 3.74<lb/></table>
<p>Eq. (6) has been used for each telescope and for several<lb/> realistic scenarios: LEO (Low Earth Orbit), Lagrange points 1<lb/> and 2, Moon and Mars in conjunction and opposition (<ref type="figure">fig. 9</ref>).<lb/> For the transmitter and other general parameters, the data from<lb/> the scenario study suggested by the OLSG <ref type="biblio">[20]</ref> was used (see<lb/> <ref type="table">table II</ref>). The rest of the link budget parameters were calculated<lb/> from the simulations presented in the previous sections.<lb/></p>
<p>As an example of operation, L1 scenario is shown in<lb/> <ref type="figure">fig. 10</ref>. L1 is as a worst-case scenario regarding background<lb/> noise. FoV and detection areas have been superimposed to the<lb/> SNR in the plot for each CTA telescope. As can be seen, SNR<lb/> is not dependent on the collection area, but on the FoV (the<lb/> higher the FoV, the lower the SNR). It can be concluded that<lb/> under high background, as it is the case of L1, LEO, Moon and<lb/> Mars conjunction, it is the FoV rather than the aperture what<lb/> determines the SNR. This can be used to compare the<lb/> performance of CTA telescopes when applied to FSOC.<lb/> According to this, in the <ref type="figure">fig. 10</ref> CTA telescopes are shown in<lb/> order of preference from right to left, being MST-SC the most<lb/> advantageous CTA telescope for deep-space communications.<lb/></p>
<p>To check the ability of CTA telescopes to sustain FSOC<lb/> links, in <ref type="table">Table III</ref>, an overview of link budgets and worst-case<lb/> SNR for each scenario is shown. 3 dB was selected as the link<lb/> margin to overcome. Additionally, the condition of at least one<lb/> photon per pulse per telescope was imposed, assuming the use<lb/> of single-photon detectors, commonly used in quantum<lb/> communications <ref type="biblio">[27]</ref> and also recently demonstrated for<lb/> deep-space lasercom links <ref type="biblio">[28]</ref>. For each scenario, smaller or<lb/> DC telescopes were first selected over SC to obtain the<lb/> minimum SNR for being the simplest solutions. In nighttime<lb/> and daytime scenarios, the worst-case (daytime) sky radiance<lb/> values were used, and in night-only scenarios the Mars albedo<lb/> background noise was used. Very occasional moon crossings in<lb/> FoV have not been considered. Moon scenario is based on<lb/> NASA's LLCD, L1 on ESA-NASA's SOHO mission and L2<lb/> on ESA's Euclid mission.<lb/></p>
<p>Receiver's gain is very important and it is the reason of<lb/> higher SNR even for the smallest CTA telescopes in favorable<lb/> scenarios (especially LEO and L2) where smaller telescopes<lb/> would be enough. For example, G r difference in LEO between<lb/> OLSG projected telescope and SST-DC is 17 dB.<lb/></p>
<p>As the Moon scenario is based on NASA's LLCD, the<lb/> bitrate is variable between 40-622 Mbit/s (depending on the<lb/> background and atmospheric conditions). Here, both the<lb/> maximum bitrate and the worst-case background were used<lb/> simultaneously, as a SST-DC (the simplest CTA solution)<lb/> <ref type="figure">Fig. 10</ref>. Field of view (FoV) and aperture area compared with<lb/> signal-to-noise ratio (SNR) for each CTA telescope in L1 scenario.<lb/></p>
<figure>Fig. 9. Downlink scenarios simulated in this work.<lb/> </figure>
