Keck Adaptive Optics Note 705
Keck Next Generation Adaptive Optics:
AO-Level Control Loops
P. Wizinowich
February 19, 2010
1. Introduction
The purpose of this document is to provide a high-level summary of the AO control loops used during
night-time operation, and to distinguish between which loops are handled by the AO control system and
which loops are handled by the real-time control (RTC) system. The RTC system has been largely defined
in KAONs 695 and 696. This document assumes the build-to-cost architecture defined in KAON 650 and
the system configurations defined in KAON 550.
An overview of the control loops is provided in section 2. Section 3 provides a summary of the
functionality provided by the AO control system during night-time operation (daytime calibrations are not
addressed). Focus control can be particularly challenging and this topic is therefore discussed in section 4.
2. Control Loop Overview
2.1 Devices
Figure 1 provides an overview of all the devices used in closed loop operation.
Figure 1: AO device overview.
1
Here is a brief explanation of each of the devices, proceeding roughly from left to right in Figure 1:
 Telescope. The telescope tracks the science object.
 Rotator. The rotator tracks to keep the field or pupil fixed.
 Deformable Mirror 1 (DM1). The Low Order DM in the wide field relay.
 Tip-Tilt Mount 1 (TTM1). The high bandwidth TTM on which DM1 is mounted.
 Laser Guide Star (LGS) WaveFront Sensor (WFS). There are seven laser guide star (LGS) WFS.
The LGS WFS corresponding to the central fixed asterism are labeled A1 through A4. The LGS
WFS corresponding to the three patrolling lasers are labeled P1 to P3. Each patrolling LGS WFS
is positioned on the corresponding patrolling LGS with a  probe arm (non-tracking). All LGS
WFS’s include a TTM and a WFS (as pictured in the lower left of Figure 1). The LGS WFS’s are
mounted on a single tracking focus camera stage (FCS) to maintain conjugation to the sodium
layer (the current assumption is that separate focus stages, to compensate for field curvature, are
not required for the patrolling LGS WFS). See KAON 692 for more details.
 Interferometer. A dichroic beamsplitter can be inserted into the beam to feed light to the
interferometer (or OHANA injection module). The interferometer uses a pair of object field
selector (OFS) mirrors (non-tracking) to transmit the on-axis object and acquire an off-axis object
(these are controlled by the interferometer).
 Low order wavefront sensor (LOWFS). There are three near-infrared LOWFS. Each is positioned
on a NGS using a  probe arm (non-tracking). All three LOWFS contain a MEMS deformable
mirror and a fast tip-tilt mirror (MEMS/TT in the figure). The first two, labeled 1 and 2 in Figure
1, have a tip-tilt (TT) sensor. The third LOWFS, labeled 3 in Figure 1, contains a tip-tilt-focusastigmatism (TTFA) sensor. Co-mounted with the TTFA is a truth wavefront sensor (TWFS) that
uses the visible light. All three LOWFS have focus translation stages (non-tracking) to position
them, as a function of field position, conjugate to the science instrument or interferometer focus.
 Deformable Mirror 2 (DM2). The High Order DM in the narrow field relay. This is higher order
than DM1.
 Tip-Tilt Mount 2 (TTM2). The low bandwidth TTM on which DM2 is mounted. This is suitable
for tracking but not for atmospheric correction. See KAON 669 for more discussion.
 Natural Guide Star (NGS) WFS. A dichroic beamsplitter can be inserted into the beam to feed
light to the NGS WFS. A pair of field selector mirrors (FSM) (non-tracking) is used to acquire the
NGS. The NGS WFS is mounted on a translation stage to position its focus, as a function of field
position, conjugate to the science instrument or interferometer focus. The NGS WFS can be used
in a mode where it acts as a TTFA/TWFS type LOWFS.
 Atmospheric Dispersion Corrector (ADC). The science instrument ADC that compensates for
atmospheric dispersion as a function of zenith angle and direction. It can be moved into or out of
the science path with a translation stage.
 Science instrument. Only one science instrument is planned initially, although the NGAO system
will be capable of feeding a second future instrument. The planned NGAO instrument will have
an imager and an integral field spectrograph (IFS). The IFS will be fed by a deployable fold
mirror. No tracking devices are currently planned in the instrument, but multiple devices (e.g.,
filter wheels, gratings) will be changeable between science exposures.
