1. INTRODUCTION

The Laser Communications Relay Demonstration (LCRD) is NASA’s multi-year demonstration of laser communication between multiple ground stations and a geosynchronous satellite. LCRD will demonstrate that optical communications can meet NASA’s growing need for higher data rates while also enabling lower-power, lower-mass-communications systems on spacecraft. LCRD’s architecture will also serve as a testbed for various communications techniques—such as symbol coding, ranging, link layer protocols, and network layer protocols [1]—and as a demonstrator for a future advanced telecommunications and data relay satellite service [2].

The LCRD space terminal is a hosted payload on the U.S. Space Force’s Space Test Program Satellite-6 (STPSat-6) [3], which launched in December 2021 into geosynchronous orbit. The space terminal is capable of simultaneously communicating with two ground stations. Optical Ground Station 1 (OGS1), located at JPL’s Table Mountain Observatory in Wrightwood, California [4], uses the existing 1 m Optical Communication Telescope Laboratory (OCTL) telescope [5]. OGS2 is located at the U.S. Space Force’s Maui Space Surveillance System on Haleakala in Hawaii, and uses a 0.6 m receive telescope and a 0.15 m transmit telescope [6].

OGS1 consists of the OCTL telescope, the communication and beacon lasers, receiver and transmitter modems, the monitor and control software, a laser safety system, and the Integrated Optical System (IOS) adaptive optics (AO) instrument. The IOS has two major functions: relay light from the beacon and communication lasers to the telescope, and relay the received light from the telescope to the ground modem’s single mode fiber. Because atmospheric turbulence distorts the point spread function (PSF) of light entering the telescope, AO is required to couple the received signal into the modem fiber.

AO instruments are commonly used to mitigate the effects of atmospheric turbulence in astronomical imaging, and for telescopes imaging artificial satellites. However, key differences exist between these systems and AO systems used for laser communications. First, the Strehl ratio—the ratio of the observed peak image intensity to the diffraction-limited maximum—is often the salient performance metric for astronomical imaging, while fiber coupling is more relevant in communications applications. Also, optical communication operations can occur during the day with a corresponding increased background light and degraded atmospheric seeing. For instance, the geosynchronous location of the LCRD space terminal enables 24 h operation, compared to less than 12 h of nighttime operation typical for astronomical AO. Furthermore, because the space terminal utilizes monochromatic light, the AO system must divert some of the incoming photons to drive the wavefront sensor (WFS).

This paper discusses the design and performance of the AO system for the IOS at OGS1. Section 2 provides an overview of the instrument’s hardware and software implementation. Section 3 presents the real-time control (RTC) algorithm that maintains fiber coupling against dynamic turbulence. In Section 4, we discuss calibration techniques used to remove non-common path aberrations (NCPAs) to maximize static fiber coupling performance. Finally, Section 5 shows how the system performs at a variety of target flux levels.

2. INSTRUMENT OVERVIEW

Since the LCRD space terminal is located on a geosynchronous satellite, it is in constant view of the ground station. Operations, and thus adherence to requirements, are expected to occur at any time of the day. Most communication sessions will last from 8 to 24 h, stopping only to avoid lasing other satellites (periods that can last several minutes), and for Sun avoidance (which can last 1–2 h).

The IOS must meet its performance requirements during both daytime and nighttime, which is particularly challenging due to poor daytime atmospheric seeing. The 50th percentile of the cumulative distribution function of the Fried parameter at OCTL is estimated to be 5.2 cm (500 nm at zenith), and was the main driver of performance for the system design. The IOS has a baseline requirement of 50% coupling efficiency into the receive modem’s single mode fiber. Since fiber coupling is proportional to the Strehl ratio [7–9], the instrument was designed to provide high-Strehl-ratio/high-coupling efficiency while working in stressful seeing conditions.

The IOS operates over an input power range of 19.3–305 nW. This is equivalent to an object with a stellar magnitude of roughly ${-}7$, and is much brighter than typical targets imaged by astronomical AO instruments. Enabled by this abundance of photons, the IOS operates at relatively high closed-loop control rates between 5 and 20 kHz to achieve the required wavefront error correction.

While it was not a requirement of the system to be able to operate with satellites in low-Earth orbit (LEO), we were aware that it could be used in such a mode in the future and made sure that nothing would preclude LEO operations. The expected closed-loop bandwidth of the system is high enough to handle the increased Greenwood frequencies that it will encounter tracking a LEO spacecraft. In fact, the system was successfully used with the LEO TBIRD spacecraft [10].