<table>TABLE II. PARAMETERS USED IN THE LINK BUDGET CALCULATION.<lb/> LEO Moon<lb/> Lagrange<lb/> L1<lb/> Lagrange<lb/> L2<lb/> Mars<lb/> opposit.<lb/> Mars<lb/> conjunct.<lb/> Propagation<lb/> distance (km)<lb/> 1.3·10 3 384·10 3 2·10 6<lb/> 2·10 6 68.82·10 6 400·10 6<lb/> Mean tx power<lb/> (W)<lb/> 0.5<lb/> 0.5<lb/> 1<lb/> 1<lb/> 4<lb/> 4<lb/> Tx aperture<lb/> diameter (cm)<lb/> 8<lb/> 10.76<lb/> 13.5<lb/> 13.5<lb/> 22<lb/> 22<lb/> Tx transmission<lb/> (%)<lb/> 50<lb/> 33<lb/> 35<lb/> 35<lb/> 30.3<lb/> 30.3<lb/> Tx pointing<lb/> losses (dB)<lb/> 0.11<lb/> 0.31<lb/> 0.08<lb/> 0.08<lb/> 0.05<lb/> 0.05<lb/> Bit rate (bit/s) 10·10 9 622·10 6 120·10 6 700·10 6 260·10 6 764·10 3<lb/> Scintillation<lb/> losses (dB)<lb/> 2<lb/> 1<lb/> 2<lb/> 2<lb/> 0.2<lb/> 0.2<lb/> Atmospheric<lb/> losses (%)<lb/> 86.2<lb/> 90.3<lb/> 86.2<lb/> 86.2<lb/> 95<lb/> 95<lb/> PPM symbols (OOK) 16<lb/> 64<lb/> 16<lb/> 16<lb/> 128<lb/> Rx transmission<lb/> (%)<lb/> 50<lb/> 46.3<lb/> 35<lb/> 35<lb/> 32.4<lb/> 32.4<lb/> Operation<lb/> Night<lb/> and day<lb/> Night<lb/> and day<lb/> Day<lb/> Night<lb/> Night<lb/> Day<lb/> </table>
<p>provides enough margin to close the link.<lb/></p>
<p>The L2 scenario is the most favorable one regarding<lb/> background conditions (although the Mars opposition<lb/> background were applied as a worst case), and using only one<lb/> SST would allow improving the link. For example, instead of<lb/> the 700 Mbit/s assumed by OLSG, a 3.7 Mbit/s link would still<lb/> provide a SNR of 19.28 dB.<lb/></p>
<p>L1 is based on the same transmitter as L2. Hence, in order<lb/> to adapt the link to the worse background conditions, the bitrate<lb/> was reduced and the PPM order increased. This scenario<lb/> suffers from a lot of background noise from the Sun, but one<lb/> MST-DC could still have a link margin of 4.7 dB. If using<lb/> SST-DC, an array of five telescopes would be necessary, as<lb/> each one adds 3 dB, being mandatory at least one photon per<lb/> pulse per telescope.<lb/></p>
<p>Mars opposition shows similar difficulties as L1 regarding<lb/> background noise, adding 30 dB of losses because of the longer<lb/> distance. Increasing the aperture diameter in this case is not<lb/> useful, as Mars albedo is the only background source and it<lb/> enters totally in the FoV, being in this case an irrelevant<lb/> parameter. SST-DC cannot be used in spite of SNR>3 dB,<lb/> because 0.2 photons per pulse would be received. MST-DC is<lb/> the alternative, with a 3.15 dB link margin.<lb/></p>
<p>Mars in conjunction is the worst case scenario: the number<lb/> of background photons per pulse is three orders of magnitude<lb/> above signal photons. The only way to achieve a correct<lb/> detection is using thousands of SST-DC, hundreds of MST-DC<lb/> or tens of SST-SC. Only MST-SC in an array of 3 elements<lb/> could fulfill the 3-dB link requirement.<lb/></p>
<p><ref type="table">Table IV</ref> shows a summary of the worst-case SNR for each<lb/> scenario and each CTA telescope when used as FSOC receiver.<lb/> SNR is computed using the above described link budget and<lb/> background noise simulations. Between brackets, the number<lb/> of telescopes in an array configuration to close the link when a<lb/> single telescope is not enough, is indicated. Only L1 with<lb/> SST-DC and Mars in conjunction links are not fulfilled using<lb/> single telescopes. The rest of the cases are feasible with any<lb/> CTA telescope, proving that all the CTA telescopes could be<lb/> used in FSOC links. In this study, the MST-SC was identified<lb/> as the optimum solution and could serve as a ground station for<lb/> all the scenarios except Mars in conjunction, where an array of<lb/> 3 elements would be required.<lb/></p>
<head>G. Cost<lb/></head>
