Free-space optical communication module for small satellites

Abstract

Communication bottlenecks, particularly in the downlink direction, are a common problem for many CubeSat developers. As described herein, a CubeSat module for a CubeSat comprises an optical transmitter to transmit data to a remote terminal, a receiver to acquire an optical beacon from a remote terminal, and a fine-pointing module operably and directly coupleable to a coarse-pointing module of the CubeSat. The fine-pointing module is configured to point the optical transmitter toward the remote terminal with an accuracy range that overlaps with an accuracy range of the coarse-pointing module of the CubeSat so as to establish a communications link between the CubeSat and the remote terminal over a low-Earth-orbit (LEO) distance.

Claims

1. A Cubesat module for a CubeSat, the CubeSat module comprising: an optical transmitter to transmit data to a remote terminal; a receiver to acquire an optical beacon from the remote terminal; and a fine-pointing module, operably coupled to a coarse-pointing module of the CubeSat, to point the optical transmitter toward the remote terminal with an accuracy range that overlaps with an accuracy range of the coarse-pointing module of the CubeSat so as to establish a communications link between the CubeSat and the remote terminal over a low-Earth-orbit (LEO) distance, wherein the coarse-pointing module is configured to point the CubeSat by slewing a body of the CubeSat.

2. The Cubesat module of claim 1, wherein the CubeSat module does not include an electromechanical gimbal.

3. The Cubesat module of claim 1, wherein the fine-pointing module comprises at least one microelectromechanical systems (MEMS) micromirror, in optical communication with the optical transmitter, to adjust an orientation of an output of the optical transmitter with respect to a pointing direction of the CubeSat.

4. The Cubesat module of claim 3, further comprising at least one actuator, operably coupled to the at least one MEMS micromirror, to actuate the at least one MEMS micromirror about two axes.

5. The Cubesat module of claim 1, wherein the CubeSat module is dimensioned to fit within a volume of about 10 cm by about 10 cm by about 5 cm.

6. A method of free-space optical communication for a CubeSat, the CubeSat comprising a beacon receiver, a coarse-pointing module, an optical transmitter, and a fine-pointing module operably coupled to the coarse-pointing module, the method comprising: pointing, with the coarse-pointing module, the beacon receiver toward a terrestrial terminal with an attitude accuracy of within about 3°; acquiring, at the beacon receiver, a beacon from the terrestrial terminal; in response to acquiring the beacon, pointing, with the coarse-pointing module, the beacon receiver toward the terrestrial terminal with an attitude accuracy of within about 1°; pointing, with the fine-pointing module, a beam emitted by the optical transmitter toward the terrestrial terminal with a pointing accuracy of about 0.03°; and establishing an optical downlink between the CubeSat and the terrestrial terminal.

7. A method of free-space optical communication for a CubeSat, the CubeSat comprising a beacon receiver, a coarse-pointing module, an optical transmitter, and a fine-pointing module operably coupled to the coarse-pointing module, the method comprising: pointing, with the coarse-pointing module, the beacon receiver toward a terrestrial terminal with an attitude accuracy of within about 3°; acquiring, at the beacon receiver, a beacon from the terrestrial terminal; in response to acquiring the beacon, pointing, with the coarse-pointing module, the beacon receiver toward the terrestrial terminal with an attitude accuracy of within about 1°; pointing, with the fine-pointing module, a beam emitted by the optical transmitter toward the terrestrial terminal with a pointing accuracy of about 0.03°; establishing an optical downlink between the CubeSat and the terrestrial terminal; determining (1) a location of the CubeSat, relative to the terrestrial terminal, and (2) an attitude of the CubeSat, based on the beacon acquired at the beacon receiver; and transmitting, via the optical transmitter, the location of the CubeSat and the attitude of the CubeSat to the terrestrial terminal.

8. The method of claim 6, further comprising: transitioning from pointing with the coarse-pointing module to pointing with the fine-pointing module in response to acquiring the beacon at the beacon receiver.

9. A CubeSat comprising: a beacon receiver to acquire an optical beacon emanating from a terrestrial terminal; a coarse-pointing module to align the beacon receiver with the optical beacon over a first accuracy range prior to acquisition of the optical beacon by the beacon receiver and to align the beacon receiver with the optical beacon over a second accuracy range in response to acquisition of the optical beacon, the second accuracy range being smaller than the first accuracy range; an optical transmitter to transmit data to the terrestrial terminal; and a fine-pointing module, operably coupled to the coarse-pointing module, to point a beam emitted by the optical transmitter toward the terrestrial terminal with an accuracy range that overlaps with the second accuracy range of the coarse-pointing module, wherein the CubeSat is configured to autonomously slew, with respect to the terrestrial terminal, after an initial alignment of the beacon receiver with the optical beacon.

10. The CubeSat of claim 9, wherein the coarse-pointing module is configured to align the beacon receiver with the optical beacon using body-type pointing.

11. The CubeSat of claim 9, wherein the CubeSat module does not include an electromechanical gimbal.

12. The CubeSat of claim 9, wherein the fine-pointing module comprises a microelectromechanical systems (MEMS) micromirror actuatable about two axes to adjust an orientation of the optical transmitter with respect to the optical beacon.

13. A CubeSat comprising: a beacon receiver to acquire an optical beacon emanating from a terrestrial terminal; a coarse-pointing module to align the beacon receiver with the optical beacon over a first accuracy range prior to acquisition of the optical beacon by the beacon receiver and to align the beacon receiver with the optical beacon over a second accuracy range in response to acquisition of the optical beacon, the second accuracy range being smaller than the first accuracy range; an optical transmitter to transmit data to the terrestrial terminal; a fine-pointing module, operably coupled to the coarse-pointing module, to point a beam emitted by the optical transmitter toward the terrestrial terminal with an accuracy range that overlaps with the second accuracy range of the coarse-pointing module; and an electronics module, operably coupled to the optical transmitter, to perform interleaving to mitigate atmospheric fading so as to reduce an error rate associated with transmitting data via the communications link.

14. The Cubesat module of claim 13, wherein the CubeSat does not include an electromechanical gimbal.

15. The method of claim 9, wherein the CubeSat is configured to autonomously slew, with respect to the terrestrial terminal, at a slew rate of 1° per second.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and/or structurally similar elements).

(2) FIG. 1 is a rendering of a satellite communication system according to some embodiments.

(3) FIG. 2 is a block diagram of a satellite communication system according to some embodiments.

(4) FIGS. 3A-3C are renderings of a physical layout, including perspective, top and side views, respectively, of a communications payload, occupying a 0.5 U volume of a CubeSat, according to some embodiments.

(5) FIGS. 4A-4C show a pointing, acquisition and tracking (“PAT”) process, according to some embodiments.

(6) FIG. 5 is a rendering of a satellite communication system according to some embodiments.

(7) FIG. 6 is a rendering of a first step in a PAT process implemented using the system of FIG. 5.

(8) FIG. 7 is a rendering of a second step in a PAT process implemented using the system of FIG. 5.

(9) FIG. 8 is a rendering of a third step in a PAT process implemented using the system of FIG. 5.

(10) FIG. 9A is a rendering of a closed-loop tracking configuration using a quadcell tracking detector, according to some embodiments.

(11) FIG. 9B is a rendering of a closed-loop tracking configuration using a focal plane tracking detector, according to some embodiments.

(12) FIG. 10 is a system block diagram showing components of a ground segment according to some embodiments.

(13) FIG. 11 is a block diagram showing components of a high power laser diode, according to some embodiments.

(14) FIG. 12 is a block diagram showing components of a master oscillator power amplifier (MOPA), according to some embodiments.

(15) FIG. 13 is a diagram showing a linear single-axis model of an attitude control system, according to some embodiments.

(16) FIG. 14 is a flow-down diagram of key parameters of attitude determination and control systems, according to some embodiments.

(17) FIG. 15 is a flow-down diagram of constraints and parameters of attitude determination and control systems, according to some embodiments.

(18) FIG. 16 is a transmitter test configuration according to some embodiments.

(19) FIG. 17 is a plot of wavelength versus DC laser bias, with each curve corresponding to a different seed laser temperature, according to some embodiments.

(20) FIG. 18 is a plot of power consumption versus temperature for an exemplary transmitter, according to some embodiments.

(21) FIG. 19 is a plot of insertion loss versus frequency, comparing 5 GHz and 10 GHz passband filters, according to some embodiments.

(22) FIG. 20 is a plot showing extinction ratio measurements for a seed laser with an extinction filter, according to some embodiments.

(23) FIGS. 21A-21F show a sequence of system components and related electrical and optical input/output waveform plots, according to some embodiments.

(24) FIGS. 22A and 22B are bode plots showing the frequency response of a fine steering mirror, with and without a Bessel filter, respectively, according to some embodiments.

(25) FIGS. 23A and 23B show power/performance plots for erbium-doped fiber amplifiers (“EDFAs”), according to some embodiments.

(26) FIG. 24 is a plot showing atmospheric refractive index structure parameter profiles for a stationary beam and for a beam with 1°/s slew speed, according to some embodiments.

(27) FIGS. 25A and 25B are images simulating the identification of a beacon region of interest, according to some embodiments.

(28) FIGS. 26A and 26B are plots showing beacon acquisition simulation results, according to some embodiments: FIG. 26A is a plot of fade probability for various transmit laser power levels; and FIG. 26B shows the percentage pointing accuracy during centroiding.

(29) FIG. 27 is a plot showing attitude error for systems using a coarse pointing stage with and without a fine pointing stage, according to some embodiments.

