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# Calibration at elevation of the WEAVE fibre positioner

Sarah Hughes  Dept. of Physics, Keble Road, University of Oxford, OX1 3RH, UK
Gavin Dalton  Dept. of Physics, Keble Road, University of Oxford, OX1 3RH, UK
RAL Space, Science and Technology Facilities Council, Rutherford Appleton
Laboratory, Harwell Oxford, OX11 OQX, UK  Kevin Dee  Isaac Newton Group, 38700
Santa Cruz de La Palma, Spain  Don Carlos Abrams  Isaac Newton Group, 38700
Santa Cruz de La Palma, Spain  Kevin Middleton  RAL Space, Science and
Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Oxford,
OX11 OQX, UK  Ian Lewis  Dept. of Physics, Keble Road, University of Oxford,
OX1 3RH, UK  David Terrett  RAL Space, Science and Technology Facilities
Council, Rutherford Appleton Laboratory, Harwell Oxford, OX11 OQX, UK  Alfonso
L. Aguerri  Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife,
Spain  Marc Balcells  Isaac Newton Group, 38700 Santa Cruz de La Palma, Spain
Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain  Dep.
de Astrofísica, Universidad de La Laguna, 38200 La Laguna, Spain  Georgia
Bishop  RAL Space, Science and Technology Facilities Council, Rutherford
Appleton Laboratory, Harwell Oxford, OX11 OQX, UK  Piercarlo Bonifacio  GEPI,
Observatoire de Paris, Université PSL, CNRS, Place Jules Janssen, 92195
Meudon, France  Esperanza Carrasco  Instituto Nacional de Astrofísica, Optica
y Electronica (INAOE), Mexico  Scott C. Trager  Kapteyn Instituut,
Rijksuniversiteit Groningen, Postbus 800, 9700 AV Groningen, Netherland
Antonella Vallenari  Osservatorio Astronomico di Padova, INAF, Vicolo
Osservatorio 5, 35122, Padova, Italy

###### Abstract

WEAVE is the new wide-field spectroscopy facility[1],[2],[3] for the prime
focus of the William Herschel Telescope in La Palma, Spain. Its fibre
positioner is essential for the accurate placement of the spectrograph’s 960
fibre multiplex. We provide an overview of the recent maintenance, flexure
modifications, and calibration measurements conducted at the observatory prior
to the final top-end assembly. This work ensures that we have a complete
understanding of the positioner’s behaviour as it changes orientation during
observations. All fibre systems have been inspected and repaired, and the
tumbler structure contains new clamps to stiffen both the internal beam and
the retractor support disk onto which the field plates attach. We present the
updated metrology procedures[4] and results that will be verified on-sky.

###### keywords:

fibre spectroscopy, WEAVE, WHT, robotic positioners, high multiplex
spectroscopy, metrology, calibration

##  1 INTRODUCTION

WEAVE is the new spectroscopy facility[5] for the William Herschel Telescope
(WHT) on La Palma. WEAVE has a multiplex of 960 optical fibres and a 2° field
of view. It consists of four distinct subsystems: the prime focus system[6],
the spectrograph system[7], the optical fibres[8], and the fibre
positioner[3],[4]. The prime focus system consists of a six lens wide-field
corrector with atmospheric dispersion compensator[9] (ADC), an instrument
rotator[10] (WRS), and a new top end structure incorporating focus/tilt
adjustment to the spider vanes. The ADC components comprise two air-spaced
prismatic doublets which counter-rotate to correct for dispersion along the
direction of the parallactic angle. The corrector prescription delivers
$<0.6"$ polychromatic images over a flat focal surface. The positioner is
mounted to the field rotator, and the corrector is fixed to the top end
structure. WEAVE has three fibre observing modes: the multi-object
spectrograph (MOS) fibres, the mini integral field units (mIFUs), and the
large integral field unit (LIFU). Each of the 20 mIFUs is a bundle of 37
fibres, whilst the LIFU has 547 central fibres and 8 bundles around the edge
with 7 fibres for sky subtraction. The positioner has two 410 mm diameter
field plates (plate A and plate B) located on either side of the central
tumbler, that can rotate 180° between the two. Each field plate has an
independent set of fibres, which allows the next field to be configured by the
robots whilst the other field plate is being used for observations. This
minimises the overhead time between observations. The positioner uses pick-
and-place technology to arrange the optical fibres in the focal plane
according to the targets allocated in the field of view. Two robots (called
Nona and Morta) move along x, y, z, and $\theta$-stages to pick up individual
fibres arranged around the edge of the field plate in retractors. These are
shown in figure 2. A gripper system attached to the each robot is used to
place the fibres in their desired position, to within ±8 µm. Attached to the
side of each gripper unit is an optical system that allows the imaging of the
fibres (gripper camera) and field plate (upper focus). A detailed description
of the positioner’s design and operational capabilities can be found in Dalton
et al. (2012, 2016, & 2020)[2],[5],[3], and the top-end assembly is shown in
figure 1. A complete summary of the WEAVE survey and the early testing of the
data pipeline processing systems can be found in Jin et al. (2022, _in
preparation_)[11] .