A. Hardware

The IOS is mounted on an optical bench in the coudé room of the OCTL facility. Compared to an instrument mounted directly to the telescope, the static gravity vector simplifies mount design and improves mechanical stability. OCTL is an alt-azimuth telescope, and light is relayed to the coudé through a series of optical flats, the last of which can be turned to one of the four available optical benches [5].

The IOS is contained in an enclosure that helps isolate the system from ambient atmospheric turbulence, and also blocks stray laser light from leaving the optical bench. Since the uplink laser power is a factor of ${10^{10}}$ brighter than the downlink signal, internal panels are required to prevent uplink laser light from intruding into the IOS WFS path.

The AO system components are mounted on three optical breadboards that are in turn mounted on the bench. This modularization facilitated moving the system from the development laboratory to the telescope. WFS alignment in particular was greatly simplified by this approach.

LCRD downlink lasers have a wavelength of 1545 nm, while uplink lasers operate at 1555 and 1565 nm. A dichroic transmits the downlink laser to the AO system while reflecting the uplink lasers to the telescope. A portion of the downlink beam is picked off and sent to an acquisition camera (ACAM), which receives the uncompensated beam. The ACAM also measures the Fried parameter throughout operations using the modulation transfer function (MTF) and the full width half maximum (FWHM) methods [11]. Solar rejection filters, with a 3 nm FWHM bandpass centered at 1545 nm, are installed throughout the acquisition and AO arms of the instrument.

Figure 1 shows the layout and major components of the AO system. Achieving the required wavefront correction in the Table Mountain turbulence environment necessitates both a high density of deformable mirror (DM) actuators, and a large actuator stroke. At the time of the instrument design, no commercially available DM satisfied both conditions; thus a woofer/tweeter configuration was selected based on the design of the PALM-3000 AO system [12]. The “woofer,” or low-order DM (LODM), is a Boston Micromachines Multi-DM containing a $12 \times 12$ grid of actuators with 3.5 µm stroke. The “tweeter,” or high-order DM (HODM), is a Boston Micromachines Kilo-C possessing 952 actuators (in a circular grid with a diameter of 36 actuators) with 1.5 µm stroke. Of these, only 28 HODM actuators span the illuminated portion of the instrument pupil. Both DMs have protective windows with coatings optimized for transmission at 1550 nm. The LODM is controlled by the standard version of the Multi-DM electronics. The HODM is controlled with the low-latency version of Boston Micromachines’ Kilo-DM electronics, and uses a fiber link connector between the DM and the controller. Tip/tilt aberrations are corrected by a 12.7 mm fast steering mirror (FSM) bonded directly to a Physik Instrumente S331 actuator. The actuator is controlled with standard Physik Instrumente E-509.S3 and E-503.00S electronics. A series of off-axis parabolic mirror pairs places pupils on the FSM and DMs.

 

Fig. 1. Layout of the IOS, with significant components labeled: (1) FSM, (2) HODM, (3) LODM, (4) WFS, (5) Score camera, (6) fiber positioner, (7) ATS, and (8) acquisition camera. The blue line is the light path for the downlink signal; the red line is the light path for the uplink, which is not discussed in this paper. The black lines represent the walls of the optical enclosure. Light from the telescope enters from the top of the figure.

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A Shack–Hartmann WFS was selected for the IOS to utilize heritage software and experience gained from previous AO systems [12–14], and because it has an attractive balance of sensitivity and dynamic range. The WFS camera is an Xenics Cheetah InGaAs, with each Shack–Hartmann lenslet illuminating $2 \times 2$ pixels on the focal plane array (FPA) and no guard pixels are used. This configuration was necessary to achieve the required frame rate. Using either $4 \times 4$ pixel quad cells or using guard bands would improve performance, but would increase the time to read out the frame, with a corresponding lower frame rate and reduced system bandwidth. To provide signal to the WFS, a beam splitter diverts 30% of the downlink light entering the IOS instrument to the WFS.

After the WFS, a second beam splitter sends less than 1% of the light towards a Score camera, which images the post-correction PSF of the downlink beam. The Score camera is the same model as the WFS (enabling it to be used as a spare), and is mounted on an axial stage to allow focus adjustment, a feature used for the calibration methods described in Section 4. The Score optics are telecentric to maintain a constant plate scale at various focus positions, also necessary for the calibration methods.