DETAILED DESCRIPTION

(30) Communication bottlenecks, particularly in the downlink direction, are a common problem for many CubeSat developers. Radio frequency solutions have poor link power efficiency (joules per bit), may be limited by antenna gain, and often carry complex regulatory burdens. Most CubeSats are in LEO and have fairly short ground station access times (<10 min/pass). CubeSats often use low-rate ultra-high frequency (UHF) links, with data rates for amateur bands of ˜1200 bps and for industrial, scientific and medical (“ISM”) radio bands of <115 kbps. High-rate radio frequency (RF) commercial off-the-shelf (COTS) products are available for UHF and S-band communications, but very large ground apertures are typically required. Furthermore, the pointing accuracy required for a high bandwidth downlink exceeds the capabilities of traditional CubeSats. The current state-of-the-art in demonstrated CubeSat absolute pointing accuracy ranges from 1-5° RMS. However, to achieve a 10-50 Mbps link within the power constraints of a typical CubeSat, a finer pointing accuracy is required.

(31) Systems of the present disclosure comprise an optical transmitter to transmit data to a remote terminal, a receiver to acquire an optical beacon from a remote terminal, and a fine-pointing module operably and directly coupleable to a coarse-pointing module of the CubeSat. A two-stage control approach to pointing, acquisition and tracking (“PAT”) is used, in which coarse body pointing of the CubeSat (e.g., the host attitude determination and control system, “ADCS”) is augmented with a fast-steering mirror (FSM) for fine control (a “coarse” stage and a “fine” stage, respectively). In some embodiments, a free-space optical (“FSO”) communications system is “asymmetric,” in that it includes both a high-rate optical downlink (“DL”) and a low-rate RF link (“UL”), as well as an optical beacon for acquisition and tracking. CubeSat FSO communication payloads described herein are designed to be compatible with a typical 3-axis stabilized CubeSat, and the system architecture of the disclosure takes into account the fact that many operators of FSO communications systems need a high-rate downlink (e.g., for remote sensing).

(32) FSO communications systems of the disclosure provide functionality for day and/or night operation, with better access and throughput than has previously been possible. In some embodiments, sun sensors are used for attitude determination. In some embodiments, the PAT system does not use a 2 axis electromechanical gimbal. PAT systems of the disclosure can improve coarse pointing by about 4 orders of magnitude as compared with prior methods. Fast beam steering can be performed using microelectro-mechanical systems (“MEMS,” e.g., fast-steering mirrors, micro-mirror arrays, etc.), acousto-optical methods, optical phased arrays, and/or the like.

(33) In some embodiments, an incoherent (direct) satellite FSO communications system includes a coarse stage pointing subsystem, a fine stage pointing subsystem, and a beacon acquisition subsystem. The coarse stage pointing subsystem has an accuracy range of +/−about 5 degrees when “unlocked” with respect to a beacon, and +/−about 1.25 degrees or +/−about 1 degree when locked to the beacon. The fine stage pointing subsystem has an accuracy range of ˜+/−1 degree. The accuracy range of the coarse stage can overlap with the accuracy range of the fine stage. In some embodiments, the coarse stage subsystem and the fine stage subsystem have accuracy ranges that overlap the improved uncertainty range (e.g., after acquisition of a beacon and the corresponding improvement in satellite position knowledge). Collectively, the two-stage pointing control mechanism can achieve a pointing performance of ±0.09 mrad 3-σ without bias, sufficient for a 2.1 mrad downlink laser.

(34) In some embodiments, terminal designs of the disclosure are budgeted for a volume of 10 cm×10 cm×5 cm (i.e., smaller than a standard CubeSat, which is 10 cm×10 cm×10 cm, also referred to as “1 U”), a weight of <1 kg, and a power of <10 W, while delivering a user data rate of 10 Mbps to 50 Mbps—a full order of magnitude improvement over prior RF solutions. In some embodiments, commercial off-the-shelf (COTS) components are used. CubeSats typically have short missions (<1 year) in low Earth orbit (LEO) where radiation and thermal stresses are relatively benign.

(35) CubeSat FSO Communications System

(36) FIG. 1 is a rendering of a satellite communication system according to some embodiments. As shown in FIG. 1, a CubeSat 100 acquires an optical beacon B for acquisition and tracking, a low-rate radio frequency (RF) link (uplink and downlink) is established between an RF station 102 and CubeSat 100, and a high-rate optical downlink is established from the CubeSat 100 to an optical station 104. The RF station 102 and the optical station 104 are positioned at one or more ground stations. In some embodiments, potential channel impairments such as cloud cover can be mitigated through strategic placement of ground stations (e.g., in areas of favorable weather) and/or through the use of onboard storage memory. The CubeSat contains a payload comprising a two-stage pointing system, having a coarse pointing module (providing functionality for a coarse pointing “stage,” e.g. comprising a host ADCS), and a fine pointing module (providing functionality for a fine pointing “stage,” e.g. using an integrated fine-steering mirror (“FSM”)).

(37) During a communications pass, the CubeSat 100 uses an on-board propagated orbit to point towards the ground station and wait for an uplink beacon. The field-of-view of a beacon camera on the CubeSat 100 is selected to cover the entirety of the uncertainty region so that no additional maneuvers are needed to search for the ground station. Once the CubeSat beacon camera detects the beacon signal from the ground station, it uses this information to improve the pointing accuracy to within the range of the fine stage. Finally, the FSM steers the transmit beam to the accuracy desired for downlink. The FSM is in a bistatic configuration, so there is no feedback on the position of the FSM. An on-orbit calibration procedure can be performed to ensure transmitter/receiver alignment. Such calibration can utilize the low-rate RF link to communicate the received power measurements on the ground back up to the satellite. Using this feedback, the satellite can adjust its pointing until peak power is received on the ground.

(38) FIG. 2 is a block diagram of a satellite communication system according to some embodiments, showing interactions between a host spacecraft 200 and a lasercom payload 203. The lasercom payload 203 includes high-speed electronics 207 (to perform, for example, data encoding, interleaving, modulation, and/or framing) that swap data and control commands with a host on-board computer 205 of the host spacecraft 200 (e.g., a CubeSat), a low-rate radio modem 209 (configured for communication via antenna “A”) and a telemetry buffer 211 each electrically coupled to the high-speed electronics 207, as well as to an optical assembly 213. The optical assembly 213 of the lasercom payload 203 includes a transmit laser and modulator (collectively 215), the transmit laser being optically coupled to at least one microelectromechanical system (“MEMS”) fine-steering mirror (“FSM”) 217 for fine pointing of the host spacecraft 200. The MEMS FSM 217 is, in turn, optically coupled to a transmit (“TX”) aperture 219, through which the transmit beam passes during operation. The transmit laser and modulator 215 are electrically coupled to, and driven by, the high-speed electronics 207 (e.g., for encoding, interleaving, modulation, framing, etc.). A receiver (“RX”) aperture 221 (e.g., having a diameter of about 2.5 cm), configured to receive an incoming optical transmission (e.g., a beacon or beam), is optically coupled to a tracking detector 223 (e.g., comprising a focal plane array) whose output is fed into a positioning, acquisition and tracking (PAT) module 225 that applies one or more PAT algorithms to the detector data (e.g., for centroiding and/or feedback control by a proportional-integral-derivative (“PD”) controller). The PAT module 225 can provide a boresight offset estimate to high voltage (“HV”) drive electronics 227 that drive the MEMS FSM. The PAT module 225 can also electrically transmit coarse corrections (e.g., for body pointing) to an ADCS subsystem 229 of the host spacecraft for coarse pointing and/or slew. In some embodiments. The optical assembly 213 includes at least one actuator, operably coupled to the at least one MEMS FSM (or “micromirror”), to actuate at least one micromirror about two axes.

(39) FIGS. 3A-3C are renderings of a physical layout, including perspective, top and side views, respectively, of a spacecraft laser communications payload 306, occupying a 5 cm×10 cm×10 cm (“0.5 U”) volume of a 3 U CubeSat 300 and having coarse and fine stage pointing capability, according to some embodiments. The lasercom payload 306 includes high-speed electronics 307 to control focal-plane readout (e.g., of tracking focal plane 335), centroiding of a received beacon, forward error correction (“FEC”), interleaving (e.g., to mitigate atmospheric fading so as to reduce an error rate associated with transmitting data via the communications link), framing, and modulation. The lasercom payload 306 comprises two main subsystems: a downlink transmitter and an uplink beacon receiver. The lasercom payload 306 uses a bi-static design, with separate downlink and uplink beacon paths through downlink aperture 341 and uplink aperture 343, respectively. A sun blocking filter 339 and a narrow filter 337 are disposed in the uplink path.

(40) The transmitter design follows a Master Oscillator Power Amplifier (MOPA) architecture, where an Erbium Doped Fiber Amplifier (“EDFA”) 345 is used in conjunction with a 1550 nm seed laser 310 to provide a high peak-to-average power optical waveform. EDFAs are widely available due to their use in the telecommunications industry. The industry standard “MSA” form-factor for an EDFA is (9 cm×6 cm×1.5 cm), which can fit within a 10 cm×10 cm chassis cross-section. EDFAs are offered in a variety of power output levels and gains (e.g., 200 mW optical). In some embodiments, mechanical modifications are made to the EDFA so that fiber egress points are located along a “long edge” of the CubeSat chassis to ease fiber routing within the CubeSat chassis. The EDFA can comprise a modified COTS fiber amplifier (e.g., from NuPhoton Technologies, Inc.) with a form factor of about 9 cm×7 cm×1.5 cm, and can be configured for electrical input of 5V at 5.7 W and have an optical output of 200 mW avg., a gain of 40 dB and a “wall plug” efficiency of ˜3.5%.

