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Design and realization of ancillary control loops for the MMT adaptive optics system George Z. Angeli *, Bruce C. Fitz-Patrick, Michael Lloyd-Hart Steward Observatory, University of Arizona, Tucson AZ 85721 ABSTRACT The adaptive optics system of the Multiple Mirror Telescope is going to realize a high speed (1 kHz bandwidth) and high order (336 actuators) wavefront correction. However, to achieve the required 0.08 arcsec pointing stability the focal point of the Shack-Hartman wavefront sensor must be kept aligned to the Cassegrain focus better than 10 µm in spite of the noncommon path tip/tilt error due to mechanical and thermal deformation of the telescope structure. The wave-front sensor must also be rotated with high precision to keep it aligned with the deformable secondary mirror in spite of the parallactic angle correction of the telescope. Our approach is to use a feed-forward loop to eliminate the adverse effect of deformation. A fast, deterministic field bus is applied to interconnect the actuators, sensors and computers. The bandwidth (500kbs) and latency (less than 1 ms) of the DeviceNet serial bus is adequate to support our distributed control system. The field bus architecture simplifies and standardizes the control software as well as improves the reliability of the electronics by reducing the wiring. Keywords: adaptive optics, telescope control, distributed control, DeviceNet
1. INTRODUCTION The conversion of the Multiple Mirror Telescope (MMT) of the Steward Observatory/University of Arizona is nearing to the end. The originally segmented primary mirror has already been replaced with a single 6.5 meter honeycomb mirror built in the Steward Observatory Mirror Lab. Scientific observations are expected to start this fall. To take advantage of the high resolution the huge primary mirror can theoretically provide, the atmospheric effects degrading image quality must be corrected. For this reason, the Steward Observatory is developing an adaptive optics (AO) system. Astronomical adaptive optics systems are utilizing the wave-front of a sufficiently bright star – the guide star – to determine the spatial structure and time evolution of the atmospheric turbulence. This information is applied then to correct the wavefront with some kind of deformable reflection surface. In conventional astronomical adaptive optics systems several optical elements are introduced between the telescope focus and the science imaging camera. These additional surfaces – collimator optics, deformable mirror – cannot be cooled because of the lack of precision cryogenic actuators. Consequently, the adaptive optics system usually increases the thermal background in the IR region. To avoid this adverse effect, the MMT adaptive optics will use the f/15 Cassegrain secondary mirror itself for wave-front correction 1. The block diagram of the MMT AO system2 is shown in Figure 1. The major building blocks are the following: • Deformable secondary mirror with local electronics securing quick and stable deformation control; • Top Box containing all the necessary optics, electronics and mechanical actions for fast and reliable wave-front sensing; • Wave-front (reconstructor) computer, a custom built hardware and software for high speed matrix operations; • Laser beam projector system to generate an artificial “star” in the Na layer of the atmosphere; • Science instrument – for example ARIES spectrometer – including the science camera and an additional IR camera (the IR tip-tilt sensor) to detect the global tilt of the incoming beam. The electro-mechanical control (EMC) subsystem performs all the ancillary functions described in this paper as well as general data acquisition, temperature control, safety and other “housekeeping” functions. *
Correspondence: E-mail
[email protected]; Telephone (520)621-6636
Figure 1. The block diagram of the MMT adaptive optics system as it will be when fully implemented.
The Top Box is located just above the f/15 focus; its major role is wave-front sensing, however in its final form several alignment, correction and observing instruments will also be incorporated. The bare minimum of the Top Box is shown in Figure 2. A dichroic window on the ARIES Dewar reflects the visible portion of the incoming light into the Top Box. An offaxis parabolic mirror (OAP1) collimates the beam that forms an image of the pupil on a steerable mirror. This mirror is used to select the guide star as well as to correct the deformation of the structure. Another off-axis parabolic mirror (OAP2) focuses the beam again just in front of the wave-front sensor camera consisting of a front (collimating) lens and a ShackHartman sensor. Since the wave-front sensor camera is attached to the science instrument, it is rotated – actually de-rotated with the parallactic angle – to follow the sky. However, the wave-front information should ultimately be aligned with the non-rotated deformable mirror. To avoid software rotation of all the 224 slopes of the wave-front sensor – which would introduce additional lag in the main AO loop – the wave-front sensor camera itself is rotated in real time.
