1.1.

Quantum Key Distribution

QKD uses physical properties of light to distribute randomized or entangled quantum states between two distant parties, enabling them to establish shared secret encryption keys.^15,16 As any attempt to measure an unknown quantum state necessarily perturbs it, any such intrusion by an eavesdropper can be detected. Moreover, an unknown quantum state cannot be cloned so an eavesdropper cannot save a copy of the state to gain information about the secret key, preventing man-in-the-middle attacks. These guarantees are derived from the postulates of quantum mechanics; therefore, unlike classical key distribution, QKD can be proven to be secure without any computational assumption.¹⁷

There are several approaches to achieve QKD over optical links and entanglement is not required for all of them, but nonentanglement-based QKD approaches require a trusted random number generator to perform the protocols. In contrast, with entanglement-based QKD, the randomness is intrinsic to the quantum process. Furthermore, an entanglement-based QKD system can natively supply the means for clock synchronization between the communicating parties.¹⁸ This reduces the number of trusted components that must be incorporated into the overall system.

In entanglement-based QKD, pairs of entangled photons are generated and sent to two separate parties, such that each party is sent one photon from each pair. The two parties independently make measurements on a preselected property of the photons (e.g., their polarization state). Once many such pairs have been distributed and measured, the two parties can perform statistical tests and discuss publicly if the photons they received were entangled. Provided the entanglement measured exceeds a calculated threshold and their hardware is free from vulnerabilities, they can be certain of the security of the protocol. They can then use their private knowledge of the quantum states—information that has not been publicly shared—as a common source of entropy from which to derive symmetric keying material for encryption schemes.

In this study, we use the BBM92 protocol,¹⁹ which is procedurally equivalent to the older BB84 protocol²⁰ but uses entangled photon pairs instead of weak laser pulses. Satellite-based QKD is currently in its infancy; the first fully operational QKD satellite, Micius, developed by the Chinese Academy of Sciences, demonstrated space-to-ground QKD and entanglement distribution in 2017,^8,21,22 but many more missions are in development.⁴

1.2.

Intersatellite Optical Links

A single QKD satellite in a polar orbit can, in principle, serve the entire planet, but to serve large numbers of users in reasonable timescales, constellations of satellites will be required and for any near-term implementation, these satellites would operate as trusted key management nodes.⁴ Such satellite nodes would establish a cache of keys with the ground stations they pass over and, via an RF relay, XOR keys from their cache on demand to allow any two ground stations to establish symmetric keys. While such satellites could all operate independently of each other, if the satellites feature intersatellite QKD crosslinks they are able to balance the keys in their caches to allow for more efficient operations.

Intersatellite optical communication systems and technologies have undergone performance developments and enhancements for several decades.²³ Satellite QKD is essentially a specialized version of free space optics (FSO) communications,²⁴ and the performance capacity of these future systems will be limited primarily by diffraction spreading of the transmitted beam and by the line-of sight (LOS) errors caused by inaccuracies and disturbances generated within the optical transceivers. To mitigate these performance degradation factors, conventional, space-based FSO systems are designed with gimbal-based telescopes to provide course and fine tracking functions.^25–27 Establishing even a traditional optical link between CubeSats is more challenging as the size, weight, and power (SWaP) constraints limit the size of the optical transceivers. We are not aware of any publications on inter-CubeSat QKD, although recent efforts to enable classical optical communications from CubeSats to ground^28,29 and between CubeSats have been reported.³⁰

There are several technological challenges that impact the overall feasibility of any intersatellite quantum communications. These include noise in the receiver path due to stray light, which potentially limits daytime QKD transmission,³¹ diffraction that degrades the optical link margin and therefore places limits on the achievable secure key generation rates and the provision of a pointing, acquisition, and tracking subsystem (PATS) to maintain alignment between the transmitter and receiver as the spacecraft are in a constant motion.³²

2.1.

Mission Operations

During the on-orbit commissioning phase, the spacecraft systems can be tested prior to separation, thus enabling verification of the quantum link at the start of spacecraft commissioning. This led to a design configuration, where the two 6U spacecraft are launched as a single composite 12U spacecraft. The spacecraft is injected into an initial sun-synchronous circular orbit at an altitude between 500 and 550 km (LTDN 10:30) and upon separation they are steered into their operational positions as shown in Fig. 1.