(41) A fiber collimator 333 forms the transmit beam, which is subsequently directed by a fine-stage fast steering mirror (FSM) 317 (e.g., driven by the fine-steering mirror driver 331) in a “gimballed-flat” topology. The FSM 317 can be a SWaP-compliant MEMS tip/tilt mirror having a steering range (e.g., of +/−about 1°) that is sufficient for coarse stage hand-off. This hand-off can be autonomous and can be based on quality metrics comprising one or more of the following: beacon signal-to-noise ratio (“SNR”), beacon transmitter power, receiver power, and attitude stability of the coarse stage. The transition could also be driven by a ground command, either manually or in response to detection of the downlink signal. Once the readouts from the beacon receiver meet some confidence criteria (e.g., a reliable bright signal across multiple frames, or a signature that matches a known modulation scheme), the fine stage begins steering. The beacon receiver camera comprises a CMOS focal plane array with high sensitivity in the near-infrared (NIR) range to detect an 850 nm beacon transmitted from the ground station. The uplink beam image can be processed using centroiding algorithms for fine attitude determination.

(42) Example System Design Parameters

(43) Tables 1-12 (below) provide design parameters of an FSO communications system, according to some embodiments. The ground segment can include a transportable telescope and mount (e.g., 30 cm) and can use COTS detector technology (e.g., avalanche photodiode detectors (APD), PIN photodiode, etc.). In some embodiments, a downlink radiometry involves a 1550 nm (at 1 W (optical)) transmitter, a ground segment downlink receiver with a ˜30 cm aperture and a sensitivity of about 1000 photons/bit, and channel/pointing losses of ˜6 dB. In some embodiments, the half-power beamwidth needs to be 0.12 deg to achieve 10 Mbps and the FSO pointing capability is about 1/10.sup.th the beam width (0.012 deg or 0.21 mrad or 0.72 arcmin).

(44) TABLE-US-00001 TABLE 1 Example Top-Level Design Parameters Link Parameters Link rate 10 Mbps, 50 Mbps Uncoded channel rate Bit error rate 10.sup.−4, (e.g., using code) Conservative baseline for FEC Range 1000 km (400 km LEO orbit) 20° elevation above horizon @ 400 km LEO Space Segment Parameters Size, Weight 10 cm × 10 cm × 5 cm, 1 kg “0.5 U” CubeSat mid-stack payload Power 10 W (transmit), 1 W (idle) Excludes host ADCS Coarse Pointing 5° (3-sigma), 1°/sec slew Host CubeSat ADCS Fine Pointing 0.1 mrad (3-sigma) FSO Payload fast- steering mirror Downlink Beam 1550 nm, 2.1 mrad (0.12°) FWHM divergence divergence Beacon Receiver Uncooled focal-plane array 850 nm (TBR) Ground Segment Parameters Apertures RX: 30 cm, beacon: TBD Mount capable of tracking LEO object Acq. Detector InGaAs Camera Informs tip/tilt FSM Comm. Detector COTS APD/TIA Module Cooled module Pointing Coarse: Reaction wheel(s), Detector size demands magnetorquer(s), and/or fine stage two-line element(s) (“TLE”), Fine: tip/tilt FSM (e.g., 2-axis)

(45) TABLE-US-00002 TABLE 2 Example Top-Level Design Parameters Link Parameters Data rate 10 Mbps, 50 Mbps (stretch) User data rate Bit error rate 10{circumflex over ( )}−4 without coding Conservative baseline for FEC (7% RS Path length 1000 km ~20 deg elev @ 400 km LEO Space Segment Parameters Size, Weight 10 × 10 × 5 cm, 1000 g “0.5 U” CubeSat mid-stack payload Power 10 W (transmit), 1 W (idle) Excludes host ADCS Coarse Pointing +/−3° (3-sigma), 1°/sec slew Host CubeSat ADCS Fine Pointing +/−0.03° (+/−525 urad) 3-sigma Lasercom payload fast-steering mirror Downlink Beam 1550 nm 0.12° (2.1 mrad) FWHM Radiometric constraint for 10 Mbps Beacon Receiver Uncolled Si focal-plane array 850 nm Ground Segment Parameters Apertures RX: 30 cm, beacon: TBD Mount capable of tracking LEO object Acq. Detector InGaAs Camera Informs tip/tilt FSM Comm. Detector COTS APD/TIA Module Cooled module, link operating at 300 Pointing Coarse: TLE, Fine: tip/tilt FSM Detector size demands fine stage

(46) TABLE-US-00003 TABLE 3 Example Design Parameters Value Optics Focal Length 25 mm Centroid Error 0.018 mrad RMS Reaction Wheel (MAI-400) Max. Torque 635 mNm Resolution 0.005 mNm Gyroscope (ADIS-16534) Angular Random Walk 2 deg/√hr Output Noise 0.75 deg/s RMS Resolution 0.0125 deg/s Spacecraft True Moment of Inertia 0.05 kgm{circumflex over ( )}2 Est. Moment of Inertia 0.0475 kgm{circumflex over ( )}2

(47) TABLE-US-00004 TABLE 4 Example Top-Level Design Parameters Notes Optical Link Parameters Optical link rate 10 Mbps (goal) Uncoded channel rate 50 Mbps (stretch) Bit error rate 1 × 10.sup.−6 BER Without coding Operational range ≦1000 km Appropriate for most LEO missions Optical Space Segment Parameters Size 0.5 U 5 cm × 10 cm × 10 cm Mass 2 kg Power 10 W (TX) Includes FSO payload, 1 W (idle) excludes host ADCS PAT scheme closed-loop Using uplink beacon Coarse pointing satellite body-pointing Provided by host ADCS goal: 2.0″ (TDR) 3σ, absolute stretch: 0.5° (TBR) 3σ, absolute Coarse slew rate 3.0 deg/s (′fBR) Provided by host ADCS Fine point/track single two-axis MEMS Shared by TX and RX op- tical paths Fine point range ±5.0″ (TBR) Greater than coarse pointing accuracy Fine point resolution TBD Beam width dependent Ground Segment Parameters Receive aperture ≦30 cm COTS telescope Mass 50 kg For portability PAT scheme open-loop Based on TLE/ephemeris Detector APD, PMT, etc. Commodity/COTS unit is desirable Uplink beacon TBD eye-safe laser Req. for closed-loop tracking

(48) TABLE-US-00005 TABLE 5 Link and Module Parameters Link parameters Data rate 10-50 Mbps Bit error rate 10.sup.−4 (no coding) Conservation baseline Path length 1000 km (at 20° elevation) LEO orbit at 400 km altitude NODE module Size, weight 10 × 10 × 5 cm, 0.6 kg 0.5 U CubeSat Power 10 W (transmit) CubeSat constraints Downlink 0.12° FWHM Provide required data beam rate Beacon Silicon array, 7° FOV COTS components, cover receiver coarse pointing range Coarse pointing +/−3° (3-σ) Host CubeSat ADCS Fine pointing +/−0.03° (3-σ) Fast-steering mirror

(49) TABLE-US-00006 TABLE 6 Example FSO Payload Mechanical Parameters ID Parent Description MECH-1 The FSO payload shall fit within a 0.5 U (10 × 10 × 5 cm) volume envelope MECH-2 The FSO payload shall have a mass no greater than 1 kg MECH-3 The FSO payload shall have “side-looking” so that it can be situated in the midsection of the CubeSat MECH-4 The FSO payload's bistatic apertures shall maintain alignment within X mrad (TBD) across expected environmental disturbances (thermal gradients, vibe, shock)

(50) TABLE-US-00007 TABLE 7 Example FSO Payload Electrical Parameters ID Parent Description ELEC-1 The FSO payload shall consume no more that 1 W (idle) and 10 W (during TX) ELEC-2 The FSO payload shall accept unregulated bus voltages between 6 V and 10 V

(51) TABLE-US-00008 TABLE 8 Example Communication Link Parameters ID Parent Description COMM-1 The optical dowlink shall provide 10 Mbps (goal), 50 Mbps (stretch) user information rate COMM-1.1 COMM-1 The optical downlink shall operate at channel BER less than 10{circumflex over ( )}−4 COMM-1.2 COMM-1 The FSO payload shall provide FEC COMM-1.3 COMM-1 The FSO payload shall provide interleaving to mitigate atmospheric fading COMM-2 The optical downlink beam divergence shall be 2 mrad (FWHM)

(52) TABLE-US-00009 TABLE 9 Example Ground Station Parameters ID Parent Description GND-1 The ground station telescope(s) shall be capable of continuously tracking a LEO object without entering gimbal lock GND-2 The ground station shall provide an uplink beacon signal GND-2.1 GND-2 The beacon signal shall not be visible or listed as a distraction hazard. GND-2.2 GND-2 The beacon signal shall be eye-safe (i.e. below MPE) at the beacon transmit aperture GND-2.3 GND-2 The beacon beam divergence shall be large enough to ensure 3-sigma probability of illumination given satellite position uncertainties GND-3 The ground station shall provide a 30 cm (TBR) aperture for receiving the downlink communication signal GND-4 The downlink receiver shall use COTS detector technology such as APO/TIA modules GND-5 The ground station shall incorporate a wide FOV acquisition sensor GN0-5.1 The ground station shall provide a means to calibrate alignment of acquisition sensor and communication detector