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Figure 2. The Top Box of the MMT AO system. This figure shows only the parts absolutely necessary for natural guide star AO operations
In order to limit the anisoplanatic error in adaptive optics – that is the correction error emerging because the measured atmospheric cone is not in absolute coincidence with the cone actually affecting the image quality – the guide star must be in the close vicinity of the science object. The guide star should also be sufficiently bright otherwise the higher order mode information is buried in noise. If there is no natural star available for a given science object, a laser guide “star” is required. This artificial star is a laser excited area in the Na layer of the upper atmosphere. The radiative recombination of Na atoms results in a bright spot well above the turbulent layers of the atmosphere. Since the distance of this spot from the telescope depends on the telescope elevation, the focus alignment of the wave-front sensor camera must be continuously adjusted. The apparent position of the laser guide star does not depend on the actual atmospheric tilt since the outgoing laser beam is refracted on the same atmospheric wedge as the incoming light. Consequently, for tip/tilt correction the AO system must still rely on a natural star. Since the wave-front sensor is locked on the laser guide star for higher order correction, the IR tip-tilt sensor is the one to be locked on the natural guide star. Unfortunately the drift between these two sensors will result in increased anisoplanatic error due to the laser guide star wandering away from the science object.
2. CONTROL MODEL Besides the obvious technical challenge of controlling a large, fast response time deformable mirror, the choice of an adaptive secondary raises other concerns, too. A major one is the effect of telescope deformation. The science camera and the wave-front sensor for the adaptive optics are spatially separated; there is quite a mechanical structure between them. Any – gravitational or thermal - drift of this structure will certainly influence the telescope pointing stability. To gain a better understanding of this fairly complex system, first we need control variables. Characterizing the pointing of the telescope with the 2nd and 3rd Zernike coefficients of the wavefront (tip and tilt, i.e. m=n=1) provides the major advantage that unlike the actual tilt of the beam, they are invariant of the pupil diameter in a telescope. These coefficients (B11 and C11) expressed in waves are even dimensionless. The vector variables used in our model combine the two coefficients: [B11, C11]T. However, at the telescope image plane – which is not a pupil - we have to use the position as a variable.
Since the details of the main adaptive optics loop are outside of the scope of this paper, the deformable mirror and wave-front sensor are considered part of the reconstructor represented with a lossy integrator (20 dB gain, 16 Hz bandwidth). Although there are more sophisticated reconstructors 3,4, the difference shows mainly for higher order modes while this study focuses on slow effects only. The models presented in this paper are described in Laplace transform domain even if it is obvious that most of the control laws are actually realized in software. We will discuss the associated sampling constrains later. Using a natural guide star, the major objective of the deformation control loop is to synchronize the wave-front sensor to the Cassegrain focus, i.e. to ensure that the error signal measured by the wave-front sensor is a good estimate of the real error appearing at the telescope focus. A highly simplified zero-order model of the AO system is shown in Figure 3a. It is obvious from the control scheme, that the structural deformation signal d is transferred into the real error e practically without any damping. A straightforward way of improving the suppression is to incorporate a feed-forward branch in the scheme with a gain of F(s), as shown in Figure 3b. The achieved suppression is [-1]/[1+F(s)] in the bandwidth where |A(s)|>>1. The feed-forward loop can be realized by a tiptilt sensor attached to the Cassegrain focus of the telescope as the detector and the steering mirror in the Top Box as the actuator. Since the real Cassegrain focus is reserved for the observing CCD, right above the focal point the light is diverted to the IR tip-tilt sensor with a small pick-off mirror. The x-y position of the mirror is adjustable allowing to find the natural guide star in the FOV of the telescope. Note that inside the bandwidth of the feed-forward loop the effective tip/tilt sensor is not the wave-front sensor but this IR tip-tilt sensor (TTS).
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Figure 3. The zero-order model for Top Box deformation control. c(s), e(s) and d(s) are the command, error and deformation signals, while A(s) and F(s) are the feedback and feed-forward gains.