Fig. 1

Spacecraft deployment and separation sequence. They are deployed as a single 12U CubeSat, which, after functional checks, separates into two 6U spacecraft. These are then maneuvered to fly in formation.

During the mission, differential drag maneuvers are used to control the relative velocity of the spacecraft. One spacecraft is commanded to a maximum drag attitude and the other spacecraft to a minimum drag attitude. The total orbital energy of one spacecraft will then decrease more rapidly than the other and cause it to drop to a lower altitude while attaining a higher velocity and shorter orbital period.³³ Once a constant relative separation velocity of $\sim 10\mathrm{cm}/\mathrm{s}$ is achieved, QKD operations can begin.

As the separation range increases, the photon detection rate decreases as the free-space losses increase with the separation distance. As the SNR drops, there will come a point where the percentage of errors in the quantum measurements—the quantum-bit-error-rate (QBER)—will exceed a threshold above which BBM92 QKD^19,34 cannot be realized. Beyond the corresponding separation distance, it should still be possible to perform entanglement distribution demonstrations.

The mission concept is that QKD will be conducted when the spacecraft are in eclipse to minimize noise due to scattered sunlight. With further developments, daylight QKD links³⁵ may be possible, but significant technology challenges remain to develop future operational QKD service networks.^31,36

2.2.

Spacecraft Concept

Both satellites will have a QM, which can both send and receive entangled signal photons. The two satellites will also use a beacon laser and a beacon tracking detector (BTD) to monitor the other satellite’s beacon and control the relative pointing between them. The centroid of the received beacon is determined relative to the boresight of the receiver and a beam pointing correction signal is provided to a two-axis fast steering mirror (FSM). The FSM compensates for high-frequency beam misalignment between the two spacecraft and optimizes the optical link for the transmission of entangled photons. The optical link and spacecraft elements are envisioned as a combination of commercial and custom components.

Figure 2 shows a layout of the key spacecraft and payload subsystems that are supported on an optical bench. The optical bench provides thermal and mechanical isolations and is attached to the spacecraft structure via a three-point mount scheme. The spacecraft platform subsystems are organized within the remaining volume and are shown in Table 1.

Fig. 2

(a) Layout of the main optical payload and (b) the block configuration of the 6U spacecraft including main platform subsystems.

Table 1

Acronym glossary and functional description of spacecraft and payload subsystems.

The orientation of the two 6U satellites in the launch volume is shown in Fig. 3. The launch packing arrangement positions the telescopes with their boresights co-aligned allowing the optical links to be tested prior to the spacecraft separating and facilitates the alignment of the spacecraft and checks of on-orbit functionality.

Fig. 3

(a) Layout of one spacecraft and location of its subsystems. (b) View of both spacecraft in their pre-launch configuration; the thick dashed line indicating the division between the two. In this configuration the telescope boresights are aligned, as indicated by the thin dashed line, allowing for end-to-end functional testing.

The reaction wheels (RW) have been placed, so that their spin axes are as near as possible to the center of gravity to minimize jitter on the pointing stability of the telescope.

2.3.

Quantum Module

Each CubeSat contains a QM composed of a miniaturized polarization entangled photon pair source^12,37 and single-photon detectors. The transmitting QM locally measures and timestamps one of the photons in each pair and sends the other photon in each pair to the receiver spacecraft, where it is detected and timestamped by a nearly identical receiving QM.¹⁸ These timestamp and measurement outcomes are used to synchronize the detections and subsequently to create a symmetric encryption key.

The QM contains a 405-nm laser diode as the pump source that initiates spontaneous-parametric-down-conversion³⁸ in beta-barium-borate crystals generating pairs of photons with wavelengths of 760 and 867 nm, respectively. The photons in each pair are entangled such that their individual polarization states are undefined until a measurement is made, at which point they will have correlated polarizations. In the transmitter QM, 760-nm “signal” photons are transmitted out of the spacecraft and the 867-nm “idler” photons are detected within the QM by silicon avalanche photo diodes (APDs) operating in a Geiger mode (GM-APDs). The basic layout of the QM is shown in Fig. 4.

Fig. 4

QM components, with cover removed. Four APD polarization analyzers and liquid crystal rotator for sampling the output beam are indicated. Sections indicating the electronics and high-voltage power supplies for the detectors are mounted on the underside of the module.