Figure 1: The assembled top end of WEAVE on the William Herschel Telescope in
La Palma, Spain. This photo was taken on the $25^{\rm{th}}$ of May 2022.

The dual-arm spectrograph system[7] has continuous wavelength coverage
(3660-9590 $\mathrm{\text{\AA}}$) in the low-resolution mode (R $\sim
5750$\mathrm{\text{\AA}}$$) and coverage over several narrow regions (either
4040-4650 or 4730-5450, and 5950-6850 $\mathrm{\text{\AA}}$) in the high-
resolution mode (R $\sim 21000$\mathrm{\text{\AA}}$$). The spectrograph is not
located on the top-end of the WHT, but on the Nasymth platform. This has
significant advantages; such as improving the stability of the system when
making an observation, and reducing restrictions on the size of the
spectrograph due to weight balance. This paper will focus on the positioner
and its fibre sub-systems, specifically the maintenance and calibration work
completed in preparation for on-sky operations.

Figure 2: $\left(\rm{\emph{Left}}\right)$ A schematic diagram of the
positioner, which identifies its main components. Some design modifications
have been made, specifically the counterweight system, however this is outside
the scope of this paper. $\left(\rm{\emph{Right}}\right)$ An image of several
retractors, highlighting their tiered structure and the park positions of the
MOS fibres.

##  2 Positioner maintenance

After the positioner’s arrival at the observatory in January 2021, we quickly
realised that it had been damaged during it’s journey. We suspect that it
experienced a large shock, due to several (small) bolts, attaching some
elements to the main structure, had been sheared off. This resulted in many
months being spent detaching and reassembling the central tumbler structure,
as well as a complete redesign of the robot counterweight system. The details
of this procedure is outside the scope of this paper, and will instead focus
on the flexure behaviour that was observed after the tumbler reassembly. We
then describe the process of extracting, inspecting, and repairing all 336
retractors in the positioner, as many were disturbed as a result of the
transport and maintenance work.

Once the positioner’s main structure had been repaired and reassembled, it was
attached to the WEAVE rotator system (WRS) via an interface plate. Together
they were then placed on a testing rig that allowed us to shift its elevation
angle manually. The result is a system that can mimic the positioner’s
orientation on the telescope.

###  2.1 Flexure behaviour

The focus adjustment of the WHT was designed to meet a number of requirements
such as the thermal expansion and flexure of the top-end structure. However,
the maximum tilt and position of the field plates is driven by the allowed
defocus across each fibres button when the field plate is in the observing
position. The tolerances to meet this defocus budget are:

  * •

The tilt of the field plates must be less than $\pm 0.0045^{\circ}$.

  * •

The separation between the field plate in the observing position and the WRS
interface plate should be $273.2\pm 0.025$ mm.

To remain within the focus tolerances, it is crucial that we understand how
the structure of the positioner will move when its orientation is changed. In
the design phase, a Finite Element Analysis (FEA) model was created from the
positioner’s 3D Computer Aided Design (CAD) model. The FEA model was used to
calculate the flexure due to varying the gravitational loading on the
telescope. The tumbler itself was modelled as a series of solid bodies; the
central beam, the retractor support disk (RSD) drum, the field plates, the
motor, and the bearing. The model considered the combined flexure of these
elements.

Figure 3: $\left(\rm{\emph{Left}}\right)$ The arrangement for a single DTI to
measure the shift in position of the observing field plate with respect to the
WRS interface plate, as the positioner’s orientation is changed. It is
attached to an angle iron spanning the width of the interface. The tilt was
measured with two DTIs and the distance to the interface was measured with a
depth micrometer, where it is zeroed at ZD $0^{\circ}$.
$\left(\rm{\emph{Right}}\right)$ The positioner mounted to the WRS, on a
testing rig that allows the system to change elevation.

The flexure of the positioner was measured once it was mounted to the WRS and
placed on a test rig designed for the WRS. The testing rig can adjust its
elevation angle up to $90^{\circ}$ from its zenith position, referred to as ZD
$90^{\circ}$. Previously, ZD $0^{\circ}$ had been used for all metrology
measurements in the Oxford laboratory[4] .