The downlink modem single mode fiber receives the balance of light from the second beam splitter, and is installed in a motorized fiber positioner that can be adjusted to maintain alignment [15]. A Thorlabs five-axis NanoMax stage is used for this purpose. The Score camera and fiber positioner are designed to be as athermal as possible, and thus have minimal non-common path wavefront drift.

To facilitate system testing and tuning of RTC parameters, the IOS has an atmospheric turbulence simulator (ATS) [16] that can inject light from a 1554 nm stimulus laser into the system via an injection mirror on a motorized stage that slides into place for internal testing. The ATS consists of two spinning phase plates with computer-controlled rotation rates to simulate a wide variety of turbulence conditions. Changing the position and focal length of field lenses in the ATS optics varies the Fried parameter and Rytov number of the simulated disturbances. The rotation speed of the phase wheels sets the Greenwood frequency. During operations, the ATS is used for daily regression testing for tracking of system performance over the course of the mission and, potentially, early detection of failing components. While the ATS source is designed to mimic the downlink laser, the turbulence simulator creates non-uniform pupil illumination that can degrade the Strehl ratio by approximately 5%. This can be mitigated somewhat by adjusting the alignment of the ATS optics, but the adjustment is specific to each combination of field lenses. While vital for optimizing the IOS control parameters and demonstrating closed-loop performance, the ATS does not simulate other factors that can impact fiber coupling during on-sky operations, such as dome seeing, jitter, or thermal drift of the telescope optics.

B. Software

The IOS software is written in the nesC programming language [17] and is divided into six main components: a database component, command/automation server, device driver server, wavefront processor (WFP), graphical user interface (GUI), and RTC component. A central instrument computer runs all the software with the exception of the GUI, which runs on a dedicated machine. A publish/subscribe communication method is used to transfer messages between components. Under this design, all message types are published to a common database, and components subscribing to a specific message type receive data from the database automatically. For example, pixel data are published by the WFP component, and the GUI subscribes to these data and displays them in a GUI widget. A command issued to move a motor is published by the AO Command Dispatch and Automations Server (AOCA) component, and the AO Device Driver (AODD) MOTOR component subscribes to this command and acts accordingly. All published data remain in the database and may be retrieved at any time.

The database component (AODB) is an enhanced version of the Berkeley DB database engine, and is the interface between the IOS software and database hardware. All IOS message types are published to the database and timestamped upon writing to disk, and data are bundled for archival storage every 24 h. A solid state drive in the IOS control computer is capable of capturing all telemetry data types at the highest possible log rate of 20 kHz.

AOCA is the interface to all external clients and runs on the main IOS computer. External clients, such as the observatory control system, use a NetServices interface to connect to the AOCA, and AOCA publishes all incoming primitive commands to the database. AOCA also redirects all incoming automation commands to an internal server that manages the automation functions, error checking, and status.

AODD is the interface to the IOS hardware. AODD subscribes to all primitive ACAM, motor, Score, and stimulus laser commands, and passes these commands to the appropriate internal component, which then acts on the commanded request. AODD manages all hardware functions, error checking, and status, and publishes these status messages to the database. Control of the ATS phase plates, when in use, is performed via an independent computer connected directly to the ATS electronics.

The WFP manages the real-time processing. WFP subscribes to all primitive WFP commands, and publishes the requested WFP telemetry data products and status to the database. The WFP also controls the WFS camera component.

The GUI is a Javascript interface to the IOS software accessible via a web browser. IOS software architecture prohibits the GUI from executing any control logic; thus it functions as a command routing and status display service only. The GUI is divided into a server that incorporates the full publish/subscribe communication layer, and GUI widgets written using a standards-compliant web browser protocol (i.e., HTML or Javascript), allowing for multiple-platform web browser operation from any host within the local VPN. The GUI server accepts connections from multiple hosts to enable monitoring of the system by multiple users, but permits commands only from a single user at a given time.

 

Fig. 2. Software architecture of the IOS real-time control component. WFS images are exchanged among the frame grabber, the DSP card, and the active mirror elements via direct memory access, without going through the CPU, which would add timing jitter and increase the control loop latency.