The QM output flux in this study was estimated at $5\times {10}^6\text{photons per second}$, or equivalently $\sim 125\mathrm{pW}$ at 760 nm.¹² This rate must be matched by the detector unit, which is currently the limiting factor to speed increases. The receiver QM detects 760-nm photons, and, in future design iterations, it is intended for it to be able to transmit 867-nm photons (and for the other QM to be able to receive 867-nm photons) for reversing the transmitter and receiver roles.

2.4.

Detector Cooling System

GM-APDs are often cooled with thermoelectric coolers; however, for power- and heat-management reasons, CubeSat thermal control subsystems (TCS) are typically passive and control the temperature of critical items by providing internal thermal resistances and inertias. Accordingly, the baseline design features a dedicated deployable radiator connected to the APDs using copper straps and low surface area mounts between the QM and the optical bench [reference Fig. 2(a)]. A deployable baffle (shown in Fig. 5) and a low emissivity reflective finish on the radiator minimize heating by infrared radiation.

Fig. 5

The spacecraft requires only passive thermal control features. The APDs are connected by a thermal strap to a radiator, which is shielded from external radiative heat sources by a deployable baffle.

The on-orbit thermal performance of the spacecraft has been modeled analytically using finite difference models produced in ESATAN-TMS.³⁹ The spacecraft model contains 244 shells representing the structure, optical subsystems, solar arrays, RF antennas, and external panels. The surface material thermo-optical properties, heat sources, thermal couplings, and the spacecraft geometric model are also modeled. The output is a set of predicted temperature values for various thermal load conditions experienced by the spacecraft in its orbit. The worst-case temperatures predicted during the mission allow an assessment of the system performance and indicate that the TCS can lower operational temperatures of the APDs to $\sim -10°\mathrm{C}$. In many cases, it is desirable to lower APD temperatures to $-20°\mathrm{C}$ or even $-30°\mathrm{C}$ to further suppress dark counts, especially as dark counts increase with radiation damage.⁴⁰ In this design study, however, it will be seen that detector noise is not the limiting factor in the achievable range for the two satellites.

3.1.

Telescope Sizing

The first step in designing the optical link was to select an aperture for the telescopes that respected the SWaP constraints of the 6U CubeSat and could provide reasonable gain. The on-axis telescope gain is directly proportional to the aperture diameter and inversely proportional to the wavelength, such that $G_T=G_R={(\pi D/\lambda )}^2$, where $D$ is the telescope diameter.

Larger apertures produce smaller beam divergences resulting in higher gains, but the power levels measured by a receiver will be more sensitive to beam deflection, because there is more power contained in a narrower beam and the peak intensity can more easily be deflected from the receiver aperture leading to signal fading and dropout. A trade-off between transmitter/receiver gain and uncompensated beam deflection becomes necessary in the design of the optical terminal.

The 6U CubeSat volume limits the size of the telescope, and this impacts the range over which a link can be maintained. The baseline telescope (OTA) is a two-mirror, $F/9$, Ritchey–Chrétien telescope with a clear aperture of 80 mm and a 13% obscuration produced by the secondary mirror. It provides an optical gain of $\sim 110\mathrm{dB}$ ($\lambda =760\mathrm{nm}$) with an assumed average optical transmission factor of 0.7 to account for a worst-case (i.e., end of life) efficiency of the optical coatings.

3.2.

Optical Layout

The optical design of the payload was created using Zemax OpticStudio^®. The size of the active area of the APD detectors in the QM sets a limit on the maximum angular beam deflection that can be tolerated before the transmitted photons would no longer strike the APD. The APD has an active area with a diameter of $\sim 0.5\mathrm{mm}$ and the QM coupling lens is an achromatic doublet with a focal length of 50 mm. The optical layout for the QM channel is shown in Fig. 7, where the received beam is collected by the OTA and relayed to the FSM and dichroic mirror and then into the QM.

Fig. 7

Optical layout of quantum channel; $\lambda =760\mathrm{nm}$; internal optics of QM, including 50-mm lens focus at APD are not shown; on-axis and $\pm 0.01\mathrm{deg}$ off-axis rays are traced using Zemax OpticStudio^®.