 Not shown are the sources that can be inserted on the telescope side of the rotator (via a fold
mirror) for alignment, calibration and testing purposes. These are not expected to be required
during routine night-time operation.
2.2 NGS AO Control Loops
Figure 2 and Figure 3 show the control loops used in NGS AO mode with the science instrument and
interferometer, respectively.
2
Figure 2: NGS AO control loops for the science instrument.
The real-time wavefront sensing is provided by the NGS WFS. The NGS WFS camera data is fed to the
real-time control (RTC) system. The RTC computed tip-tilt is sent to TTM1 and the higher order
commands are sent to DM1. In the case of the science instrument the highest order corrections can be
applied to DM2 (DM2 is fixed, nominally flat, for the interferometer); these are higher order terms than
DM1 is capable of correcting.
Figure 3: NGS AO control loops for the interferometer.
The AO control system keeps track of the tip-tilt applied to TTM1 and the focus applied to DM1. Tip-tilt
and focus are then periodically offloaded to the telescope pointing and focus (secondary piston). Telescope
Az/El position information is used to make the transformation to telescope coordinates.
The AO control system provides tip-tilt offsets. These are applied to the FSM when the tip-tilt loop is
open. For the science instrument case the offsets are used as centroid offsets by the RTC when the tip-tilt
loop is closed. For the interferometer case these offsets are applied to TTM2 when the tip-tilt loop is
closed. The AO control system computes differential atmospheric refraction (DAR) between the NGS
WFS wavelength and the science instrument or interferometer wavelength. Keck angle tracker (KAT)
offsets are provided by the interferometer and are combined with DAR offsets in the case of the
3
interferometer. Any pre-measured tip-tilt errors from the ADC rotation can also be included as part of the
AO control system provided offsets. Differential tracking can also be handled with offsets.
The AO control system provides position and rotation control for the science instrument ADC when it is in
the science path. This control is based on the Az/El of the telescope, the rotator orientation and the science
instrument wavelength band. Any tip-tilt errors introduced by the ADC rotation should be corrected via
AO control system offsets to TTM2 (based on a previously calibrated lookup table or algorithm).
2.3 LGS AO Control Loops
2.3.1 Science Instrument Case
Figure 4 shows the control loops used in LGS AO mode with the science instrument. Two “AO Control”
boxes are used in the figures for drawing simplicity; these are the same system. Two “RTC Tomo.” boxes
were used for the same reason. The RTC algorithms are described in KAON 695.
The real-time wavefront sensing is provided by a central set of four fixed LGS WFS, three patrolling LGS
WFS and the three LOWFS.
Figure 4: LGS AO control loops for the science instrument.
Data from the central fixed asterism LGS WFS and LOWFS are used by the real-time control (RTC)
tomography engine to compute the best correction to be applied to the science path. Two options will exist
as to how to distribute the science path correction between DM1 and DM2. One option is to apply the
ground layer turbulence to DM1 and the high altitude turbulence to DM2. The second option is to apply
the lower order corrections to DM1 and the higher order (higher than DM1 can handle) corrections to
4
DM2. In either case DM2 must deal with the highest order terms that cannot be handled by DM1. In the
interferometer case DM2 is nominally flat so all of the possible correction must be applied to DM1.
The real-time wavefront sensing data from each patrolling LGS WFS is used to control the MEMS in the
corresponding LOWFS via a separate RTC control loop (labeled RTC1, RTC2 and RTC3 in the figures).
The tip-tilt information from the three LOWFS is used via the RTC tomography engine to control TTM1.
This information is also used by the AO control system to determine if there is any field rotation; which
could be corrected with an offload to the rotator.
Offloading of tip-tilt and focus from TTM1 and DM1 to the telescope is done in the same way as for NGS
AO mode. Science instrument ADC control is also the same as for NGS AO mode.
The seven LGS WFS are mounted on a tracking focus camera stage (LGS FCS) to maintain conjugation to
the sodium layer. Fast focus information from the TTFA (via the RTC) is used by the AO controller, with
appropriate time averaging, to provide a focus correction to the FCS (see section 3). On a slower time scale
more accurate focus information from the TWFS is used by the AO controller to provide a focus correction
to the FCS.