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The RTC component performs all real-time AO computation, and operates on an Advantech digital signal processor (DSP) board, model DSPC-8682G2-00A2E. This board contains eight Texas Instrument TMS320C6678 DSPs on a single PCIe card. WFS frames are sent to the DSP board from an Alacron Fast1703 frame grabber using direct memory access (DMA) transfers that are multicasted over PCIe, the key innovation of this RTC system. We use PCIe multicast functionality to simultaneously distribute pixel data to all DSPs without executing additional transfers through a CPU, eliminating any timing jitter that would be incurred by routing through the host machine.

The architecture of the RTC is illustrated in Fig. 2. One period of RTC computation beings after WFS camera integration. The image frame is read out with 5 µs latency from end of frame integration to first pixel data availability. Processing of the image begins as soon as the first four lines of pixel data are received on the DSP to parallelize with the collection of pixel data. The full readout time takes 46 µs; however, with this parallelization image frame, processing takes only an additional 1 µs. As detailed in Section 3, wavefront reconstruction is then performed by a single vector–matrix multiplication distributed over the eight octal-core floating point DSPs. The DSP board receives the full set of WFS pixel data, and each core is responsible for computing a sub-region of WFS centroids, then multiplying by the associated segment of the reconstructor matrix. Finally, computation of the FSM, LODM, and HODM commands is done on DSPs, then transferred via DMA to the DM electronics.

3. WAVEFRONT RECONSTRUCTION AND REAL-TIME CONTROL ALGORITHM

The purpose of the IOS RTC algorithm is to reject dynamic wavefront disturbances, and maintain the wavefront specified by WFS centroid offsets generated via the methods described in Section 4. The RTC algorithm architecture is shown in Fig. 3, and runs on the eight DSPs as described in Section 2.B. Each control iteration begins with the measurement of the WFS image and the subtraction of a dark image. This is followed by a center-of-mass centroid computation performed over the pixels corresponding to each WFS lenslet. An alternative “denominator-free” calculation is also available for improved performance on faint targets, where the sum intensity for each subaperture is replaced with a normalized value computed from the intensity over the illuminated pupil [18]. In both cases, the centroid error is then computed to be the difference between the calibrated NCPA centroid offsets, and the measured centroids.

 

Fig. 3. Diagram of the IOS real-time control algorithm that maintains the optimized WFS centroid offsets. Frames from the Shack–Hartmann WFS are processed through a standard reconstruction computation before wavefront residuals are sent to the IOS control algorithm. Dimensions of the FSM, LODM, and HODM residual vectors are at the reconstructor output.

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Next, the centroid error is multiplied by a set of reconstructor matrices, shown as the orange box in Fig. 3, with individual reconstructors for the FSM, LODM, and HODM. This matrix–vector multiplication constitutes the bulk of the RTC computational burden, and computation is parallelized among the DSP cores as described in Section 2.B. The resulting wavefront residuals are the projection of centroid errors onto the actuator subspaces for each DM and FSM.

The reconstructor matrices are generated offline via a “reconstructor pipeline” that combines the instantaneous WFS subaperture illumination with pre-measured DM centroid influence functions. Reconstructors are currently re-generated on a daily basis, or as needed when the pupil illumination or turbulence conditions change appreciably. The general form of each reconstructor matrix, $R$, follows from a standard weighted least-squares solution:

Different approaches for selecting $Q$ and $P$ are used for each active mirror. For the FSM, regularization is not used by default, and $Q = 0$. For both LODM and HODM, the baseline regularization matrix follows a Bayesian approach incorporating knowledge of the signal/noise ratio and the magnitude of seeing [19–22]. This method essentially rolls off the integrator gain for high spatial frequencies in a noise-optimal way, as a function of the Fried parameter, ${r_o}$, and the measured flux. The Bayesian regularization matrix is given as

In addition to the Bayesian approach, the regularization matrix may also be chosen to be a diagonal matrix $Q = \rho I$, where $\rho$ is a scalar selected to mitigate ill-conditioned WFS modes, and is optimized via tuning experiments with the ATS. The HODM may also use an additional de-waffle term that specifically penalizes high-spatial-frequency components in the reconstructed residuals, following the approach in [23], permitting a more liberal overall regularization parameter $\rho$. The optimal combination of these parameters for on-sky operation is a topic of ongoing work.

