2.1

Limiting noise counts

The most challenging aspect of designing a CubeSat is minimizing total noise counts R_B+D which therefore influences many design parameters. Unavoidable stray light collected by the CubeSat’s receiving telescope (i.e., background counts R_BG) and the intrinsic thermal/radiation damage counts of the detectors (i.e., dark counts per detector R_DC) add up to R_B+D = R_BG + 2R_DC and significantly degrade the signal-to-noise ratio (SNR). R_DC, which we assume to be constant, has to be below 200 cps per detector to achieve a reasonable SNR. Firstly, the detector noise is reduced when operating at low temperatures. –30°C diode temperature is desirable. Two 250 cm² radiators on the sun-averted sides of the CubeSat could dissipate the 0.6 W of thermal energy required to cool both detectors. A heating resistor should be used to further regulate the temperature to within ±1°C. While R_DC of such a cooled detector can be less than 5 cps in laboratory conditions¹⁷, it is increased by damage due to energetic particles and ionizing radiation in space. This can be mitigated by using very small active detector areas d_B. The smallest commercially available ones have a d_B of 20 μm, which we expect to be small enough to keep R_DC well below the 200 cps limit¹⁸ despite a radiation damage equivalent to a 2 year mission lifetime. Using other satellite components such as high density batteries accounts for additional radiation shielding. We therefore assume a constant 200 cps of thermal and radiation noise per detector which is, at least for the first months of operation, a conservative estimate.

R_BG are the erroneous measurement clicks due to near-infrared noise photons originating from the ground area which are not blocked by the spectral filters. As a worst-case scenario, we account for scattered sunlight from a full moon (brightness: 4000 cd/m²)¹⁹ reflected from earth (mean albedo: 0.3)²⁰ into to the CubeSat (we used the solar radiation spectrum). We then translate the luminous intensity into photons per second per m² footprint impinging on the CubeSat telescope with aperture D_B = 10 cm and calculate how many of these photons would pass through our 3 nm wide bandpass filters centered at 810 nm. We arrive at values of 0.55 photons s^–1m^–2 in zenith and 0.17 photons s^–1m^–2 for the lowest elevations (because of the larger distance between OGS and satellite). This effect of decreasing background counts per area for low elevations is however less significant than the increase in area because of the larger footprint on ground. The closer the CubeSat is to the horizon, the more ground area is covered by the satellite’s FoV since the circular footprint in zenith changes to a substantially larger elliptical one. Optical losses and detection efficiency of the CubeSat on the other hand reduce the background count value again (see below in this section). In total this gives us a worst-case estimate of total noise counts which we use for all orbits regardless of the moon phase: R_B+D varies from ≈480 cps in zenith to ≈575 cps at 30° elevation from horizon. This assumption is very conservative, especially when considering the 350 cps total noise counts at full moon of a similar uplink experiment²¹.

2.2

Field of View (FoV) and attitude control

For a given orbit height of 500 km and imperfect filters, R_BG can only be reduced by reducing the field of view (FoV = d_B/f_B where f_B is the CubeSat telescope’s effective focal length). This has two additional benefits: A long f_B improves the polarizing beam splitter’s (PBS) extinction ratio since it reduces the divergence of the impinging beam within the PBS. More importantly, a small d_B strongly reduces the radiation damage to the detector due to its small cross sectional area. However, the FoV must be large enough to maintain the OGS in view despite the pointing errors of the CubeSat. Until recently, the attitude control of small CubeSats was too imprecise, requiring a large FoV that would have resulted in too many background counts to make the mission possible. The latest commercially available CubeSat attitude control systems based on star trackers have shown a body pointing precision σ_B of better than 40 μrad RMS (full angle)^22,23. The resulting pointing losses Λ_PB due to this error, which are caused by an effective spot size broadening on the detectors when averaging over time, can be shown to be

This attitude precision allows us to limit the FoV < 50 μrad while introducing pointing losses 1/Λ_PB of 2.5 dB. These comparably high losses are outbalanced by the strongly reduced R_BG because of the narrow FoV. Roll axis precision is about a factor of 10 worse²⁴, however misalignment here only leads to an increase in erroneous detections e_d on the CubeSat. Even with misalignment in the order of tens of mrad, its contribution to e_d stays below 0.1%. Optically tracking the beacon signal holds the potential to further improve Λ_PB. Another attitude system requirement is a sufficient slew rate. To keep the OGS in view, the CubeSat should be able to turn with up to 1°/s; this can easily be provided by the system in consideration (10°/s slew rate in pitch and yaw axes for a 4 kg 3U CubeSat²²). To achieve an optimal f_B, a Cassegrain-type reflector is a good choice for the receiving telescope despite the decreased telescope transmission due to the secondary mirror (which we estimate to be –1.5 dB in total). This is because the overall design is lightweight and the required f_B of 40 cm can be realized with a 10 cm long telescope. The telescope covers the CubeSat’s square Z+ surface of about 9 × 9 cm. For simplicity, our calculations assume a circular telescope with D_B = 10 cm.

2.3

Dead time and timing resolution

To ensure that saturation and dead time effects do not cause losses >0.1 dB, we require a maximum count rate of each CubeSat detector in the order of 100 kHz. The detectors consist of actively quenched silicon-based avalanche photo diodes (APDs) operated in Geiger mode, placed at the output ports of the PBS. The detector diameter d_B of only 20 μm strongly reduces the cross sectional area for harmful radiation. Therefore little to no radiation shielding is required, which also has a positive effect on the mass budget.

Errors in Q.Com arise from accidental coincidences and are therefore related to the coincidence detection time window τ. To correctly identify and distinguish at least 98% of all pairs, τ has to be greater than ≈2√(t_A² + t_B²), where t_A = 10 ps is the timing jitter on ground and t_B that on the CubeSat. Thus t_B, including the jitter of the detectors¹⁷ and the time tagging electronics that note the arrival time of each pulse²⁵,²⁶, should be less than 40 ps to ensure that we can choose τ = 80 ps which is crucial to improving the SNR. The detection efficiency of the detectors η_B we chose is ≈15%. This might seem low, however we trade this for excellent temporal resolution.

In addition to the quantum payload, the CubeSat optics should also accommodate an earth-facing beacon diode to aid in the ground station’s tracking of the CubeSat. There should also be a dichroic mirror to separate the quantum signal from the OGS beacon. The latter assists in locating and tracking the OGS and can be detected by a fast quadrant photo diode. The OGS’s beacon signal is pulsed to facilitate clock synchronization, and the detection pulses from the fast photo diode (along with GPS signals) are used to discipline the local clock on board the CubeSat.