Although the quantum signals are individual photons, their propagation in this context can be analyzed classically to show that if the deflection of the received quantum beam is within $\pm 175\mu \mathrm{rad}$ ($\pm 0.01\mathrm{deg}$), then a lateral beam displacement on the APD of $\sim \pm 0.23\mathrm{mm}$ is produced ensuring the photons strike the APD. A larger beam deflection would cause the photons to arrive outside of the APD active area (in the absence of beam pointing correction). The spacecraft ADCS has a pointing uncertainty of $\sim 52\mu \mathrm{rad}$, which is within the uncorrected limit of the system to transmit the received photons to the APDs. However, the predicted channel attenuation given by the link equation and the allowable QBER provides the true requirement for the overall uncompensated pointing error.

3.3.

Beam Pointing

When a laser beam traveling between the transmitter and receiver is deflected, the received optical power is reduced as the Gaussian intensity profile is shifted across the receiver aperture. The intensity of the signal at the receiver can be described as a convolution of the beam intensity and a function of the circular receiver aperture in the local radial coordinate of the aperture, $r$, and the range, $R$, between the terminals.

Figure 8 shows the total attenuation in the optical channel as a function of range for a transmitter/receiver pair with an 80-mm aperture in the presence of uncompensated beam jitter. The attenuation is computed for the cases with rms beam jitter of 0, 0.5, 1.0, 2.0, 5.0, and $10\mu \mathrm{rad}$. The beam divergence ($\lambda =760\mathrm{nm}$) is $6.1\mu \mathrm{rad}$ at the $1/e^2$ intensity values of the peak of the Gaussian beam intensity. The beam divergence is half of the full beam angular dimension. The pointing error loss was modeled as a two-dimensional (2-D) convolution of the Gaussian beam diffraction intensity profile, and the receiver aperture to calculate the final received power at the detector.^44,45 The red horizontal line represents a link attenuation of 39 dB, which corresponds to the QBER threshold of 11% in our system.

Fig. 8

Total link attenuation as a function of spacecraft separation and beam pointing error. APD temperature is assumed to be −10°C, the horizontal threshold line indicates a $\mathrm{QBER}=11\%$.

In the absence of other system perturbations, and if closed-loop tracking can be maintained, a QKD link could be established up to 400 km if an uncompensated beam pointing error of $10\mu \mathrm{rad}$ can be achieved. In this separation limit, the QBER is just below 11% and the key rate is almost zero.

As the CubeSat body pointing capability provided by the ADCS cannot, by itself, meet such pointing and tracking requirements a dedicated fine pointing capability is needed. Appendix A describes an architecture that uses a laser beacon, a BTD, and an FSM to provide fine angular beam control. Further design iterations of this subsystem will be required, however, for it to function reliably at distances beyond 150 km as the SNR of the measured tracking signal is currently too low at this range.

5.1.

Optical Beacon

The optical beacon subsystems include a laser diode, relay optics, optical fiber, and a second, smaller telescope—the Beacon Telescope Assembly (BTA). The diameter of the BTA is chosen such that the projected beam covers an area larger than the predicted location zone of the partner spacecraft beyond the minimum desired operation distance. In the baseline configuration, the beacon laser module includes temperature-controlled laser diode driver circuitry and control electronics. An optical fiber coupled to the output of the laser diode package is routed through the spacecraft to the focus of the BTA, which is mounted on the OTA metering structure and coaligned to the OTA optical axis.

Several commercially available laser diode modules with varying output powers and wavelengths were considered. The baseline beacon is a commercially available 785 nm, 250 mW Fabry–Perot laser diode integrated in a 14-pin butterfly package. The module contains an integrated thermoelectric cooler (TEC), thermistor, and laser output monitor photodiode. The laser output is coupled into a 1-m-long polarization preserving fiber, which has a loss factor of $-3.5\mathrm{dB}/\mathrm{km}$. The output power is lower than typical telecommunications lasers, but a laser that emits in the visible spectrum is easier to align. A beacon at 785 nm is also ideal for generating photocurrent in silicon, where the normalized responsivity is at its peak. It will not, however, allow the QM units to be operated where the 867-nm idler photons are chosen for transmission. In the baseline configuration, the transmitter/receiver role switching would have to be sacrificed or an alternative design arrangement sought, where the beacon wavelength is greater than the entangled photon wavelengths. For example, a telecommunications laser operating at 1550 nm could be used for the beacon.

5.2.