The orthogonal projection matrix $P$ is used to prevent cross talk between mirrors. Projection is not required with the FSM, in which case, $P = I$. For the LODM, $P$ is selected to retain Zernike modes 4 through 45 via the expression

After the reconstructor matrices are applied, wavefront residuals are routed to standard “leaky-integrator” controllers operating in parallel for each FSM, LODM, and HODM channel. Each of these controllers, applied individually to each actuator channel, has the Z-transform description

 

Fig. 4. Closed-loop disturbance rejection performance for one axis of the FSM at three different control gains. The blue curves were measured using open- and closed-loop residuals with ATS disturbances applied, while red curves were measured via pokes applied to the centroid offset input. The black dashed lines delineate the theoretical best performance modeled by Eq. (7). Note that data were logged at a lower rate than the WFS sampling rate.

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Assuming one sample of delay to account for the WFS integration time [i.e., a simple plant model of $P(z) = 1/z$], the controller in Eq. (6) results in a closed-loop disturbance rejection transfer function for each actuator of the form

The disturbance rejection tests show broadly consistent results, with similar control bandwidth and low-frequency attenuation that is in-family with the theoretical performance predicted by Eq. (7). For higher control gains, the tests show somewhat higher levels of disturbance amplification beyond the control bandwidth; the current theory is that this is due to unmodeled behavior in the plant dynamics. For example, the FSM is known to have hysteresis in both axes, and additional delays due to computation time are not included. Modeling and mitigating these effects, including incorporating an analog strain gauge on the FSM or exploring more advanced RTC algorithms, are under investigation. Work is also ongoing to similarly characterize the dynamic performance of the DMs.

While integrator controllers are sufficient for the IOS to meet the disturbance rejection requirements at OCTL, future laser communications systems may be situated at locals with more challenging turbulence conditions. Indeed, the ability to satisfy wavefront requirements in sub-optimal locations could enable the proliferation of optical communications ground stations. Achieving the required closed-loop performance in such scenarios may not be possible by simply increasing the RTC sampling rate due to limitations on downlink flux, and resonant dynamic behavior of the active optical elements. Instead, more advanced, predictive control algorithms, which use models of the turbulence statistics to optimally reject incident wavefront error, may be required to achieve broadband disturbance rejection without increasing the control frequency. A demonstration of this technique was performed on the IOS using an adaptive predictive controller for control of the IOS FSM [24]. In contrast to the leaky-integrator employed in the baseline RTC, the predictive controller used a recursive least-squares filter to estimate the statistics of the incident turbulence, followed by a linear-quadratic regulator control algorithm (LQR) to minimize disturbances in a mean-squared error sense. An example of the performance with this architecture is shown in Fig. 5, which depicts closed-loop FSM residual power spectra, using the ATS as a disturbance source, for the adaptive controller compared to the integrator in Fig. 3. These results show notable improvement in closed-loop performance compared to those using just the baseline integrator, including significant attenuation of high-frequency harmonics up to 250 Hz, without the need for manual tuning by instrument operators.

 

Fig. 5. Closed-loop power spectra for one axis of the FSM under strong and weak turbulence regimes, tested using the ATS. Results compare the performance of the integrator in Fig. 3 with an adaptive predictive controller detailed in [24], with the RTC running at a rate of 1 kHz.

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4. REMOVAL OF NON-COMMON PATH ABERRATIONS

Even with careful mechanical alignment of the IOS instrument optics and perfect RTC performance, NCPAs between the WFS and modem input fiber ultimately limit the achievable fiber coupling. These NCPAs are chiefly due to quasi-static thermal drift between the sensing and fiber injection arms of the instrument, and require periodic calibration to re-establish a set of optimal WFS centroid offsets that are used for RTC.

The IOS uses a combination of image- and fiber-based alignment techniques to mitigate NCPAs. First, PSF images are used to perform wavefront sensing and control (WFSC) to minimize low- and high-spatial-frequency aberrations between the WFS and Score camera, the dominant source of NCPA error. Next, a Zernike tuning algorithm further optimizes low-order modes to maximize received power at the fiber. In both cases, corrections are applied in open loop to the LODM, HODM, or Score axial stage. At the conclusion of the calibration process, the WFS centroids, measured while the final LODM and HODM flatmaps are applied, serve as the control target (i.e., centroid offsets) for the RTC algorithm described in Section 3. During operations, a fiber lock algorithm can be run to adjust the five degree of freedom positions of the fiber tip to further optimize performance.

The cadence for NCPA calibration is still being investigated as the IOS undergoes commissioning in an operational environment. The current expectation is that full calibration may be required approximately every two months, with Zernike fiber tuning and fiber lock algorithms performed more frequently as needed.