(53) TABLE-US-00010 TABLE 10 Example Transmitter, Channel and Receiver Parameters Symbol Value Units Notes Transmitter Parameters Laser optical output power PLD, elec 1 W Laser wavelength > ... peak 1550 nm Peak wavelength Modulation duty cycle 0.5 Simple RZ for now Laser avg. optical power (dBW) PLD, opt, avg, dB −3.0 dBW Half-power beam width θ½ 0.120 degrees Full cone angle where power is half of peak intensity Transmit antenna gain (dB) Gt, dB 65.60 dBi Based on divergence above Channel Parameters Path length d 1000 km LEO at 400 km can be tracked down to 20 degrees above horizon Path loss (dB) Lpath, dB −258.2 dB Standard free-space path loss equation Atmpheric loss placeholder Latm, dB −6.00 dB Placeholder value for absorbtion, scattering, turbulence Receiver Parameters Aperture di11meter 30 cm Receive antenna gain (dB) Gr, dB 115.7 dB Diffraction limited gain Power at detector (dB) Prec, dB −85.9 dBW Power at detector Prec 1.28E−09 W or J/s Photons per socond 1.00E+10 photons/sec Required photons/bit 1000 photons/bit An “easy# to achieve receiver sensitivity Predicted data rate 10000102 bits/sec

(54) TABLE-US-00011 TABLE 11 Example Power Budget Breakdown Mode: IDLE TX UL_ACQ DL_ACQ Accept, Comm downlink in Search/acquire UL Track UL beacon, encode, store Nominal progress beacon transmit DL acq. telemetry from host Component Power (W) Duty (%) P_avg Duty (%) P_avg Duty (%) P_avg Duty (%) P_avg Focal plane array FPA quiescent 0.05 100% 0.05 100% 0.05 100% 0.05 FPA readout power 0.11 100% 0.11 100% 0.11 100% 0.11 PAT Processor 0.25 100% 0.25 100% 0.25% 100% 0.25 Fast-steering mirror + driver 0.25 100% 0.25 100% 0.25 High-Speed Electronics 0.25 100% 0.25 100% 0.25 FEC encoder 0.25 100% 0.25 100% 0.25 100% 0.25 Non-vol telem. buffer (SSR) 0.25 100% 0.25 0.25 100% 0.25 100% 0.25 Modulator/framer 3.00 100% 3.00 100% 3.00 Laser transmitter EDFA 3.00 100% 3.00 100% 3.00 Seed laser driver 0.25 100% 0.25 100% 0.25 Seed laser TEC 0.25 100% 0.25 100% 0.25 100% 0.25 Radio Modem Receive only 0.10 95% 0.10 50% 0.05 50% 0.05 100% 0.10 Transmit/receive 1.50 5% 0.08 50% 0.75 50% 0.75 Mode Total (W) 7.58 1.71 8.21 0.60 Mode Budget (W) 10.00 10.00 10.00 1.00 Power Margin (%) 24% 83% 18% 40%

(55) TABLE-US-00012 TABLE 12 Example Downlink Budget Overview Value Units Link Budget Input Parameters Informationrate R_info 1.00E+07 bps 10 Mbps Code overhead eta_FEC 0.00% Codeless for now PPM order M 16 Number of slots per symbol Laser Transmitter Laser electrical input power PLD, elec 3.00 W Electrical input power Laser wavelength λpeak 1550 nm Peak wave length Electro-optical efficiency η_TX 0.07 — Extinction ratio ER dB 27.04 dB Used for “power robbing” correction. Half-power beam width θ 0.120 deg Power is 0.5*peak, full cone 2.09-1 mrad Transmit optical losses (dB) L t, o pt, dB −3.00 dB Real values from OCTL Channel Pathlength d_path 1000 km LEO at 400 km -+ 20 deg above horizon Atmospheric loss Latm, dB −1.00 dB Pointing loss Latm, dB −3.00 dB Receive Telescope & Optics Focal length FL 3 M Aperture diameter d 30 cm Receive optics losses L_RX, optics −3.00 dB Background Noise (Sky Rad.) Field of view (full cone angle) 6.67E−05 rad PPM: C30662EH has 0.2 mm diameter Sky Spectral Radiance L_sky 6.00E−04 w(cm{circumflex over ( )}2*S Daytime. 2 km above sea level at 975 nm [Hemmati FIG. 8.16] Optical filter bandwidth B opt 1 nm Receiver Electronics Module Responsivity (w/gain) R_V_per_W 340,000 V/W Transimpedance R_fb 68,000 ohm Approximated from responsivity curve Excess noise factor F 5.5 Noise equivalent power NEP 6.50E−14 W/sqrt(Hz) W/sqrt(Hz) Electrical BW B 3.20E+07 Hz OOK: 0.8 * bit rate PPM: 0.8 * slot rate Link Budget Summary Laser avg. optical power PLD, opt, avg, dB −6.8 dBW Based on manuf specifications Transmit optical losses (dB) L t, o pt, dB −3.0 dB Placeholder Transmit antenna gain (dB) Gt, dB 65.6 dBi Uniform plane wave assumption G = 16 theta{circumflex over ( )}(Lambert eq 3.78) Path loss (dB) Lpath, dB −2581 dB Standard free-space path loss equation Atmospheric loss Latm, dB −1.0 dB Placeholder Pointing loss Lam, dB −3.0 dB Placeholder Receive antenna gain (dB) Gr, dB 115.7 dBi Diffraction limited gain Receive optics losses L_RX, optics −3.0 dB Placeholder Signal power at detector P_sig, dB −93.7 dBW Average received power Signal power required P_req, dB −97.1 dBW BER = 1e−4 Margin for 1e−4 BER 3.4 dB

(56) Coarse Stage

(57) The coarse stage of the system uses CubeSat body-type pointing (see, e.g., coarse pointing of FIG. 2 and corresponding description above). In some embodiments, the coarse pointing sensors and actuators are not contained within the FSO communications payload, but rather are contained within or are part of the host CubeSat. CubeSats can use a combination of magnetorquers, reaction wheels, and/or thrusters for attitude control. Actuators that can slew include: thrusters, magnetorquers, reaction wheels, miniature control moment gyros, or any other mechanism that can generate a torque. The FSO communications payload can be agnostic to the choice of sensors and actuators in the host system. The host CubeSat has sufficient orbit and attitude knowledge to initially point within 3° (i.e., initial pointing accuracy of 3°) of the ground station (e.g., based on the field-of-view of the beacon receiver). The CubeSat can be configured to autonomously slew with respect to inertial space to achieve initial alignment of the beacon receiver with the optical beacon (e.g., in advance of the CubeSat's pass of a ground terminal, such that the lasercom beacon camera is staring at the point on the horizon where the terrestrial station will appear).

(58) Once an initial alignment is achieved and/or the beacon has been located/acquired, the CubeSat can slew with respect to the ground/terrestrial terminal at a slew rate of 1° per second, or up to 1.1° per second (e.g., orbit dependent, to slew to track the terrestrial terminal through the pass). The beacon can provide very fine attitude knowledge, approximately 30 μrad, and the CubeSat undergoes a transition to become actuation-limited (during tracking). At this point, the host CubeSat points to within 1° of accuracy to overlap with the pointing range of the fine stage. The FSO communications payload, which contains a FSM for fine steering, can then “dial in” the transmitter to the desired accuracy for downlink. A distinction between attitude determination and orbit (position) determination can be made, in that position/orbit determination is relevant to both ends of the link. For example, position/orbit determination impacts how the ground station points the uplink beacon laser. For the satellite, orbit determination along with attitude determination impact satellite pointing.

(59) Fine Stage

(60) With regard to the fine steering mechanism (see, e.g., fine pointing/steering of FIGS. 2-3 and corresponding description above), component selection criteria can include (but are not limited to): field of regard, accuracy, bandwidth, size, weight and power (SWaP) considerations (e.g., as affected by a mirror and its driver). In some embodiments, a MEMS fine-steering mirror (“FSM”) is used (e.g., having a mechanical resonance of 430 Hz), and a Bessel filter can be employed to protect the FSM. The MEMS fine-steering mirror can comprise a 2-axis MEMS tip/tilt mirror (e.g., a Physik Instrumente S-334 piezoelectrically actuated tip/tilt mirror or a Mirrocle Technologies, Inc. S1630DB gimbal-less two-axis scanning MEMS micromirror) with a steering range (e.g., of about +/−1.25° or about +/−2.86° or about +/−5.73°), a size (e.g., of about 1.25 mm, or of about 4.2 mm), and a bandwidth (e.g., of about 300 Hz, or of up to 200 Hz, or of up to 1 kHz). The MEMS fine-steering mirror can be disposed within a small, chip-scale package having no integrated feedback sensors. Qualification parameters for a fine steering mechanism can include positioning repeatability, thermal stability, and/or the ability of a mirror to be driven open-loop.

(61) The fine-pointing module can be configured to point the optical transmitter toward a remote terminal with an accuracy range that overlaps with an accuracy range of the coarse-pointing module of the CubeSat. In some embodiments, overlap is desired because, for example, if the CubeSat can only get to within 3° accuracy for example, and the FSM can only reach 1° at the edge of its motion, it would be difficult or infeasible to apply an error correction. As such, in some embodiments, the fine stage range is driven by the actuation-limited CubeSat pointing capability. In some embodiments, the cubesat payload does not include an electromechanical gimbal. The gimbal is replaced by the fine steering mirror combined with the fact that it is generally acceptable to body slew a CubeSat.

(62) Specifications for the accuracy of the fine stage can be based on a detailed link budget analysis to size the beamwidth of the CubeSat payload. With a beamwidth of 2.1 mrad, the 3-pointing accuracy is set as a quarter of the beamwidth, e.g., 525 μrad (0.03°). The pointing loss is thus limited to 3 dB in the worst case. Therefore, the fine stage provides a range of 1° to overlap with the CubeSat body pointing and a final accuracy of 525 μrad. The combination of the coarse and fine stage control can achieve a pointing accuracy of ±90 μrad, excluding consideration of pointing bias. This gives approximately 7 dB of margin over ±525 μrad. In the worst case scenario (i.e., the worst possible pointing that still meets the requirements described herein), the pointing loss is maintained within 3 dB.