Beacon Telescope

The beacon telescope projects the beacon light emanating from the optical fiber into space for the partner spacecraft to track. The fiber has a NA of $\sim 0.13$. The baseline beacon telescope is a commercially available fiber-coupled collimator assembly with an NA of $\sim 0.14$, an effective focal length of 60 mm, and a clear aperture of 16 mm. It produces a collimated beam with a width of $\sim 11\mathrm{mm}$ and a full divergence angle of $\sim 90\mu \mathrm{rad}$ at 785 nm. Considering transmission losses of the fiber and lens insertion losses an 80% optical path efficiency was assumed yielding an overall gain of $\sim 92\mathrm{dB}$.

The beacon signal transmitted by the BTA on one spacecraft is collected by the OTA on the receiver spacecraft. The optical path layout for this portion of the system is shown in Fig. 9. In addition to a dichroic beam splitter, spectral isolation is provided by two 10-nm narrow bandpass filters (not shown) where one is tuned to 760 nm in the QM path and another tuned to 785 nm in the beacon path. The overall throughput for the beacon receiver optical path is $\sim 0.6$, which includes transmission factors for each of the optical elements.

Fig. 9

PATS beacon detector optical path; on-axis and off-axis ($\pm 0.05\mathrm{deg}$) rays are traced using Zemax OpticStudio^®.

5.3.

Beacon Detector

The beacon detector must provide ample sensitivity to detect the imaged beacon while providing fast readout and low noise to produce accurate error correction data to the FSM controller. Several candidates have been investigated including Si-based CCD and CMOS arrays, Si- and InGaAs quadrant detectors, and position sensing detectors.^26,50

The preliminary design uses a commercially available CMOS array. Reasonable pixel size, dynamic range, and readout rate were key design drivers. For the PATS system, a minimum frame rate of $\sim 50$ to 100 Hz is needed to achieve adequate beacon tracking. The baseline detector has global shuttering and region of interest selection capability. The pixel size is $\sim 4.8\mu \mathrm{m}$ providing sufficient sampling of the beacon image point spread function (PSF), which has a full-width of $\sim 25\mu \mathrm{m}$ on-axis. The array active area is $\sim 3.6\mathrm{mm}\times 2.7\mathrm{mm}$.

In a receiver mode, a $5\mu \mathrm{rad}$ angular offset in the incoming beam yields a shift of the beacon image centroid of $\sim 5.2\mu \mathrm{m}$ (slightly $>1.2\text{pixels}$). A one-pixel centroid offset provides a conservative indication of the minimum uncompensated pointing error correction that the PATS can achieve. For the baseline, this value is then $\sim 5\mu \mathrm{rad}$. Subpixel motion detection may be possible, but the total system noise must first be assessed.

The beacon detector field of regard (FOR) is limited by the physical size of the array and any vignetting in the optical path. The SWaP constraints of the spacecraft limit the size of the optical components that can be accommodated. In the baseline configuration, a $\pm 0.1\mathrm{deg}$ ($\pm 1.75\text{milliradians}$) angular deflection produces almost 50% vignetting of the beacon beam. When the beam deflection is kept below $\pm 0.06\mathrm{deg}$ ($\pm 1.0\text{milliradians}$) there is no vignetting (which is the case in closed-loop tracking). During open-loop acquisition, some beam vignetting may be incurred; however, during closed-loop tracking no vignetting of the beacon occurs. Correcting for beam jitter with a resolution of $5\mu \mathrm{rad}$ ensures the received photons will fall on the APD active area.

5.4.

Beacon Deflection Sensitivity

The optical components and detector are sized, so that the receiver can acquire the transmitter beacon in a open-loop mode without additional scanning. For example, at a range of 50 km, the BTD dimensions are projected into a zone that would have $\sim 0.23\text{-}\mathrm{km}$ diagonal. Given the uncertainty in the GPS location of the two spacecraft and uncertainty in the AOCS pointing capability (which is estimated at $52\mu \mathrm{rad}$ $1-\sigma$), the BTD on the receiver spacecraft should still see the transmitted beacon without the need for raster scanning by the FSM.