A. Phase Retrieval and Wavefront Control

Removing NCPAs between the WFS and Score involves iteratively measuring wavefront aberrations at the IOS exit pupil, while the AO system is in open loop, and generating a static, open-loop control command to either the LODM or HODM to minimize the error. This process is repeated until a controllable floor is reached.

Wavefront measurement is performed using the modified Gerchberg–Saxton phase retrieval algorithm (MGS) [25–28], which produces non-parametric, high-resolution wavefront maps at the Score exit pupil. MGS belongs to a class of iterative-transform phase retrieval algorithms where the electric field is estimated at alternating pupil and image planes. At each plane iteration, the algorithm imposes the pupil amplitude mask or measured image intensity, with the pupil phase left as a free variable. A phase prior may be provided to initialize the algorithm if available. Convergence is declared when the estimated pupil phase no longer changes (per a small threshold) between iterations.

MGS operates in parallel on multiple pairs of narrowband, defocused images that provide a known phase diversity to avoid sign ambiguities in the final estimate. The MGS estimate is susceptible to phase wrapping if the true peak-to-valley wavefront error exceeds half the narrowband wavelength. This is a particular issue on the IOS, where a “stuck” LODM actuator often results in a localized wavefront minimum. To resolve this, the IOS employs a modal fitting procedure that serves as an “outer loop” to resolve wrapping artifacts [29].

The wavefront measurement process begins on the IOS by switching to the stimulus laser with the ATS phase plates set to the clear position, and applying pre-calibrated flatmaps to the HODM and LODM actuators. The approximate best-focus location for the Score camera is found by scanning the axial stage and maximizing the encircled energy of the measured PSF. Next, MGS measurement images are captured, consisting of a pair of defocused images with the Score stage adjusted to provide ${\pm}1.3$ peak-to-valley waves of defocus at 1554 nm via the equation

Basic processing is performed on the Score frames to remove bad pixels, background, and detector noise, before the frames are centroided and stacked to form high-SNR composite images at each defocus position. Then, the MGS algorithm is executed using the processed images. A simple gradient threshold determines whether wrapping is present in the resulting piston-free estimate. If wrapping is detected, the estimate is fit to a set of low-order Zernike modes via the methods in [29], which serves as a phase prior for an additional round of MGS using the same Score images.

Once an acceptable phase estimate is obtained, the wavefront control process begins to compute updated DM flatmaps that minimize the wavefront error. For both DMs (HODM or LODM), this begins by offloading the measured focus error to the Score stage, again via Eq. (8), then removing focus from the estimate. Let $w$ represent the vectorized form of this focus-removed phase estimate, and $u$ the update to the DM flatmaps. Then, for updates within the DMs’ linear range, the post-control wavefront, $\tilde w$, can be modeled as

 

Fig. 6. Four iterations of wavefront sensing and control applied to the LODM, showing a decrease in the measured wavefront error. MGS phase estimates (left) and in-focus Score PSFs (right) are shown for each iteration. Wavefront phase maps are depicted on a variable color scale to illustrate the emergence of high-spatial-frequency error, while PSF images are on a fixed color scale.

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In the IOS calibration process, several WFSC iterations are first performed on the LODM due to its larger stroke. Once a controllable floor has been achieved, typically after four iterations, higher-spatial-frequency aberrations are mitigated by continuing the process with the HODM. A typical example of this process as applied to the LODM is shown in Fig. 6. In this instance, four LODM control iterations reduce the measured wavefront error from approximately 197 nm rms, the initial wavefront error using the default DM flatmaps, to 42 nm, leading to a corresponding improvement in the maximum flux and morphology in the in-focus Score PSF. By the final iteration, residual phase aberrations approach the unconstrained LODM controllable floor, shown as the black line in Fig. 6 and computed by solving Eq. (10) for each measurement without control constraints, revealing high-spatial-frequency residual error to be further corrected by the HODM. Note that the “stuck” LODM actuator is evident in the phase measurements shown in Fig. 6; this region of the pupil is masked while performing subsequent high-order control iterations to prevent saturating neighboring HODM actuators. Currently, the total wavefront error is reduced to approximately 35 nm rms after both LODM and HODM controls are completed in a typical WFSC calibration, with the majority of the residual error localized to the stuck LODM actuator.