The AO control system provides tip-tilt offsets (for DAR, KAT offloads and differential tracking). These
are applied to the three LOWFS  probe arms when the tip-tilt loop is open. The offsets are applied to
TTM2 when the tip-tilt loop is closed (this is different than for the NGS case).
2.3.2 Interferometer Case
Figure 5 show the control loops used in LGS AO mode with the interferometer. The real-time wavefront
sensing is provided by the four fixed LGS WFS and by the LOWFS/TWFS mode of the NGS WFS (the
fold dichroic that feeds the interferometer does not transmit NIR light to the LOWFS). Data from the
central fixed asterism LGS WFS and single LOWFS are used by the real-time control (RTC) tomography
engine to compute the best correction to be applied to the interferometer science path using DM1. The tiptilt information from the LOWFS is used via the RTC tomography engine to control TTM1.
Offloading of tip-tilt and focus from TTM1 and DM1 to the telescope is done in the same way as for NGS
AO mode.
The LGS WFS are mounted on a tracking focus camera stage (LGS FCS) to maintain conjugation to the
sodium layer. Fast focus information from the single TTFA (via the RTC) is used by the AO controller,
with appropriate time averaging, to provide a focus correction to the FCS (see section 3). On a slower time
scale more accurate focus information from the TWFS is used by the AO controller to provide a focus
correction to the FCS.
The AO control system provides tip-tilt offsets (for DAR and KAT offloads. These are applied to the NGS
WFS field steering mirrors when the tip-tilt loop is open. The offsets are applied to TTM2 when the tip-tilt
loop is closed (this is the same as for the NGS case).
5
Figure 5: LGS AO control loops for the interferometer.
2.4 Fixed Pupil Mode
The control loops for fixed pupil mode are not yet discussed in this document. A discussion of this mode
can be found in KAON 666. In this mode the only NGS sensor used is the on-axis NGS WFS. In LGS
mode the NGS WFS must therefore act as a LOWFS/TWFS (to be confirmed as part of the NGS WFS
design effort).
3. AO Control Summary for Night-time Operation
The AO control system must provide the following functionality during night-time operations. Many, but
not all, of these have been illustrated in the other sections of this document. These functions are roughly
ordered to follow the light from the sky through the system. The purpose of this summary is not to define
how to provide each of these functionalities but rather to identify all the required AO control
functionalities. Note that daytime calibration functions, not normally required during nighttime operations,
are not included in this list.






System configuration. The AO controller must configure the system appropriate for the current
science mode. KAON 550 provides a summary of the science mode configurations.
Patrolling LGS positioning. To point the patrolling LGS to the appropriate point in the sky to be
used for real-time correction of the LOWFS images.
LGS rotator tracking. To track the LGS to stay fixed on the sky.
LGS pointing flexure compensation. Coordinated pointing mirror positioning and tracking to
compensate for flexure of all LGS beacons.
Laser launch telescope focus compensation. TBD whether this will be required. Would likely be
based on input from temperature sensor(s).
Tip-tilt offload to the telescope. To offload TTM1.
6





















Focus offload to the telescope secondary mirror piston. To offload focus from DM1.
Coma offload to the telescope secondary mirror tip-tilt. At least hooks should be provided for this
capability; based on Keck AO experience it may be infrequently used.
Rotator mode, positioning and tracking. To select the appropriate tracking mode and position
angle and to track the rotator.
Rotator offload. To offload rotation errors based on tip-tilt measurements from the LOWFS.
Patrolling LGS WFS positioning. To point the patrolling LGS WFS to the appropriate point in the
sky to be used for real-time correction of the LOWFS images.
LGS WFS focus positioning and tracking. The stage should initially be positioned as a function of
sodium altitude and telescope zenith angle. It must then track as a function of zenith angle. TTFA
and TWFS focus inputs are used to correct for the assumed height of the sodium layer. See
section 4.
LOWFS positioning. Each LOWFS must be correctly positioned to acquire the required NGS
based on telescope pointing, rotator position and any NGAO field distortions. This can be based
on target files and acquisition camera images (appropriately compensated for by DAR).