Even with the worst-case uncertainty in pointing and location of the two spacecraft, the BTD FOR can capture a point source that is up to $\pm 0.1\text{-}\mathrm{deg}$ off-axis. In addition to acquiring the beacon, the BTD must also sense when the beacon angular position varies. The link analysis of the optical channel showed that a maximum uncompensated pointing jitter of $\sim 10\mu \mathrm{rad}$ can be tolerated. The BTD has a pixel plate scale of $\sim 5.1\mu \mathrm{rad}/\text{pixel}$. This is the minimum beam deflection that can be sensed, and the FSM must provide at least this level of steering accuracy to yield a system capable of maintaining alignment between the spacecraft. The uncertainty in the pointing capability of the baseline AOCS would result in a beacon image displacement at the detector of $\sim 23\mu \mathrm{m}$. This multiple pixel displacement should be easily detected.

5.5.

Fast Steering Mirror

A central element of the PATS is the FSM. The FSM provides beam pointing compensation and scanning capability. Several commercially available two-axis fast-steering mirrors with angular resolutions of $<1\mu \mathrm{rad}$ have been considered. The baseline FSM contains an $18\text{-}\mathrm{mm}\times 24\text{-}\mathrm{mm}$ glass substrate with a high-reflectance coating having a rms wavefront error of $<\lambda /4$ @ 633 nm. The FSM actuator mechanism has a travel range of up to 160 milliradians and a step size in closed-loop operation of $1.0\mu \mathrm{rad}$ with a total induced jitter of $0.7\mu \mathrm{rad}\mathrm{rms}$. The closed-loop servo bandwidth is $\sim 350\mathrm{Hz}$.

5.6.

Beam Control

The control bandwidth of the FSM servo system will depend on the actual spacecraft disturbance spectrum. A preliminary analysis shows that the frequency disturbance due to AOCS single reaction-wheel imbalance at 3000 rpm is $\sim 3\mu \mathrm{rad}$ at 60 Hz. A passive isolation system can be used as a possible feature of the PATS, depending on other trade-offs.

The main PATS hardware elements are shown in Fig. 9. The received light is acquired by the OTA and recollimated by relay lens 1. The beam then reflects from the FSM to the dichroic beamsplitter (DBS), which transmits light $>770\mathrm{nm}$ to relay lens 2, which focuses the beam onto the BTD. The DBS reflects light with wavelength $<770\mathrm{nm}$ to the QM.

The centroid of the beacon image is calculated by the detector readout electronics and fed to a proportional integral derivative (PID) controller. The PID control signals are sent to the FSM driver to change the angular position of the FSM in response to input beam angular deflections. The focused beacon beam is steered to stabilize the beacon image at the pixel corresponding to the LOS of the receiver optical path.⁵¹ The detector can operate at full-frame readout rates up to 545 fps at $10\text{bits}/\text{pixel}$. Performance should be improved by implementing subpixel tracking error compensation. A breadboard system is being constructed at UNSW Canberra to validate tracking models and determine sensitivities for the PATS.

5.7.

Control Loop Limitations

The total tracking error will be the sum of the uncompensated error plus any noise-induced error. The noise equivalent angle (NEA) is that angle that cannot be corrected due to all noise sources present in the system. As the NEA is a combination of error sources including the detector noise, beacon brightness variations, PATS noise, and statistical uncertainties in beam centroid computations, the frequency characteristics of all these terms must be considered with respect to the control bandwidths of the elements comprising the PATS. It will be important to understand the proportion of the total disturbances that are not corrected as well the fraction that are not sensed in determining the total uncompensated pointing error.⁵²

A first step in assessing the PATS capability is to estimate the radiative transfer of beacon energy from the transmitting spacecraft to the receiver. In radiometric terms, the receiver at-aperture beacon radiance is transferred along the optical path to form an image at the BTD, which can be described in units of energy per unit area. The energy is converted on a per-pixel basis into photocurrent and then into a digital number (DN), where the range of DN spans the charge capacity of the pixel. The conversion characteristics of the BTD provide the conversion from irradiance to photocurrent and an estimate of the detected beacon SNR. The beacon will appear to the receiver as a point source rather than as an extended object. The ensquared energy of the beacon image formed on the detector predicts that 90% of the energy is contained within an image diameter of $\sim 40$ to $50\mu \mathrm{m}$.

The link equation accounts for the expansion of the beacon beam from the transmitter BTA to the aperture of the receiver OTA. The baseline BTA has a gain equal to $\sim 95\mathrm{dB}$, (where the beam at the $1/e^2$ points just under-fills the BTA aperture). The OTA receiver has a gain of $\sim 110\mathrm{dB}$, and the optical throughput and QE of the BTD have been used to compute the signal electrons generated by the BTD.