B. Zernike Fiber Tuning

Wavefront control of the Score pupil aberrations removes the majority of NCPA error. However additional aberrations exist between the Score and fiber input, mostly dominated by low-order modes. Zernike fiber tuning on the IOS is a calibration procedure to reduce these errors. Because these aberrations are not present on the Score arm of the instrument, maximizing fiber coupling typically lowers the observed Strehl ratio.

Past fiber-fed instruments have employed manual tuning of individual Zernike terms to search for an update to the DM flatmaps that maximizes coupling performance. This tends to be labor-intensive since significant coupling exists between the impact of Zernike modes on a scalar performance metric, such as fiber coupling. To avoid this, the IOS employs a Nelder–Mead optimization algorithm to perform automated, joint optimization of multiple Zernike modes simultaneously. Nelder–Mead is a direct search algorithm that iteratively explores the feasible space without computing an explicit cost function gradient [30]. At the start of an iteration, the algorithm generates a simplex consisting of feasible points sorted by increasing cost function (i.e., the Nelder–Mead “amoeba”). A new candidate point is then selected based on the simplex shape, and replaces the worst-performing point according to a set of heuristic update rules. For the large majority of iterations, the update rules require no more than two evaluations of the cost function, making Nelder–Mead attractive when cost function evaluation is expensive or time consuming.

 

Fig. 7. (left) Improvement in fiber coupling, quantified as an increase in photodiode voltage, over 50 trials of the Zernike fiber tuning algorithm performed after WFSC calibration of the Score exit pupil wavefront. (right) Distribution of optimized Zernike terms for each trial showing relatively consistent solutions at the conclusion of the calibration.

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In the context of the IOS, the optimization process occurs over Zernike modes 2 through 11 (Noll ordering) applied to the LODM. Thus the search space is 10-dimensional, and the Nelder–Mead simplex consists of 11 points. The cost function is the received power in the fiber, quantified as the voltage reported by a measurement photodiode. The fiber tuning calibration begins by switching the IOS to the stimulus laser source, and initializing the algorithm with a randomized starting simplex. At each optimization step, the algorithm polls the photodiode voltage while the candidate Zernike vector is applied to the LODM. The algorithm then proceeds per the Nelder–Mead update rules. Each optimization iteration requires several seconds to complete, largely limited by the time required to inject non-real-time updates to the DM, and the 1 Hz reporting rate of the photodiode measurement. At the conclusion of the process, WFS centroid offsets are recorded that serve as the control target for the IOS RTC as described in Section 3.

Because Nelder–Mead is susceptible to stagnation at a sub-optimal local extremum, fiber tuning is performed after the WFSC has generated DM flatmaps minimizing the wavefront error at the Score pupil. Thus, Zernike tuning is performed in addition to these optimized DM flatmaps. This ensures that the optimization needs to compensate only for residual NCPAs between the Score camera and fiber input. Future AO instruments, however, may be able to rely on Zernike Fiber tuning alone to maximize fiber coupling if no high-order NCPAs exist in the system.

Several realizations of the fiber tuning process are shown in Fig. 7, which depicts 50 calibration trails increasing the received photodiode power after approximately 700 optimization iterations. The rightmost plot in Fig. 7 shows the distribution of Zernike modes applied to the LODM to achieve the improvement in each trial. While some variation exists, particularly in tip/tilt modes, the overall structure of the applied correction is relatively consistent. At this time, the impact of intensity changes of the stimulus laser source over several hours, as well as further tuning of the algorithm hyperparameters, remains to be investigated.

C. Fiber Lock

While receiving the downlink signal, thermal changes may cause additional alignment drift between the fiber tip and WFS. To mitigate this, we created a fiber lock algorithm that optimizes the rigid body alignment of the fiber tip using the received modem signal. The fiber lock software, when enabled, runs continuously in the background and monitors the modem received power. The calibration algorithm begins if the received power drops below a pre-defined threshold.

The algorithm is a multi-dither, hill-climbing optimizer that performs small perturbations of selected degrees of freedom of the fiber positioner, measures corresponding changes in received power, and drives the fiber tip in the direction of increasing received power. The dither is bipolar, with magnitude set to result in a power change of 1%–2% from zero dither when the fiber is optimally positioned.

The fiber positioner has five degrees of freedom: $x$, $y$, $z$, ${\theta _x}$, ${\theta _y}$; each has a loop gain ${K_x}$, ${K_y}$, etc. Nominally, the fiber lock algorithm adjusts only $x$ and $y$; the loop gains for $z$, ${\theta _x}$ and ${\theta _y}$ are set to zero, which disables both dithering and adjusting those degrees of freedom.