LOWFS focus. Each LOWFS focus must be positioned to be conjugate to the science instrument
focal plane. Focus adjustments are therefore required when the LOWFS is repositioned, when
optics are inserted or removed from the science path, when switching between science
instruments, or when changing configurations within a science instrument (e.g., filters, plate
scales, etc.).
Acquisition camera acquisition and processing. Acquisition camera images are required as part of
the acquisition process.
TWFS image acquisition and processing. The TWFS images are processed to determine what
corrections (focus and centroid offsets) are required. The focus measurements are provided for
LGS WFS focus positioning. The centroid offsets are provided to the RTC tomography engine.
LGS spot size. There is a TBD here. The AO control system may need to be involved in
determining the LGS spot size to determine what gain to apply the LGS WFS centroid processing.
At minimum it should be possible, as done in the current system, to measure the individual
segment LGS spot size on the acquisition camera. The AO control system may need to coordinate
a dithering approach to determining the gain.
TWFS offloading. The TWFS measured centroid offsets are processed by AO control to provide
the RTC tomography unit with centroid offsets for the LGS WFS. Note that the shape of the
LOWFS DM in front of the TWFS will contribute to the measured centroid offsets and this
contribution must be removed before providing centroid offset corrections to the RTC tomography
unit.
TTM2 positioning and tracking. See KAON 669 for a discussion of the multiple roles of this
second relay tip-tilt mount in such areas as DAR, non-sidereal tracking and dithering.
NGS WFS positioning. Positioning of the field steering mirrors (FSM) to acquire the NGS.
Note that interferometer OFS positioning is provided by the interferometer.
NGS WFS focus. The NGS WFS must be positioned to be conjugate to the science instrument
focal plane.
Atmospheric dispersion corrector (ADC) positioning and tracking. The ADC must be positioned
and track as a function of zenith angle, zenith direction and science pass band.
Differential atmospheric refraction (DAR) compensation. Open-loop corrections are provided to
the positioning of the LOWFS or NGS WFS. Closed-loop corrections are provided to the 2 nd relay
tip-tilt mount (TTM2) or in some cases to centroid offsets. The DAR corrections are a function of
zenith angle, zenith direction, wavefront sensor wavelength and science wavelength.
Interferometer angle tracker (KAT) offloads. In NGS mode these are fed to the NGS WFS field
steering mirrors for positioning and the NGS WFS centroid.
WFS sky background acquisition. AO control must provide the appropriate control to offset to
sky and obtain sky background measurements on all of the wavefront sensors.
Rayleigh background acquisition. AO control must provide the appropriate control to detune the
laser in order to obtain Rayleigh backgrounds on the LGS WFS.
7


NGAO parameter recording. A TBD set of AO parameters needs to be provided for writing to the
science instrument FITS image header. In the case of the Interferometer a number of keywords
need to be available to the interferometer telemetry stream. In all cases a set of AO parameters
will need to be written to the AO data storage system along with selected real-time data.
AO enclosure environment control/monitoring. At minimum need to maintain the temperature of
the cold enclosure around the AO science path.
In addition to the above functionality a number of observing sequences must be provided and/or supported
by the AO control system. These are defined at some level in the observing operations concept document
(OOCD; KAON 636).
 Acquisition. See sections 8.2 and 8.3 of KAON 636.
 Dithering. AO control must provide the appropriate control to support dithering (i.e., taking a
series of science exposures with the science field moved by a few arcseconds between exposures).
 Offsetting. The astronomer may want to adjust the position of the science field on the science
instrument. Small offsets could be handled with TTM2 for the science instrument case. Larger
offsets may require opening the NGS loops and repositioning the NGS sensors.
User interfaces are required to support the astronomer, AO or laser operators and the observing assistant.
4. Focus Control
The Strehl ratio and measured FWHM on the science instrument are a function of the focus of everything
in the optical path to the science instrument. The dynamic focus contributors include the atmosphere,
telescope and deformable mirrors. There are some fixed focus terms due to the AO and science instrument
optics. There are some fixed, but changing focus terms such as when science instrument filters or plate
scale are changed or an atmospheric dispersion corrector is installed. In LGS mode the change in the
altitude of the sodium layer can be perceived as a focus shift.