Besides the feed-forward loop, the effect of parallactic angle is also incorporated in the more detailed model of Figure 4. The Top Box consists of a cast aluminum optics bed and an octagonal frame around this bed. The structure has two distinct kind of deformation: • Shear flexure - perpendicular to the telescope axis - results mainly in common-path error. The drift is the same for the science instrument at Cassegrain focus as for the wave-front sensor optics in the Top Box. This kind of deformation can be neglected in our analysis. • Bow like flexure - parallel to the telescope axis - causes non-common path offset manifested as tilt and de-center of the mirrors in the Top Box. The OAPs and the wave-front sensor are at the edge of the optics bed where both the tilt and flexure are negligible. However, at the steering mirror location – half way to the center – the tilt and at the fold flat mirror location – in the middle – the de-center is considerable. Both of these effects are independent of the parallactic angle, but proportional to the sine of the telescope elevation. The FEA results for the bare minimum Top Box show acceptable optics bed deformations. However, these results reflect neither the weight of the science instruments to be installed on the optics bed (FSPEC, MIRAC, wide- and narrow-field cameras) nor the shimmulator assemblies essential to the alignment of the AO system. The shimmulator as well as the science instruments are expected to add considerable localized mass and so increase the flexure of the optics bed.
In addition to the mechanical deformation of the structure, transversal thermal gradients can develop in the beam path. The high thermal inertia of the optics bed can result in – worst case - as high as 1.2 oC temperature gradient across the 5 cm diameter collimated beam. Over the approximately 3 m beam path between the OAPs this gradient can introduce a tilt of 72 µrad (3.05 wave at λ=589 nm). The temperature gradient certainly can be improved by means of active cooling of the Top Box. Our thermal simulation shows that acceptable gradient – 0.13 oC corresponding to a coefficient of 0.33 wave – can be achieved by forced air flow in the Top Box; the feasibility – and possible adverse effects - of this solution should be experimentally verified on the telescope though.
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Figure 4. The control model used to predict the effect of deformation on science image
Although the control architecture is somewhat unusual, the system startup procedure is relatively straightforward: 1. The telescope is guided to the science object on the sky. The initial (blind) pointing precision of the MMT is expected as 1 arcsec rms, which is adequate for our startup procedure. 2. The steering mirror in the Top Box is offset to move the guide star on the wave-front sensor. The sky offset between the science object and the guide star is well known; the mirror must be calibrated though, since it has to find the star relying only on the wave-front sensor that has a FOV of no more than 2.5 arcsec. It should be noted that the slope sensitivity of the wave-front sensor is highly impaired due to the large, uncorrected spots on the quadrant detectors. 3. The main AO loop is closed. That will deform the secondary to center the guide star on the wave-front sensor and eventually minimize the spot size on the detectors. 4. The pick-off mirror for the IR tip-tilt sensor is offset to reflect the guide star on the sensor. This offset is also pre-calibrated; the FOV of the mirror is 4 arcsec. 5. The feed-forward loop is closed. It will move the science object exactly to the desired (offset) position, and keep it there in spite of any thermal or mechanical drift.
3. SIMULATION The telescope elevation h is defined by the geographic latitude φ, the star declination δ and the hour angle η 5:
h = asin[sin φ sin δ + cos φ cos δ cos η ] It is obvious that the sine of this elevation function has maximal slope (highest bandwidth) for a hypothetical star with zero declination. Consequently the worst case simulation should emulate the tracking of that star at around an hour angle of 6
hour. The result of the Matlab/Simulink simulation is shown in Figure 5. And 6. The geographic latitude was chosen to 31.689o corresponding to those of the MMT. The sampling rate for the Top Box control system is driven by the slippage (following error) allowed between the wave-front sensor and the deformable secondary. The instrument rotator of the telescope is set to the parallactic angle q of the sky object5. cos φ sin η q = asin cos h The real telescope is obviously not capable of tracking the infinite speed of parallactic angle change at Zenith. The fastest tracking rotation of the MMT is 1.3 o/s, which corresponds to 89o50.6’ elevation. The declination of a hypothetical star running that close to Zenith is 31.845o.
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Figure 5. Top Box deformation suppression using a PI feedforward loop with 10 s time constant
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Figure 6. The simulated non-common path deformation at the highest elevation slew rate, as it appears on the science instrument in closed feed-forward loop.
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Figure 7. The parallactic angle for a star with declination of 31.8450 close to Zenith
Figure 8. Simulation model for determining the appropriate sampling rate
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Figure 9. The slippage between the wave-front sensor and deformable secondary mirror.