(63) To characterize the fine pointing stage, a 650 nm red laser was directed through a focusing lens, and steered into a Si camera by a FSM. The angle of the FSM was determined based on the geometry of the setup. Since there was no feedback available on the device's position, it was necessary to characterize repeatability of the device to ensure that it could meet performance requirements. To test repeatability, the mirror was commanded to visit each of the points in a 5-sided die pattern covering its entire range. For each iteration, points were visited in a random order. Statistics on the position repeatability for a significant number of trials (N=500) show that the RMS error of the device is 12 μrad, well within the desired performance.

(64) Beacon Design

(65) With regard to the beacon (see FIG. 1 and corresponding description above), design drivers can include (but are not limited to): satellite position uncertainty, eye safety (e.g., ANSI Z136.6, “Safe Use of Lasers Outdoors,” NASA Use Policy for Outdoor Lasers, FAA Regulation: Order JO 7400.2), and/or detector technology. In some embodiments of the disclosure, a broad, near infrared uplink beacon is used, and is intercepted by a focal plane array on the satellite (i.e., the CubeSat). Beacon system analysis can include atmospheric fading, detector noise modeling and centroiding algorithm performance. As described herein, the beacon system can provide an average attitude knowledge accuracy of 30 μrad with 2.3% fading probability in each frame read-out.

(66) CubeSat FSO Communications System—Operation

(67) FIGS. 4A-4C illustrate a sequence of a pointing, acquisition, and tracking (“PAT”) process executed by a CubeSat with fine a coarse pointing stages. During operation, a host CubeSat 400 autonomously slews from a mission-defined attitude. In FIG. 4A, an acquisition sensor (e.g., having a FOV 401 of 6.6°×8.7° (full-angle)) of an FSO communications module of the host CubeSat 400 stares for a beacon signal B with a coarse ADCS accuracy of ˜2° (e.g., based on attitude knowledge and/or position knowledge). The beacon can originate from a remote terminal 404 or from its general vicinity. In systems where uplink and downlink wavelengths are similar, it can be advantageous to provide some spacing between the beacon transmitter and the downlink receiver in order to reduce noise caused by scattered light from the uplink.

(68) In FIG. 4B, a centroid algorithm, running on the FSO communications module, estimates a boresight offset, and the ADCS subsystem of the host CubeSat closes control loops using a beacon offset. The beacon beam divergence is ˜5 mrad full width at half maximum (“FWHM”), which accommodates a tracking error of less than +/−1 km. The point-ahead angle in LEO is orders of magnitude smaller than the specified beamwidth. As such, the point-ahead angle is ignored due to beamwidth and orbit geometry (10 arcsec (51 μrad)). In FIG. 4C, an integrated fine-steering mechanism rejects residual error, and coarse corrections are fed to the host ADCS. Although some degree of range, resolution, and/or bandwidth limitation is inherent to all actuators and sensors, multi-stage solutions (i.e., the staged control approach described herein) can alleviate such limitations.

(69) Tables 13 and 14 (below) provide exemplary overviews of the coarse and fine stages of a staged control approach to PAT, according to some embodiments.

(70) TABLE-US-00013 TABLE 13 Overview of Coarse Stage (Host CubeSat) Requirements Parameter Requirement Initial pointing accuracy ±3° Actuation-limited pointing accuracy ±1° Max. slew rate up to 1.1°/s (orbit dependent)

(71) TABLE-US-00014 TABLE 14 Overview of Fine Stage Requirements Parameter Requirement Range ±10 Pointing accuracy 525 μrad (0.03°)

(72) FIG. 5 is a rendering of an FSO satellite communication system according to some embodiments. An FSO module on board the satellite 500 has a data rate of about 10 Mbps to about 50 Mbps, with comparable power consumption as compared with existing RF solutions. While the high-rate downlink and beacon uplink are both optical, the system also uses a low-rate RF uplink and downlink 501 (via RF station 502) for high-level command and control and limited data downlink, for example during periods of optical link unavailability, should they occur. The RF link 501 can be supported with minimal resources in terms of licensing, ground systems, and power.

(73) As shown in FIG. 5, an uplink optical beacon B (e.g., originating from optical station 504), having a wavelength of about 850 nm, is used for acquisition and tracking, and an optical downlink beam 503 at about 1550 nm is used for high-rate data transmission. The transmitter optical power budget can be a function of the downlink data rate and/or the size, cost and/or the portability of the ground terminals. A link budget analysis can be performed to determine a target transmit beamwidth (e.g., 2.1 mrad) as well as other PAT considerations for minimizing pointing losses to acceptable levels. In some embodiments, the transmitter is configured to output (e.g., via an EDFA) high-fidelity waveforms with an extinction ratio (“ER”) of >about 33 dB, at an electrical power margin of about 18% and a modulation bandwidth of >about 600 MHz (e.g., FPGA-limited).

(74) FIGS. 6, 7 and 8 are renderings of first, second, and third steps (respectively) in a PAT process implemented using the system of FIG. 5. During the first step (FIG. 6), the CubeSat 600 slews toward a ground station 604 or other remote terminal (i.e., seeking to acquire an uplink beacon emanating therefrom) using one or more coarse sensors and one or more reaction wheels as actuators, with a pointing accuracy of +/−about 3°. Coarse pointing can be based on two-line element (“TLE”) information. Two line element sets are published by the Joint Space Operations Center for satellite operators to utilize. Based on the satellite's orbital position from the TLE and the known location of the ground station, the satellite can point towards the ground station.

(75) During the second step (FIG. 7), the CubeSat 600 closes its control loop around a beacon offset using a beacon camera and one or more reaction wheels as actuators, with an improved pointing accuracy of +/−about 1.25°. The beacon camera determines (“sees”) the location of the beacon and, correspondingly, where it should point to achieve a high degree of accuracy (the accuracy being limited, in some embodiments, by the actuators' capabilities). A beacon camera can comprise a CMOS focal plane array (e.g., 5 megapixels) such as an Aptina MT9P031 (e.g., having an optical format of 1/2.5″, a resolution of 2,592 H×1,944V, a pixel pitch of ˜2.2 μm, and a quantum efficiency (“QE”) at 850 nm of ˜15%), a lens systems (e.g., 1″, f=35 mm), one or more bandpass filters to reject background light, and/or one or more UV/VIS-cut filters to reduce system heating.

(76) During the third step (FIG. 8), the fine steering mechanism of the CubeSat 600 is activated. This step continues to use the beacon camera for sensing, but transitions to using a fast-steering mirror as its actuator, with a pointing accuracy of +/−about 0.03°. The CubeSat can then steer its downlink based on a beacon boresight offset. Example parameters for the transmitter shown in Table 15 below. Example parameters for the beacon camera optics are shown in Tables 16 and 17 below.

(77) TABLE-US-00015 TABLE 15 Transmitter Design Parameters Parameter Value Justification/Driver Optical >200 mW avg Link budget, PPM-16 output power assumed Modulation PPM, M = [8-64] ER implications type Modulation >1 GHz desired To support future pointing BW improvements Wavelength ±1 nm Ground receiver filter stability Operating 0° C. to 40° C. Typical CubeSat values temp. range (inside chassis) Input power <8 W Transmitter portion of terminal Size goal <10 cm × 10 cm × 3 cm Transmitter portion of terminal Mass goal <300 g Transmitter portion of terminal

(78) TABLE-US-00016 TABLE 16 Beacon Camera Parameters Parameter Value Detector resolution 2592 H × 1944 V Pixel's pitch 2.2 μm Focal length 35 mm Field of view 7° 850 nm band-pass filter bandwidth 10 nm Long-pass filter cut-off frequency 700 nm

(79) TABLE-US-00017 TABLE 17 Beacon Camera Parameters Lens + filters Focal length 35 mm Aperture 1″ Band-pass filter (850 +/− 5) nm Long-pass filter >700 nm

(80) In some embodiments, a field-programmable gate array (“FPGA”) is used for transmitter modulation.

(81) In some embodiments, the beacon receiver camera comprises a CMOS focal plane array, a 1″ aperture lens system, and two optical filters. The detector is configured to have a high NIR sensitivity, resolution and low dark current and read noise properties. The lens system is configured to provide a wide effective field-of-view (7°) that can sufficiently compensate for the satellites pointing capability with only coarse sensors. Two optical filters are used: a bandpass filter at 850 nm and a UV/VIS-cut filter to reduce heating caused by Sun radiation. The beacon camera system size is approximately 4 cm×4 cm×6 cm with a total weight of 160 g, and can include a UV/VIS-cut filter to reduce system heating.

(82) FIG. 9A is a rendering of a closed-loop tracking configuration for an FSO communications module, using a quadcell tracking detector 923a, according to some embodiments. A single aperture 916 is used for transmitted light (passing from the transmit laser 915a through beam splitter 912, then reflecting off of the FSM 917a and directed through the aperture 916) and received light (reflecting off of the FSM 917a and directed to the beam splitter 912, which diverts the incoming light onto the quadcell tracking detector 923a). Quadcell tracking detector 923a signal data is processed by PAT circuitry 925a. Transmit laser 1015a is driven by high speed electronics 907a, and the FSM 917a is driven by high-voltage drive electronics 927a. As compared with the focal plane detector configuration discussed below with reference to FIG. 9B, the quadcell configuration has a narrower field of view (“FOV”) and more complex optics, but has a higher sensitivity.