A similar tuning algorithm can be used to optimize all five degrees of freedom of the fiber positioner, and is used with the stimulus laser source rather than with on-sky received power.

5. SYSTEM PERFORMANCE

After the assembly of the system, we carried out a series of measurements to characterize the system performance and to verify satisfaction of system requirements. Coupling efficiency data were taken while observing the internal stimulus source. We adjusted the brightness levels of the internal source from a level brighter than what we expect to encounter during the mission to very low power levels, which might be encountered during cloudy or hazy conditions. This let us explore performance over the complete set of conditions the system may experience. The light was sent through the ATS, which was set to the mission requirements of a Greenwood frequency of 32 Hz, ${r_o}$ of 5.2 cm (measured at 500 nm and zenith) and an effective elevation angle of 20°. We also captured data at the nominal mission elevation angle of 48°.

The Strehl ratio was measured over a 1 min average of Score camera data, and computed using the algorithms described in [31]. Because the Score camera is an uncooled InGaAs FPA with high read noise, it is difficult to compute accurate Strehl ratios during periods of low source brightness, especially when the Strehl ratio is lower and the PSF is more spread out. Thus there are fewer measured points at the turbulence profiles corresponding to 20° elevation angle.

As seen in Fig. 8, the Strehl ratio is relatively constant over the range of intensities, and also fairly high considering the low Fried parameter of ${r_o} = 5.2 \;{\rm{cm}}$ and the low elevation angle. This is due to the larger number of HODM actuators used for control across the pupil. A row of 28 illuminated HODM actuators corresponds to $d/{r_o}$ of 0.21 for the 48° elevation angle and 0.34 for the 20° elevation angle. High Strehl ratios such as this are essential to achieving high fiber coupling efficiency.

 

Fig. 8. Strehl ratio as a function of the flux at the entrance of the telescope. The blue circles are for an elevation angle of 48°, while the red Xs are for 20° elevation angle.

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To measure the coupling efficiency of light entering the single mode fiber, we used a fiber coupled power meter; at the time, the communication modem was unavailable. The power meter uses an SMF-28, which is the same as the input to the modem. The fiber coupling efficiency is the ratio of the power incident to the fiber to the power measured by the power meter. The power coming out of the internal stimulus laser is measured by a second power meter that uses a fiber splitter to pick off a small portion of the light to use as a reference measurement. The throughput of the system from the laser to before the focusing lens just in front of the fiber is used to calibrate the laser output power to the power in front of the fiber focusing lens. We ignore the loss in the focusing lens in front of the fiber as we assume it to be the same as the loss of the focusing lens used to couple light into the laser power meter. Input flux was computed to be at the front of the OCTL telescope. The data are plotted in Fig. 9. The blue circles are for an elevation angle of 48° and the red Xs are for 20° elevation angle.

 

Fig. 9. Fiber coupling efficiency as a function of the flux at the front of the telescope. The blue circles are for an elevation angle of 48°, while the red Xs are for 20° elevation angle. The power level is plotted on a log scale.

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It should be noted that these coupling efficiencies were measured on the unobscured pupil of the ATS; measurements made on the sky will be reduced by the impact of the secondary mirror of approximately 10% [8]. Our computations suggest that the obstruction from the secondary mirror spiders will cause an additional approximately 10% loss in throughput. These results also do not consider additional observatory effects, such as dome seeing or mechanical jitter that could further degrade performance.

6. CONCLUSIONS

Our testing indicates that the AO system has met its requirements and is ready for operations with the spacecraft. Several key takeaways were apparent after completion of the system. First, both high actuator densities and very high closed-loop control bandwidth (or, more sophisticated control algorithms) are needed to achieve high-Strehl-ratio/fiber coupling. On the IOS, these features are enabled by an adequate downlink brightness, and an RTC design that uses DMA to minimize computational latency. Second, the removal of NCPA is essential to achieving high-Strehl-ratio/fiber coupling, accomplished on the IOS through MGS phase retrieval and Zernike fiber tuning. Finally, the ability to simulate turbulence in the laboratory without observing through the telescope was a great boon to the project. It enabled significant testing and parameter optimization at the instrument level, and at the telescope once the IOS was delivered to OCTL. During operations the ATS will allow for regression testing and diagnosing of errors.