A rough estimate of the required sampling rate can be derived from the +/-90o swing with 1.3 o/s maximum slope, as shown in Figure 7. This consideration results in a time constant of about 70 s; consequently a sampling rate of 7 s would provide sufficient margin to avoid aliasing. However, the signal is clearly not sinusoidal. A simple simulation model seen in Figure 8. reveals that with 7 s sampling interval we are at the verge of seriously undersampling the input signal at the vicinity of Zenith (see Figure 9.). In this simulation we used bandwidth limited proportional feedback. The gain is 60 dB to reduce the swing to 0.09o.
4. DESIGN CONSIDERATIONS The Rayleigh resolution of the 6.5 meter MMT at λ=2µm is 0.077 arcsec. Measuring this separation with visible light (λ=0.589µm) the corresponding Zernike coefficient is 2.07 wave. As long as the deformation effects and resolution of all the actuators are well below this level – say fifth of it, 0.4 wave – even cumulative errors are not likely to degrade the image quality of the telescope. Considering the mirror effect and the 5 cm pupil diameter, the resolution of the angular motion of the Top Box steering mirror must be 1 arcsec. Since the tangent arm of the Newport 605-1 gimbal mount used for the pupil mirror is 5 cm, 1 arcsec angular resolution results in 0.24 µm linear resolution for the actuator. A major role of the steering mirror is to capture the guide star on the wave-front sensor. Since the mirror is driven blindly to the capture position using only the co-ordinates of the star, the absolute accuracy of the control system must equal to the mirror capture range. The FOV of the wave-front sensor camera – with an aperture stop placed in the focus of its front lens – is 2.5 arcsec on the sky. Assuming a capture range of half of the FOV, considering again the aperture scaling factor and mirror effect, the capture range of the pupil mirror is 81 arcsec. Correspondingly, the absolute accuracy of the linear actuators is 20 µm. Allowing 100 arcsec off-axis anisoplanatism, the total range of motion is 1.8 degree, that is 1.5 mm with the 5 cm tangent arm. The pupil diameter on the wave-front sensor lenslet array is 1.87 mm. Assuming a maximum of 0.4 wave edge tilt after the front collimating lens of the wave-front sensor, the tolerance for de-center of the front focal point of the same lens is 11µm. The major dynamic effect causing this de-center is the flexure of the Top Box optics bed. The focal depth of the wave-front sensor camera is defined by the maximum allowed beam tilt error on the lenslet array of the Shack-Hartman sensor. Considering the collimated beam diameter of 1.87 mm, the angular tolerance is 52 arcsec after the wave-front sensor collimator lens. This tolerance results in 0.52 mm focal depth that should also be the repeatability of the wave-front sensor focus control. Because of this rather loose requirement, the focus stage can be controlled in open loop, from a look-up table experimentally determined for different telescope elevations. Considering the infinite conjugate (natural guide star) position
as zero, the laser guide star image position is ranging from 162.6 mm (telescope elevation 45 degree, Na layer distance 130 km) to 234.4 mm (telescope at Zenith, Na layer distance 90 km). The resolution of the wave-front sensor rotation is driven by the maximum allowed misalignment between the wave-front sensor and deformable secondary. The subapertures of the wave-front sensor are 144 µm squares. One percent slippage in subaperture position (corresponding to 0.09 o) is a safe choice for following error of the wave-front sensor rotation control. The pick-off mirror for the IR tip-tilt sensor in ARIES has a lateral dimension (shadow) of 2 mm and it is placed 10 mm above the f/15 focal point. The front collimator lens of the sensor is moving together with the mirror. Considering the 470 µm/arcsec scaling factor of the image plane, the required resolution for pick-off mirror lateral motion is 7 µm.
5. REALIZATION Although the precision requirements for the MMT AO electro-mechanical control system – both for positioning and position sensing – are extremely high, the motions to be tracked are relatively slow. This combination of requirements asks for a distributed control system, where the high precision is maintained by the localised DSP-based controllers while the outside commands are updated through a highly reliable serial fieldbus. DeviceNet has been chosen as the fieldbus for this application, mainly because (i) its high reliability (ii) relative maturity and (iii) wide vendor base and good availability in the US market. DeviceNet is based on the Controller Area Network (CAN) lower layer (ISO layer 2) protocol that is one of the most reliable in the industry. Both the CAN protocol and the DeviceNet application layer (ISO layer 7) are optimized for control applications6. Although its bandwidth is relatively modest (500 Kb/s), the latency (cycle time) on the bus (less than 1 ms) is comparable to those of much higher bandwidth busses (Profibus DP, for example). It is so because of the very slim communication overhead and non-destructive arbitration procedure. The 8 byte telegram size of the CAN protocol is perfectly adequate for control commands and status reports in our application.