(83) FIG. 9B is a rendering of a closed-loop tracking configuration using a focal plane tracking detector, according to some embodiments. Separate apertures (941 and 943) are used for transmitted light (passing from the transmit laser 915b to the FSM 917b where it is reflected and directed through aperture 941) and received light (passing through uplink aperture 943 and incident directly onto the focal plane tracking detector 923b), respectively. Focal plane tracking detector 923b signal data is processed by PAT circuitry 925b. Transmit laser 915b is driven by high speed electronics 907b, and the FSM 917b is driven by high-voltage drive electronics 927b. As compared with the quadcell detector configuration discussed above with reference to FIG. 9A, the focal plane configuration has a wider FOV and simpler optics, but is less sensitive.

(84) Ground Segment

(85) FIG. 10 is a system block diagram showing components of a ground segment according to some embodiments. Control electronics 1045, configured to receive ephemeris data, are electrically coupled to a beacon laser and amplifier 1047 whose collective output is optically transmitted through a beacon aperture 1049 (e.g., about 10 cm in diameter). The control electronics 1045 are also electrically coupled to an azimuth-elevation (“Az/El”) mount 1046 that is mechanically coupled to the beacon aperture 1049 as well as to a receive aperture 1051 (e.g., about 30 cm in diameter). The receive aperture 1051 is configured to pass an incoming optical transmission to an optical detector 1053, whose output is electrically fed to a high-speed electronics module 1067. The high-speed electronics module 1067 contains a sequence of functional blocks: a demodulator 1055, a framer 1057, an interleaver 1059, and an encoder 1061. The output of the encoder is checked using a pseudorandom binary sequence (PRBS) checker 1063, and is optionally (e.g., if no or low error is found) stored to a mass storage unit 1065. Data in the mass storage unit 1065 (e.g., a downlink request) can then be retrieved using one or more transport protocols 1068 (e.g., automatic repeat request (“ARQ”)) via the low-rate RF TT&C link 1009.

(86) Transmitter Selection

(87) A radiometric link budget analysis was performed to estimate the optical transmit power to close a 10 Mbps link for a CubeSat implementation. This analysis was constrained by the expected pointing capability of the space segment/terminal (e.g., which sets the downlink beam divergence to 2.1 mrad FWHM), the link range (e.g., <1000 km) as well as the sensitivity of the ground receiver (e.g., 1000 photons per bit, allowing for the use of COTS detectors), and indicated that approximately 1 W of optical power would close the link at a 10 Mbps user data rate in a receiver thermal-noise-limited system. At 1 W power levels, two optical sources were identified as candidates for the system: a high power laser diode (HPLD), such as a “pump” laser at 980 nm, and a master-oscillator power amplifier (MOPA) design incorporating a fiber amplifier at either 1 μm or 1.55 μm. The effectiveness of each of these configurations, based on end-to-end link performance, is discussed below. This performance analysis incorporated realistic transmitter assumptions (e.g. modulation type) and receiver parameters (e.g. suitable detector technology for transmitter wavelength). System parameters were matched where possible, and notable differences are enumerated in Table 18.

(88) TABLE-US-00018 TABLE 18 Differences in HPLD and MOPA system parameters Option A Option B HPLD MOPA Wavelength 980 nm 1550 nm TX power (avg) 500 mW 200 mW Modulation OOK PPM-16 Receiver BW Per modulation specifications Detector Si InGaAs APD/TIA APD/TIA Performance Modulation Wall-plug Limiter bandwidth power

(89) FIG. 11 is a block diagram showing components of a HPLD configuration, suitable for use in the optical transmitters of FIGS. 2-4. The HPLD configuration consists of a directly modulated high-power laser diode, such as a 980 nm “pump” laser diode 1122. These devices can be obtained in convenient single mode fiber-coupled butterfly packages. The electrical-to-optical (EO) conversion efficiency of HPLD lasers is typically greater than 30%. Operation at 980 nm is also advantageous from a receiver perspective, as silicon detectors are near their peak responsivity at this wavelength. Conditioned power (e.g., DC/DC conversion at 1118) is supplied to a high-current driver circuit 1120 that drives the pump laser 1122, and the laser output is fiber-optically routed to collimation optics. A disadvantage of the HPLD approach stems from the associated driver circuitry, which switches large amounts of current at the modulation bandwidth. Assuming on-off-keying (OOK), which minimizes modulation bandwidth relative to data rate, and a typical pump diode efficiency (η=0.6 W A.sup.−1), the driver circuit would switch over ˜1.5-2 A at 10 MHz rates. This approach is feasible, and is used in some systems (e.g., laser video projection systems), but may be fundamentally limited by the packaging of the laser. Nevertheless, this configuration is well within power budget: 3.3 W estimated of 8 W budget and an estimated wall-plug efficiency of 15%.

(90) FIG. 12 is a block diagram showing components of a MOPA configuration, according to some embodiments, suitable for use in the optical transmitters of FIGS. 2-3. Drive circuit 1269 provides FPGA direct modulation, bias, and TEC control, and is electrically coupled to seed laser 1271. Alternatively or in addition, the drive circuit 1269 includes one or more laser drivers and/or one or more thermoelectric cooler (“TEC”) drivers. Seed laser 1271 comprises a transmitter optical subassembly (“TOSA”) module including a distributed feedback (“DFB”) laser diode and a TEC (which may be part of the TOSA module). Output from the seed laser 1271 is optically coupled to an extinction filter 1273 (e.g., an athermal FBG filter, circulator, bandpass spectral filter, etc.), for example to improve the extinction ratio (“ER”) of the seed laser signal through FM-to-AM conversion. Precise alignment between the seed laser wavelength and the filter passband can simultaneously achieve high ER and low insertion loss. In some embodiments, athermal fiber Bragg grating (“FBG”) filters can provide both steep transition regions (>>1 dB/GHz) and high stopband attenuation (>30 dB) along with a thermally stable center wavelength (≈100 MHz/° C.). A temperature sensor can be mounted to a FBG filter and used to compensate for the slight thermal dependency of the FBG filter. The overall wavelength shift of the transmitter during such compensation can be acceptable, for example when the ground station receive filter bandwidth is 250 GHz (2 nm).

(91) The filtered signal (i.e., the output of extinction filter 1273) is then fed to an amplifier. The MOPA configuration uses an average-power-limited fiber amplifier such as an Erbium-doped fiber amplifier (“EDFA,” e.g., 1.55 μm) 1275a or an Yttrium-doped fiber amplifier (“YDFA,” e.g., 1 μm), and is amplified by EDFA 1275 (e.g., with a gain of ˜40 dB). Average-power-limited amplification allows the system to take advantage of low duty-cycle waveforms with high peak-to-average ratios such as pulse position modulation (“PPM”). Although YDFAs can provide roughly twice the wall-plug efficiency of EDFAs, these efficiency levels can be difficult to realize at lower (<1 W) power levels, and may be less commercially available. For purposes of analysis herein, a 200 mW “MSA” form-factor EDFA that is compatible with the volume constraints of CubeSats was used as a baseline. The lower output power of the MOPA (relative to the HPLD) is roughly balanced by the link margin gains afforded by moving to PPM from OOK modulation. The EDFA 1275 amplifier output is fiber-optically routed to collimation optics.

(92) The EDFA 1275 amplifier output is then fiber-optically routed to collimation optics. In some embodiments, a MOPA transmitter produces high fidelity PPM waveforms at 1550 nm at 200 mW average output power while consuming 6.5 W of electrical power.

(93) Aside from the amplifier, the modulator (e.g., see 215 in FIG. 2 and corresponding description above) is typically a large power consumer in MOPA designs. For PPM waveforms, the modulator can provide high extinction ratio (“ER”) in order to avoid “power robbing” losses in the fiber amplifier (e.g. for PPM-16, ER>27 dB). To avoid the power penalty associated with an external modulator, a direct modulation (“directly modulated laser,” “DML”) approach can be used. The transmitter digital electronics (e.g. an FPGA) can directly modulate the seed laser with the communication waveform. Direct modulation alone can provide ≈10 dB of ER if the laser is kept above a threshold (i.sub.th). To further improve ER, the laser's adiabatic frequency chirp can be used in conjunction with a narrow bandpass filter to produce FM-to-AM conversion. The MOPA design is estimated to consume about 6.5 W, yielding a wall-plug efficiency of approximately 3%. This is lower than the HPLD design, however the MOPA is capable of producing higher fidelity waveforms at much faster modulation rates. MOPA designs can have high modulation bandwidths, high peak-to-average power ratios, good component availability and a clean spectral output.

(94) Seed-to-EDFA power budget data for MOPA architectures according to some embodiments is provided in Table 19 below.

(95) TABLE-US-00019 TABLE 19 Seed-to-EDFA Power Budget (e.g., EDFA driven into saturation) Parameter Value Notes/Justification Seed laser power output −4 dBm Average power (+12 dB for peak at M = 16) Circulator Loss −1.2 dB FBG Filter Loss −1.3 dB Connector/coupler losses −0.5 dB Conservative budget for flight design EDFA Gain 40 dB EDFA avg output power +23 dBm Margin 10 dB EDFA driven 10 dB beyond saturation

(96) Comparisons of the HPLD and MOPA configurations are provided in Tables 20-21 below. Both HPLD and MOPA configurations gave a >3 dB link margin for a 10 Mbps data rate at a specified bit error rate (“BER”) of 1×10.sup.−4 (uncoded).