4.1 Requirement (Order of Magnitude)
We want to maintain the focus on the science instrument so that it does not significantly degrade the
diffraction-limited image quality. At H-band the diffraction-limit is 0.034 arcsec. If we said for example
that defocus, due to all contributing sources, cannot degrade the image by more than 10% at zenith then the
allowable contribution is [(1.1*0.034)2 – (0.034)2]1/2 = 0.016 arcsec * 0.727 mm/arcsec = 0.0113 mm. This
is converted to an allowable shift in the focal plane by multiplying by the telescope f/# = 15, so Z = 0.17
mm.
It would be acceptable to allow the defocus contribution to grow as a function of zenith angle. If we for
example allowed the defocus to match the diffraction-limited image size at a zenith angle of 60, then Z =
0.034 arcsec * 0.727 mm/arcsec * 15 = 0.37 mm.
The bandwidth at which LGS WFS focus control must be performed depends on the rate of change of the
telescope zenith angle (and therefore the rate of change of the distance to the sodium layer).
The bandwidth at which TTFA/TWFS corrections from measurements with natural guide stars must be
made depends on the amplitude and bandwidth of sodium altitude variations. The required bandwidth can
be obtained from the appropriate portion of the NGAO wavefront error budget excel spreadsheet.
4.2 Definitions
The wavefront sensors are all mounted on translation stages to allow for focus control:
 There is one LGS WFS focus control stage (LGS FCS).
 There is one NGS WFS FCS labeled NGS FCS.
 There are three LOWFS focus stages labeled FCSL1 to FCSL2. The TWFS is mounted on L1.
8
The following quantities are focus shifts, along the optical axis, with respect to the science instrument’s
focal plane. The effect on FSCI is positive when the individual focus terms are positive (positive is away
from the telescope = into the science instrument):
 ZSCI = focus shift on science instrument away from optimal position.
 ZATM = focus shift due to ATMospheric & dome seeing.
 ZTEL = focus shift due to the TELescope.
 ZLGS FCS = position along the optical axis of the FCS that supports the LGS WFS. Z LGS FCS = 0
when DM1 is flat and the FCS is conjugate to the sodium layer.
 ZNGS FCS = position along the optical axis of the Focus Camera Stage (FCS) that supports the NGS
WFS. ZNGS FCS = 0 when DM1 and DM2 are flat and the FCS is conjugate to the science
instrument focal plane.
 ZSOD = focus shift due to the SODium layer being at a different distance from the telescope than
the distance assumed for positioning the LGS FCS.
 Zoffset = focus offset. Zoffset = 0 when DMs are flat and the science instrument focal plane is
conjugate to the telescope focal plane.
 ZFCSLi = position along the optical axis of the FCS that supports LOWFSi. ZTSS = 0 when DM1
and MEMSi is flat and the LOWFS FCS is conjugate to the science instrument focal plane.
The following quantities are focus terms. There is a one-to-one relationship assumed in these equations
between focus terms and focus shifts:
 FDMi = focus term on DM1 or DM2.
 FMEMSi = focus term on MEMS1, MEMS2 or MEMS3.
 FLGS WFS Ai = focus term measured on LGS WFS Ai.
 FLGS WFS Pi = focus term measured on LGS WFS Pi.
 FNGS WFS = focus term measured on NGS WFS.
 FTTFA = focus term measured on the TTFA LOWFS.
 FTWFS = focus term measured on the TWFS.
The focus on the NGAO science instrument is given by ZSCI = ZATM + ZTEL + ZSCI,offset + FDM1 + FDM2.
The focus on the interferometer is given by ZIF = ZATM + ZTEL + ZIF,offset + FDM1.
4.3 NGS Mode
Ideally the time averaged <ZSCI> = 0, because the control system tries to drive the wavefront sensor
measured focus FNGS WFS = ZATM + ZTEL + FDM1 + FDM2 + ZNGS FCS to zero by driving FDM1 + FDM2 = -(ZATM
+ ZTEL + ZFCS), where the NGS WFS FCS was positioned to be conjugate to the science instrument focus
such that ZFCS = Zoffset. If the FCS position has changed since calibration (other than to compensate for
science instrument changes, then <ZSCI>= Zoffset - ZFCS.
For the interferometer it will be important to apply the focus to DM1. In the case of the NGAO science
instrument any residual focus (due to the limited actuator count on DM1) can be applied to DM2.