Figure 10. The object model of EMC software. Besides the position control class (including the laser beam projector axes), it shows the secondary mirror temperature control (not fully defined yet) and gap sensor acquisition7 objects, too.
An outstanding advantage of DeviceNet is the hot swap capability of node devices. As long as the bus is not powered down, the individual nodes keep the local loops closed. There is no information lost and time wasted for re-initialization, which speeds up not just the installation and troubleshooting, but later the maintenance, too. Further advantage of the distributed architecture is the improved reliability due to reduced wiring.
Besides defining a communication protocol and physical media carrying it, the DeviceNet specifications standardize also the nodes hooked up to the network. The object model, command and response structure is the same for all nodes realizing similar functions. As a practical consequence, in our EMC software we have just one motion control object. The actual instances of this object are capable of talking to various motion controller/driver units from different vendors (see Figure 10.). The basic topology of the DeviceNet is trunk line / drop line. In our system one trunk line is running from the host computer located in the control room to the Top Box on the telescope, while another one will extend up to the telescope hub to control the laser beam projector. The same DeviceNet cable providing the communication link is also carrying the power for the nodes.
The high precision actuators are M222.50 DC-MikeDrives manufactured by Physik Instrumente. Their repeatability (down to –20 oC) is 100 nm, while the backlash is 2 µm. The actuators can achieve a speed of maximum 1.5 mm/s. The servo controllers used are MicroMo MVP2001B02 devices with 2 kHz loop update rate which is high enough to guarantee precise and stable servo loops. Because of the very good repeatability and relatively high speed of PI actuators there is no need to attach an absolute encoder to these axes. The homing procedure is fast enough due to the low mass to be moved and rare enough due to the hot swap capability of the bus. The absolute accuracy is maintained by the opto-electric home sensor (OMRON EE-SX771A). The long-term stability of the home registration is shown in Figure 11. Although the standard deviation of the registration is definitely larger at low temperatures than at room temperature, even this decreased accuracy is much better than the required.
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The DeviceNet network is configured for the predefined master/slave connection set, since there is no need for the individual nodes to directly talk to each other. The DeviceNet master is a PC with Windows NT operating system. The software - written in a flow chart based graphical control language (Think & Do) - is polling the nodes at every scan. The scan interval is 50 ms, which is more than adequate for our requirements and easily achievable with Windows. The PC is connected to the Adaptive Optics Data Server through an Ethernet (TCP/IP) link and operating in embedded mode, without console. The local display is used only for troubleshooting, or when the system is detached from the overall AO network
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Figure 11. Long-term home registration stability of the steering mirror actuator at room temperature and –20 Co (error bars denotes standard deviation)
Figure 12. Top Box control electronics hardware. The DeviceNet trunk connectors are easily recognizable on the enclosure walls with the incoming cable on one side and a bus terminator on the other. The mid-section of the box is occupied by the bus distribution panel with the drop cable connections; above it there are the motion control nodes, below is an expandable I/O node
The wave-front sensor stage is driven by stepper motors (API MT230-04-MO) with dedicated controllers (API DM-224IEDN). To keep track of the real position of the wave-front sensor, absolute encoders are required. Using AWC58-5812-4096FBA1D203PG by FRABA on both axes ensures 4096 counts/rev, 4096 revolution precision. This encoder is specified to work down to –20 oC; it features – just like the motion controllers - direct DeviceNet interface. The realized Top Box control
electronics is enclosed in a standard NEMA box, as shown in Figure 12. The NEMA enclosure is mounted on one of the Top Box side panels with hinges; it opens to allow access to the optics bed. The absolute encoders are hooked up directly to the bus trunk line. Since the new MMT is not available yet for experimental verification of the design and simulations of this work, the real test results will be described in a later report.
ACKNOWLEDGEMENTS Work described here has been supported by the Air Force Office of Scientific Research under grant #F49620-96-1-0366 and grant #F49620-99-1-0285. We thank J. R. P. Angel, R. Sarlot, A. Aranyosi, M. Montoya and R. Gonzalez for their help with some of the work presented here.
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