(97) TABLE-US-00020 TABLE 20 Comparison of HPLD and MOPA Architectures Parameter HPLD MOPA Wavelength 980 nm 1550 nm Approx. Size 5 cm × 5 cm × 1 cm 10 cm × 10 cm × 3 cm Approx. Mass 100 g 250 g Approx. Power 3.3 W 6.5 W Modulation Bandwidth <50 MHz (package >1 GHz parasitics) Peak-to-average Limit Low (typ. <10) High (>16) Spectral Quality Poor (>1 nm) Excellent Notable Risks Driver circuit design Wall-plug power Spectral quality Achieving high ER

(98) TABLE-US-00021 TABLE 21 Comparison of HPLD and MOPA Architectures Config Config A B (Direct) (MOPA) Units Notes Laser avg. optical −3.0 −6.8 dBW Manuf. power specifications Transmit optical losses −3.0 −3.0 dB TBR Transmit antenna gain 65.6 65.6 dBi 2.0 mrad divergence Path loss −262.2 −258.2 dB Free-space path loss Atmpheric loss −1.0 −1.0 dB TBR Pointing loss −3.0 −3.0 dB TBR Receive antenna gain 119.7 115.7 dBi Diffraction limited gain, 30 cm Receive optics losses −3.0 −3.0 dB TBR Signal power at −89.9 −93.7 dBW detector Signal power required −92.7 −97.1 dBW For 10 Mbps at BER = 1e−4 Margin for 1e−4 BER 2.8 3.4 dB
PAT Analysis

(99) Analysis of a PAT attitude control system according to some embodiments was performed using a single-axis tracking simulation. FIG. 13 is a diagram showing the linear single-axis model used, and Table 22 below shows the simulation parameters used. A spacecraft 1300 was modeled to include a reaction wheel 1324, gyroscope 1326, FSM 1317, and FPA detector 1323, and to have a disturbance torque applied thereto. Simulated beacon position information was routed from detector 1323 to a centroiding/attitude determination module 1328, which determined an attitude error and passed it to a low pass filter 1332, an attitude control module 1334, and the Kalman filter 1330. Attitude correction data was routed from the low-pass filter 1332 to the fast-steering mirror 1317. The attitude control module 1334 received angular rate data from the Kalman filter 1330, as well as reference attitude data (e.g., from memory) to calculate a command torque which was then passed to reaction wheel 1324 as well as back to the Kalman filter 1330 input. Angular rate information was routed from gyroscope 1326 to a Kalman filter 1330. Attitude dynamics were expressed as follows:

(100) $x=\left[\begin{array}{c}\theta \\ \theta \end{array}\right]\stackrel{.}{x}\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]x+\left[\begin{array}{c}0\\ \frac{1}{J}\end{array}\right]{\tau }_{\mathrm{cmd}}+\left[\begin{array}{c}0\\ \frac{1}{J}\end{array}\right]{\tau }_{\mathrm{dist}}$
The feedback controller was a PID controller run at 4 Hz (based on the MAI-400 reaction wheel), and gains were selected for a damping ratio of 0.7 and crossover frequency of 0.04 Hz:

(101) $K_P=J{\omega }_n^2{K}_D=2J\eta {\omega }_n{K}_I=\frac{K_P}{10}$
where K.sub.P is proportional gain, K.sub.D is derivative gain and K.sub.1 is integral gain.

(102) TABLE-US-00022 TABLE 22 Simulation Parameters Value Optics Focal Length 35 mm Centroid Error 30 μrad RMS (0.5 pixel) Reaction Wheel (MAI-400) Max. Torque 635 mNm Resolution 0.005 mNm Gyroscope (ADIS-16334) Angular Random Walk 2 deg/√hr Output Noise 0.75 deg/s RMS Resolution 0.0125 deg/s Spacecraft True Moment of Inertia 0.05 kgm.sup.2 Est. Moment of Inertia 0.0475 kgm.sup.2

(103) During the PAT analysis, the performance of a system using only a coarse stage was compared with the system using both coarse and fine stages. A 400 km altitude, an acquired beacon, and environmental disturbances such as solar radiation, magnetic interference, a gravity gradient, and aerodynamic drag were simulated. The combined “coarse and fine stage” pointing significantly outperformed the exclusively coarse stage pointing (i.e., the attitude error was considerably lower for the combined “coarse and fine stage” as compared with the exclusively coarse stage pointing), and fell well within the limits of an exemplary downlink error range requirement. The estimated coarse pointing accuracy was +/−1.6 mrad (3-σ), while the estimated fine pointing accuracy was +/−80 μrad (3-σ).

(104) ADCS Parameters

(105) FIG. 14 is a flow-down diagram of parameters of attitude determination and control systems. Uplink parameters include uplink beacon size/power 1446 (e.g., interdependent upon COTS coarse pointing component 1440 selection) and detector selection 1448 (e.g., based upon COTS coarse pointing component 1440 selection, ephemeris knowledge 1450 and/or ground station tracking error 1452). Downlink parameters include fine stage FSM selection 1442 (e.g., interdependent upon COTS coarse pointing component 1440 selection) and acceptable pointing losses 1444 (e.g., interdependent upon the fine stage FSM selection). COTS coarse pointing component 1440 selection can depend upon maximum slew rate 1436 (e.g., ˜1°/s) and/or pointing error 1438 (e.g., <5°).

(106) FIG. 15 is a flow-down diagram of constraints of attitude determination and control systems. 3 U CubeSat SWaP constraints 1554 (an external constraint) are considered when identifying self-imposed FSO payload SWaP limits 1560. The FSO payload SWaP limits correspond to an available power that affects the FSO beam width 1566 (i.e., a derived constraint). The RF communications infrastructure 1556 used (e.g., an external constraint) is a factor in determining a target FSO link acquisition time 1562 and FSO link rate 1564. The FSO link rate also affects the FSO beam width 1566 (a derived constraint). The existing CubeSat ADCS technology 1558 used, and its associated coarse pointing capability (an external constraint), together with the FSO beam width 1566, impact the fine pointing capability 1568 that can be achieved.

(107) FIG. 16 is a transmitter test configuration according to some embodiments. Support equipment includes a laser diode controller 1670 (e.g., ILX Lightwave LDC-3724C), a modulator 1672 (e.g., FPGA evaluation board), an optical power meter 1692, a high bandwidth optical detector 1694, and an oscilloscope 1696. Seed laser 1610 includes TEC 1674, thermistor 1676, laser diode 1686 and photodiode 1688. The laser diode controller 1670 provides bias current to the laser diode 1686, and is also electrically coupled to TEC 1674 and thermistor 1676. Modulator 1672 applies a PPM-16 modulation to the laser diode 1686, whose output is fed through a coupler to both “test port 1” and to a 3-port circulator 1684 in optical communication with an FBG filter 1690. Output from the 3-port circulator 1684 is fed through a coupler to “test port 2” as well as to EDFA 1682 (powered by 5V DC power supply 1678 and controlled by control PC 1680 via an RS232 connection). The EDFA 1682 output is optically fed to “test port 3.” The test configuration of FIG. 16 was used to produce the results in FIG. 17 (laser current and temperature wavelength tuning), FIG. 18 (thermal stabilization power consumption), FIG. 19 (filter characterization), FIG. 20 (extinction ratio validation) and FIGS. 21A-F (EDFA validation), discussed in greater detail below.

(108) Seed Laser Selection and Characterization Example

(109) In some embodiments, selection criteria for a seed laser (e.g., for the MOPA configurations discussed above with reference to FIG. 12) include power consumption of the integrated thermoelectric cooler (TEC), size and/or mechanical layout. Accurate temperature control is necessary to stabilize the laser wavelength, and on many lasers the TEC requires a significant amount of power (>1 W). TOSAs can include low power TECs (<0.4 W), and are available in very compact, fiber-coupled packages (e.g., 20 mm×8 mm×5 mm). In some embodiments, a TOSA has 6 dBm continuous wave (“CW”) output power in the 1550 nm C-band.

(110) An automated testbed comprising a laser diode controller, a wavemeter and an optical spectrum analyzer was used to characterize tuning parameters of a seed laser according to some embodiments (see FIG. 17, showing a plot of wavelength versus DC laser bias, with each curve corresponding to a different seed laser temperature). The approximate tuning characteristics for a representative device were Δλ/ΔT=−11 GHz/° C., Δλ/Δi.sub.DC=−0.45 GHz/mA, and Δλ/Δi.sub.AC=0.20 GHz/mA (measured with PPM at f slot=200 MHz). The TOSA's TEC power consumption was validated by measuring both VTEC and iTEC while the setpoint (Tset) was adjusted relative to ambient. Details relating to the transmitter power budget are provided in Table 33 below.

(111) TABLE-US-00023 TABLE 23 Transmitter Power Budget Value Notes EDFA 5.7 W Manuf. worst case, (we measured: 4.1 W) Seed laser TEC 0.4 W (TBRR) Peak power, over temp Seed laser DC bias 0.2 W Worst case Seed laser AC drive 0.01 W 50 mA, 1/16 duty FPGA logic 0.2 W Only TXer related portion of FPGA Total: 6.51 W Margin: 1.49 W 8 W budgeted

(112) FIG. 18 shows a plot of the measured seed laser TEC power consumption versus temperature for an exemplary transmitter, as well as a quadratic model for both heating mode (right half of curve) and cooling mode (left half of curve). The TEC power consumption was within budget (0.4 W), with 18% margin, across the expected operational range for the device (0° C. to 40° C.).

(113) FIG. 19 is a plot of insertion loss versus frequency, comparing the insertion loss of two Gaussian passband athermal fiber Bragg grating (“FBG”) filters (having bandwidths of 5 GHz and 10 GHz, >40 dB stopband and |Δλ/° C.|<˜125 MHz/° C.), along with the expected wavelength “chirp” (Δλ/Δi.sub.AC) of the seed laser, according to some embodiments. The 10 GHz chirp shown in FIG. 23 was achieved with 50 mA of direct drive current from a Xilinx Spartan 6 FPGA LVCMOS I/O pin. Only the narrower 5 GHz FBG filter was able to produce sufficient seed suppression while maintaining low insertion loss. In some embodiments, temperature/bias wavelength tuning aligns the seed laser with the filter, and signal modulation ER is enhanced through FM-to-AM conversion.