<p>Regarding costs, <ref type="table">Table V</ref> shows a summary of the<lb/> comparative costs between different ground stations. It can be<lb/> seen that the cost of SST-SC is the lowest one, having an<lb/> excellent performance compared with the DC configurations<lb/> and making it possible to close the simulated links in every<lb/> scenario except Mars conjunction. In general, CTA telescopes<lb/> are cost-effective options when compared to FSOC telescopes<lb/> and especially with astronomical telescopes. However, the<lb/> FSOC telescopes include the adaptations for daylight operation<lb/> and CTA telescopes should be also adapted. 1-m class<lb/> telescope is estimated to need 1 M€ adaptation <ref type="biblio">[20]</ref>. Scaling<lb/> the costs for bigger apertures, CTA telescopes still would have<lb/> lower cost than previously projected FSOC telescopes.<lb/></p>
<head>H. Additional proposed PSF improvements<lb/></head>
<p>There is still an improvement margin for optical resolution<lb/> in CTA telescopes: PSF size can be reduced by using certain<lb/> techniques in order to employ just one single telescope<lb/> dedicated to FSOC at each CTA site. As exposed previously,<lb/> FoV in CTA telescopes ranges from 0.29 mrad (MST-SC) to<lb/> 6.13 mrad (SST-DC), being 0.02 mrad the one assumed at<lb/> OLSG proposals <ref type="biblio">[20]</ref>. A brief list of possible adaptations is<lb/> presented here in order to enhance optical performance in CTA<lb/> primary-focus telescopes:<lb/></p>
<item>• New mirrors to prevent aberrations: all the CTA<lb/> primary-focus telescopes use spherical optics to reduce<lb/> costs, since a huge number of mirrors need to be built.<lb/> Aspheric mirrors should be used instead to greatly<lb/> improve the optical resolution, e.g. shaping a parabola<lb/> in LST to approximate to the original structure profile.<lb/> This would be very appropriate for FSOC, as parabolic<lb/> mirrors ideally lack spherical aberration, and the coma<lb/> would not be very harmful when using the narrow FoV<lb/> needed in FSOC.<lb/></item>
<item>• Field corrector based on group of lenses or mirrors near<lb/> the focal plane: they are also made by using aspheric<lb/> optics, as in the case of COSTAR for Hubble telescope<lb/></item>
<table>TABLE V. APPROXIMATED GROUND STATIONS COSTS ACCORDING TO<lb/> THEIR TYPE (IACT, ASTRONOMICAL OR FSOC).<lb/> Telescope<lb/> Type<lb/> Cost<lb/> CTA SST-SC<lb/> IACT<lb/> <0.5 M€ [29]<lb/> CTA MST-DC<lb/> IACT<lb/> 1.6 M€ [30]<lb/> CTA LST<lb/> IACT<lb/> 7.4 M€ [30]<lb/> GTC / Keck<lb/> Astronomical<lb/> 100 M€ [34]<lb/> Hobby-Eberly / SALT<lb/> Astronomical<lb/> 50 M€ [31]<lb/> OLSG LEO<lb/> FSOC<lb/> 3.4 M€ [20]<lb/> OLSG Moon<lb/> FSOC<lb/> 15.3 M€ [20]<lb/> OLSG L1<lb/> FSOC<lb/> 12.5 M€ [20]<lb/> OLSG L2<lb/> FSOC<lb/> 10.9 M€ [20]<lb/> OLSG Mars<lb/> FSOC<lb/> 102.8 M€ [20]<lb/></table>
<table>TABLE IV. SNR IN dB FOR EACH TELESCOPE AND SCENARIO, INCLUDING<lb/> BETWEEN BRACKETS THE NO. OF TELESCOPES PER ARRAY TO OVERCOME 3 dB.<lb/> LEO<lb/> Moon<lb/> L1<lb/> L2<lb/> Mars<lb/> opp.<lb/> Mars<lb/> conj.<lb/> SST-<lb/>DC<lb/> 45.22<lb/> 3.27<lb/> -3.75<lb/> (5×) 3.2<lb/> 25.30<lb/> 6.15<lb/> -35.88<lb/> (7750×) 3<lb/> CTA-<lb/>LST<lb/> 56.52<lb/> 14.58<lb/> 7.55<lb/> 25.30<lb/> 6.15<lb/> -33.61<lb/> (4600×) 3<lb/> MST-<lb/>DC<lb/> 56.67<lb/> 14.73<lb/> 7.70<lb/> 25.30<lb/> 6.15<lb/> -24.43<lb/> (560×) 3<lb/> SST-SC<lb/> ASTRI<lb/> 67.35<lb/> 25.37<lb/> 18.35<lb/> 25.30<lb/> 6.15<lb/> -13.78<lb/> (48×) 3<lb/> SST-SC<lb/> GATE<lb/> 71.75<lb/> 29.80<lb/> 22.77<lb/> 25.30<lb/> 6.15<lb/> -9.35<lb/> (18×) 3.2<lb/> MST-<lb/>SC<lb/> 80.07<lb/> 50.03<lb/> 31.09<lb/> 25.30<lb/> 6.15<lb/> -1.04<lb/> (3×) 3.7<lb/></table>