Figure 10 shows a plot of the BTD signal electrons as a function of range between the two spacecraft, where the beacon laser is emitting at a maximum power output of 0.25 W and the BTD frame rate is set to 25 fps with an integration time of $100\mu \mathrm{s}$. The beacon channel SNR remains above 10 for separation distances approaching $\sim 100\mathrm{km}$. At spacecraft separations of $<\sim 15\mathrm{km}$, the imaged beacon flux would saturate the BTD as the full well capacity is only $\sim \mathrm{10,000}$ electrons. At these distances, a lower power setting can be selected.

Fig. 10

Beacon signal level and SNR as a function of spacecraft separation.

The loss in beacon signal and the probability of burst errors (PBE) as a function of the beamwidth to rms pointing error ratio produces an estimate equal to $\sim 1\times {10}^{-4}$. To increase the operational range for the system and reduce the PBE even further, a higher power beacon laser can be considered or longer integration times.

The initial concept of operations foresees QKD only being performed while the spacecraft is in eclipse to avoid noise from stray light. However, during operations, the BTD on each spacecraft will see a stellar background. The projection of the array on the sky will be $\sim 5\text{milliradians}$ on the diagonal and at a range of 100 km, the resultant solid angle is $\sim 2\times {10}^{-5}\mathrm{sr}$.

The number of objects brighter than the dimmest detectable object located within a solid angle as seen from the Earth leads to an estimation of the number of objects brighter than the dimmest detectable object. There could be $\sim 1600$ objects brighter than the beacon visible from Earth above the hemisphere (National Solar Observatory, Sacramento Peak, California). The sensitivity of the BTD allows stellar objects brighter than apparent visual magnitude 4 to be detected. A simple ratio of the solid angle subtended by the BTD to the hemisphere indicates that there will be virtually no stellar objects bright enough to compete with the beacon. However, the beacon signal can be further isolated from the stellar background using spectral filtering as well as temporal modulation of the beacon laser.

5.8.

Centroid Computation Methods

A preliminary estimate of the beacon centroid error has been computed assuming a simple center-pixel algorithm. The beacon source will be focused to a spot of $\sim 25\mu \mathrm{m}$, which will be oversampled with the $5.5\mu \mathrm{m}$ square pixels. Subpixel errors in centroid position estimation are foreseen. Several standard centroid estimating methods are the subjects of ongoing investigations.^53–55

5.9.

Beacon Link Margin

Errors in spacecraft location due to uncertainties in the GPS signal are assumed to be on the order of 0.5 to 1.0 m in each axis.⁵⁶ The baseline concept of operations relies solely on the body pointing of the spacecraft to acquire the beacon in a open-loop mode. Immediately after separation, the uncertainty in the locations of the two spacecraft will not allow the receiver to acquire a transmitted beacon reliably as the baseline design does not include provision for scanning. So, a minimum spacecraft separation must be reached before the transmitted beam will be within the receiver field of view. A scanning feature could be provided by the ADCS, by the addition of an additional scan mirror, or by using the existing FSM in a scan mode for which a separate scan servo loop would need to be designed.

For an example, a spacecraft separation of 5 km, the beacon beam diameter would be $\sim 2\mathrm{m}$ and would cover the uncertainty zone in which the receiver should be located. The baseline design provides margin for beacon detection for spacecraft separation $>100\mathrm{km}$. An example beacon link budget is shown in Table 2.

A preliminary pointing budget for the beacon subsystem is shown in Table 3. The estimated static bias errors can be accommodated within the FOR of the BTD. These allocations are preliminary and refinement is ongoing, but the budget is within the derived requirement of $10\mu \mathrm{rad}$ uncompensated jitter and less than the plate-scale resolution of the PATS.

The beam pointing margin for the quantum channel can only be as good as that established by the beacon-based PATS. An uncompensated beam deflection of $10\mu \mathrm{rad}$ will cause a shift of the received quantum beam on the QM APD of $\sim 25\mu \mathrm{m}$, which is well within the sensitive area of the APD detector.

Table 2

Beacon channel link budget; range 100/300  km, λ=785  nm, NEA∼10  μrad.

Table 3

Beacon pointing budget.