(114) A swept duty-cycle ER measurement (with peak power variation compensation applied) revealed that the combined seed laser, in combination with an extinction filter, was achieving an ER of >33 dB at slot frequency f.sub.slot=200 MHz (see FIG. 20, a plot showing extinction ratio measurements for a seed laser with an extinction filter, according to some embodiments). Slot frequency is the rate of PPM slots. In other words, 1/(slot frequency) is the duration (or “pulse length”) of the transmitter pulses. The aforementioned ER is sufficient for low duty-cycle waveforms, such as 64-ary PPM. The same measurement was completed at f.sub.slot=40 MHz, and showed a slightly degraded ER (≈28 dB). Without wishing to be bound by theory, this is believed to be due to fact that the modulation frequency is closer to the transition point where thermal effects begin to dominate charge carrier density effects. The higher modulation rate may have had better extinction due to a higher value of |Δλ/Δiac|. In some embodiments, the transmitter is operated at f.sub.slot≧200 MHz, and the modulation order (M) is varied to achieve a variety of link rates.

(115) FIGS. 21A-21F show an FPGA, seed laser+ER filter, and EDFA sequence, with related electrical and optical input/output time-domain waveform plots, according to some embodiments. The time-domain measurements show that the design produces high-fidelity optical waveforms, as shown in FIGS. 21B, 21D and 21F. Furthermore, the >33 dB ER of the combined seed laser and filter assembly allows operation at high order PPM (64-ary) without sacrificing the peak power gains offered by the average-power-limited EDFA. Since the design supports modulation bandwidths in excess of 600 MHz, it will be suitable for use in future systems with enhanced pointing capabilities. The power consumption of the transmitter is within budget with nearly 20% margin (see Table 24 below).

(116) TABLE-US-00024 TABLE 24 Transmitter Power Consumption Summary Transmitter power consumption summary Parameter Value Notes EDFA 5.7 W Manufacturer worst case specification Seed laser TEC 0.4 W Peak power over 0° C. to 40° C. Seed laser DC bias 0.2 W Worst case Seed laser AC drive 0.01 W  50 mA, 1/16 duty cycle FPGA logic 0.2 W Transmitter portion of FPGA (shared with other functions) Total 6.51 W  Margin 1.49 W  8 W budget for transmitter

(117) FIGS. 22A and 22B are Bode plots showing the frequency response of a fine steering mirror, with and without a low-pass (e.g., Bessel) filter, respectively, according to some embodiments.

(118) FIGS. 23A and 23B show power/performance plots for erbium-doped fiber amplifiers (“EDFAs”), according to some embodiments.

(119) Simulation of Uplink Beacon Acquisition

(120) Fine attitude sensing capabilities can depend upon the acquisition and tracking capabilities of the uplink beacon. Fading of the uplink beacon due to atmospheric turbulence can be of concern, especially with the high slew speed required to track the satellite in LEO (up to 1°/s). As such, a detailed analysis and simulation were performed to evaluate the performance of a beacon system according to an embodiment.

(121) Table 25 below presents a beacon uplink budget with a 10 W transmitter, 5 mrad beamwidth when the satellite is at 20° and 90° elevation angle, with estimates of optical and atmospheric absorption and scattering losses (see Tables 25-27, also below). Noise components in the simulation include shot noise from signal, background sky radiance, and the noise sources of the beacon camera detector. In some embodiments, background shot noise is the dominant source. Various background light conditions were analyzed including a worst case scenario consisting of sunlit clouds. The estimated spectral radiance in this condition at 850 nm is approximately 180 W/m.sup.2/sr/um. The estimated integration time is selected to maximize dynamic range given the well capacity of the detector.

(122) TABLE-US-00025 TABLE 25 Beacon Uplink Budget Beacon link budget Transmitter Transmit laser power 10 W Uplink wavelength 850 Nm Beam divergence 5 Mrad Actual transmit power 4 W 20° 90° elevation elevation Free-space/Atmospheric channel Range 894 400 Km Atmospheric absorption and scattering −6 −5 dB Receiver Receiver bandwidth 10 10 Nm Average power at detector 0.013 0.081 nW Integration time 1.6 0.5 Ms Total photons received 7.3E+04 1.8E+05 photons Noise level in ROI 7.0E+03 9.9E+03 photons Optical S/N 10.1 12.5 dB

(123) TABLE-US-00026 TABLE 26 Link Analysis Transmit power 10 W Wavelength 850 nm Beamwidth 5 mrad Range (20° elevation) 984 km Atmospheric −6 db absorption/scattering Sky radiance.sup.s 180 W/m.sup.3/sr/um Receiver bandwidth 10 nm Optics loss (Tx + Rx) −8 db Received power 0.013 nW Margin 10 db

(124) TABLE-US-00027 TABLE 27 Scintillation Statistics C.sub.n.sup.2 profile Huffnagel-Valley model.sup.3 1°/s slew speed Scintillation Strong-turbulence model.sup.3 index Spatial diversity (4 beams) Distribution Log-normal

(125) The atmospheric refractive index structure parameter (C.sup.2.sub.n) profile for a mission can be estimated using the Hufnagel-Valley model. Since uplink beam will be slewing up to 1°/s to track the satellite in LEO, the slew rate becomes the dominant “wind-speed” parameter. This slew rate was incorporated in the Hufnagel-Valley model as additional wind speed through the Bufton wind model, leading to a more turbulent C.sup.2.sub.n profile than the standard HV5/7 profile, as seen in FIG. 24 (a plot showing atmospheric refractive index structure parameter profiles for a stationary beam and for a beam with 1°/s slew speed). The scintillation index can be estimated using the strong-turbulence model. A high scintillation index, e.g. caused by a fast slew rate, can be reduced by the use of multiple independent transmitters for spatial diversity. For a satellite at 400 km altitude, the scintillation index of the uplink channel with 4 independent transmitters is approximately 0.3. Signal power fluctuations about the mean value from the above link budget can be estimated using a log-normal distribution with variance equal to the scintillation index. Additional information on the models referenced herein (e.g., Hufnagel-Valley model and Bufton wind model) can be found in “Laser Beam Propagation through Random Media,” second edition, by Larry Andrews and Ronald Phillips (2005).

(126) The fade probability and centroiding accuracy were found by running the simulation with scintillation statistics with a time series of expected beam motion at 20° elevation from a 400 km altitude orbit. A fade instance is defined as the case where the brightest pixel does not belong to the beacon image on the detector array. In this simulation, the scintillation time scale is assumed to be comparable to the detectors integration time. The fade probability indicates the probability that the beacon is not found within the time it takes to read out a frame, which is approximately 0.15 s for a 5 megapixel camera. FIG. 26A shows the simulation results of fade probability at various transmitter power levels (5 W, 7.5 W, 10 W). As shown in FIG. 26A, the fade probability can be reduced to about 2.3% given a 10 W transmit power, sufficient for acquisition and tracking given proper real-time estimation techniques.

(127) The centroiding accuracy was found using center-of-mass centroiding of the beacon image on the detector (see FIGS. 25A and 25B). The accuracy result when not fading is shown in FIG. 26B. The average centroiding accuracy is approximately 0.5 pixel, corresponding to a mean attitude accuracy of 30 μrad. This accuracy result is less than 1/10 of the pointing requirement of the fine stage, leaving margin for actuation limitations and errors.

(128) Control System Simulation

(129) A simulation of coarse and fine control stages was performed, incorporating the results of the uplink beacon simulation described in the previous section. The accuracy of the detector was taken to be 30 μrad on average. The rate at which the FSM can be driven is limited by the beacon detector readout and processing. A readout rate of 10 Hz is sufficient for an accuracy of 525 μrad, as shown in FIG. 31. Once the beacon has been acquired, the CubeSat pointing performance can be dependent upon the control authority of its reaction wheels. The CubeSat modeled in FIG. 27 is affected by torque quantization and is intended as a fairly low-performance actuator. Verifying that the fine stage can improve performance to within required accuracy (with a margin of 7 dB) for this scenario indicates that it can meet the pointing requirements for a typical CubeSat.

CONCLUSION

(130) While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure.

(131) The above-described embodiments can be implemented in any of numerous ways. For example, embodiments of the technology disclosed herein may be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers.

(132) Further, it should be appreciated that a computer may be embodied in any of a number of forms, such as a rack-mounted computer, a desktop computer, a laptop computer, or a tablet computer. Additionally, a computer may be embedded in a device not generally regarded as a computer but with suitable processing capabilities, including a Personal Digital Assistant (PDA), a smart phone or any other suitable portable or fixed electronic device.

(133) Also, a computer may have one or more input and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include printers or display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards, and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, a computer may receive input information through speech recognition or in other audible format.

(134) Such computers may be interconnected by one or more networks in any suitable form, including a local area network or a wide area network, such as an enterprise network, and intelligent network (IN) or the Internet. Such networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks.

(135) The various methods or processes outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine.

(136) In this respect, various inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above. The computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above.

(137) The terms “program” or “software” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the present invention need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present invention.

(138) Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments.

(139) Also, data structures may be stored in computer-readable media in any suitable form. For simplicity of illustration, data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a computer-readable medium that convey relationship between the fields. However, any suitable mechanism may be used to establish a relationship between information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationship between data elements.

(140) Also, various inventive concepts may be embodied as one or more methods, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

(141) All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms.

(142) The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

(143) The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and/or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

(144) As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of” or, when used in the claims, “consisting of” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.

(145) As used herein, the terms “about” and “approximately” generally mean plus or minus 10% of the value stated.

(146) As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

(147) In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.