There could be some performance advantage to using the LOWFS information even in NGS mode since
this is additional “free” information if suitable off-axis stars are available; TTFA information could be
available at higher bandwidths than the NGS WFS bandwidth. This hook should be left in the system, but
for now this will be considered a future feature.
4.4 LGS Mode
Section 2 of KAON 264 describes focus control for the existing Keck LGS AO system, with an emphasis
on how to properly control the LGS FCS position to be conjugate to the sodium layer.
The control system drives the LGS wavefront sensor measured focus
FLGS WFS = ZATM + ZTEL + ZSOD + FDM1 - ZLGS FCS
9
to zero by driving
FDM1 = -(ZATM + ZTEL+ ZSOD) + ZLGS FCS.
The average of the four central asterism LGS WFS focus measurements should be used to control the focus
on DM1. This statement assumes that non-atmospheric focus changes are slow enough that they can be
corrected with changes in the position of the LGS WFS focus camera stage (FCS) as discussed below.
Since the distance to the sodium layer varies as a function of the zenith angle, , the LGS FCS stage should
be driven as a function of zenith angle to stay conjugate to the sodium layer:
ZSOD(h,) = f h / (h - f cos) - f = f2cos / (h-fcos) and
ZLGS FCS = f2cos / (hFCS-fcos),
where h is the actual height of the sodium layer above the telescope at zenith, hFCS is the assumed height,
and f is the focal length of the telescope (150 m). The difference is
ZLGS FCS - ZSOD = ZLGS FCS [(h - hFCS)/(h - fcos)].
Table 1 provides some examples, and gives a feel for the magnitude and sensitivity of the LGS FCS
positioning.
Table 1: LGS WFS FCS positions for various LGS altitudes and zenith angles.
h (km)
ZFCS (mm)
 ()
Infinity (NGS)
0
0
85
0
265.17
89.95
0
250.56
90
0
250.42
90
1
250.38
90
59
128.87
90
59.95
125.29
90
60
125.10
The TTFA measures
FTTFA = ZATM + ZTEL + FDM1 + FMEMS3 - ZFCSL3 + Foff-axis.
Usage of the TTFA focus information may need further discussion since there are at least two options:
1) The recommended default option for AO control is to use a suitable time-average to average the
off-axis focus term to zero (the off-axis focus will instantaneously be somewhat different than the
on-axis science focus) and then use this information to correct the currently used value for the
sodium altitude (which will in turn drive the LGS FCS).
2) An alternative which would provide higher bandwidth correction would be for the RTC
tomography engine to use the TTFA plus the data from the two TT sensors to determine the onaxis focus and apply it directly to the DM. The resultant tomography computed focus error could
also be sent to the AO control system to correct the sodium altitude at an appropriate bandwidth.
In either case the AO control system must use TTFA focus data, provided either directly or through the
RTC tomography engine, to update the sodium altitude value used to position the LGS WFS.
The TWFS measures
FTWFS = <ZATM> + <ZTEL> + <FDM1> + <FMEMS3> - ZFCSL3.
Here, “<>” indicates the time-average over the TWFS integration.
If we set the TTFA/TWFS position with DM1 flat, so that the TTFA/TWFS measured focus is zero when
the fiber image is at best focus on the science instrument, then Z FCSL3 = 0.
Inserting the LGS WFS driven <FDM1> equation from above, then we get
<FTTFA> - <FMEMS3> = -<ZSOD> + <ZLGS FCS> and FTWFS - <FMEMS3> = -<ZSOD> + <ZLGS FCS>,
where the time averages for TTFA and TWFS are over different periods.
10
This is just the error in how accurately we have managed to drive the LGS FCS to match the distance to the
sodium layer. Instead of directly adjusting the LGS FCS position, the more effective approach is to correct
for the assumed sodium altitude, hFCS, which will in turn adjust the LGS FCS position. Substituting we get
FTWFS - <FMEMS3> = ZLGS FCS [(h - hFCS)/(h - fcos)].
The current value of hFCS should therefore be updated to:
h = [(FTWFS - <FMEMS3>) fcos - ZLGS FCS hFCS] / (FTWFS - <FMEMS3> - ZLGS FCS).
11