<item><ref type="biblio">[32]</ref>, or the solution of Hobby-Eberly telescope, in<lb/> which spherical aberration was corrected by using a<lb/> group of 4 aspherical mirrors, reducing the PSF in three<lb/> orders of magnitude <ref type="biblio">[33]</ref>. FSOC case is also studied in<lb/> <ref type="biblio">[34]</ref> or <ref type="biblio">[35]</ref>, where a segmented spherical reflector is<lb/> covering the 8.3-m central area of a 34-m NASA's<lb/> Deep-Space-Network RF antenna, and a group of four<lb/> 70-cm mirrors is used as a field corrector.<lb/></item>
<item>• Adaptive optics, as in the case of <ref type="biblio">[36]</ref> or <ref type="biblio">[37]</ref>, where 8<lb/> additional dB could be gained when correcting<lb/> atmospheric turbulence in a deep-space link. However,<lb/> this solution should be studied to assess whether it is<lb/> applicable or not for correcting the big aberrations of<lb/> CTA telescopes.<lb/></item>
<head>IV. CONCLUSIONS<lb/></head>
<p>Free-space lasercom holds the promise to alleviate the need<lb/> of faster communications from deep-space. A key step for<lb/> achieving this goal will be the development of a network of<lb/> optical ground stations with very large apertures. However,<lb/> such facilities will require big investments and new ideas are<lb/> needed to minimize costs while maximizing the receiving<lb/> apertures. The reutilization of astronomical facilities has been<lb/> pointed out as a strategic action in this endeavor. A big number<lb/> of Cherenkov telescopes will be built for CTA project in the<lb/> next years. In this work, the feasibility of using CTA telescopes<lb/> for deep-space FSOC has been explored. A deep analysis based<lb/> on all the types of the projected CTA telescopes has been<lb/> carried out. The reflectance of the CTA mirrors has been<lb/> validated at 1550 nm by experimental spectral measurements,<lb/> and a study of the limitations of FoV has been made,<lb/> concluding that the geometrical aberrations are the limiting<lb/> factor in CTA telescopes performance when applied to FSOC.<lb/> A series of OSLO simulations have been carried out to retrieve<lb/> the PSF of each telescope. Other simulations with MODTRAN<lb/> and Matlab were made to obtain the optical link budget for<lb/> realistic scenarios, considering worst cases.<lb/></p>
<p>With the only adaptation of replacing the Cherenkov<lb/> camera by the lasercom equipment and its suitable refocusing<lb/> by a few centimeters towards the focal plane, the possibility of<lb/> using a MST-SC telescope for deep-space FSOC has been<lb/> suggested. This telescope is able to reach over 6-dB SNR for<lb/> every scenario except Mars in conjunction, where an array of 3<lb/> elements would be necessary to close the link. Three possible<lb/> strategies have been suggested to enhance the optical<lb/> performance of CTA primary-focus telescopes in order to<lb/> improve their optical resolution to minimize their field-of-view<lb/> and the received background noise: using aspherical mirrors,<lb/> field correctors and adaptive optics. A brief discussion of the<lb/> costs of Cherenkov telescopes compared with astronomical and<lb/> communication telescopes was made. The conclusion is that<lb/> the cost of optical ground stations based on Cherenkov<lb/> telescopes would be lower than other dedicated FSOC<lb/> telescope currently projected.</p>
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