####  2.1.1 Initial measurements

A laser tracker was used to measure the positioner’s metrology with respect to
the WRS/POS interface plate, which was used as a fixed reference point. Four
magnetic Spherically Mounted Retroreflector (SMR) nests were attached to the
field plate in the observing position. The placement of the nests form a cross
along the $x$ and $y$ axes of the field plates.

| Plate A | Plate B
---|---|---
$x$ direction tilt | $0.009^{\circ}$ | $0.046^{\circ}$
$y$ direction tilt | $0.024^{\circ}$ | $0.135^{\circ}$
Movement of plate’s centre position | 0.12 mm | 2.293 mm
Table 1: The results of the tilt and shift in position of each field plate
when in the observing orientation, relative to the WRS interface.

The measurements of the tilt and position of each field plate relative to the
WRS interface with the laser tracker at ZD $0^{\circ}$ is summarised in table
1. When comparing them to the requirements listed in section 2.1, it is clear
that neither of the field plates are in the correct position.

To examine the flexure behaviour further, two digital Dial Test Indicator
(DTI) gauges were attached to an angle iron that spans the width of the
testing rig and lies close to the field plates in the observing position. An
image of this setup can be seen in figure 3. They were each positioned at
opposing sides of the field plate. For plate A, the maximum displacement was
200 $\mu$m at ZD $50^{\circ}$, with a curved profile. For plate B, the maximum
displacement was $\sim$1000 $\mu$m at ZD $90^{\circ}$ with a gradual linear
trend. The results are shown in figure 4.

Figure 4: The displacement as a function of elevation, measured using two
DTI’s at both the top and bottom positions on the field plate. The bottom
measurements show a continual increase in the displacement, with a maximum
value of $\sim 1000$ $\mu$m at ZD $90^{\circ}$. A curved profile can be
observed for the top position, where the displacement increases to a maximum
value of $\sim 400$ $\mu$m before moving back towards its original value.

The magnitude of the flexure meant that mechanical interventions were needed
to reduce this movement. Further testing revealed the central tumbler beam and
drum as the most likely candidates for the observed displacement.

Figure 5: $\left(\rm{\emph{left}}\right)$ The clamp inserted around the
bearing side of the tumbler beam, to prevent it from twisting as the
positioner’s orientation was changed. $\left(\rm{\emph{right}}\right)$ A
schematic diagram showing the reinforcement bars, which hold in place an
aluminium flat along the top of the tumbler beam. These additional structures
increase the beams rigidity, which has been weakened by the bolt holes made in
the side panels.

####  2.1.2 Prevention actions

We believe that the additional bolt holes made in the beam side plates during
the tumbler’s reassembly are responsible for reducing its overall stiffness.
An aluminium flat, attached with reinforcement brackets, were inserted inside
the tumbler beam to increase its rigidity. A clamp was designed and fitted to
the inside the tumbler structure, around the edge of the beam on this side to
restrict its movement. These elements resulted in a reduction in the
displacement magnitude from $\sim$1000 $\mu$m to 400 $\mu$m for plate B in the
observing position.

The clamp and reinforcement brackets reduced the curvature observed to the
inside of plate A’s profile however, there was still a significant difference
between the measurements from each DTI. Four jacks were inserted between the
top plates of the tumbler drum, with the results shown in figure 6. The jacks
were replaced by a reinforcement strut that attaches to the top plate and RSD
on each side of the tumbler. This is to reduce the mass budget of the
positioner.

Figure 6: Shows the displacement as a function of elevation, when both the
clamp, stiffening additions, and four additional jacks are used to hold the
tumblers structure. Here the term _Control_ refers to the measurements taken
prior to any insertions to reduce the flexure. We see that the additional
components significantly reduces the magnitude of the displacement, and
removes the curved profiles observed for each plate.

####  2.1.3 Summary of flexure measurements

Initial measurements made using both a laser tracker and DTI gauges showed
that neither plate A or B were positioned correctly with respect to the WRS
interface, and far exceeded the allowed tolerances for the telescope focusing
capabilities. A clamp, an aluminium flat with its corresponding reinforcement
bracket, and two RSD struts were installed into the tumbler’s structure to
reduce the magnitude of the displacement. The final results are shown in
figure 6, however there is still a maximum displacement of $200$ $\mu$m, which
could potentially restrict the range of positions that can be used during
observations. This will be analysed during on-sky commissioning.

###  2.2 Final focus position

Despite the preventative measures in place, we still observe some flexure
behaviour that restricts the range of orientations that can be used when
observing, to remain within the focus tolerance. Calculations have been made
as to how the final flexure results will affect the point spread function
(PSF) observed with WEAVE. Previous estimations do not account for any
variation in co-planarity of the field plates or any tilt, meaning that they
are underestimating the residual sum of squares (RSS) of defocus. Here the
updated RSS, $|\Delta x_{\rm{Tot}}|$, is defined as

$|\Delta x_{\rm{Tot}}|=\sqrt{\Delta x^{2}_{FP}+\Delta x^{2}_{0}},$ (1)

where $\Delta x^{2}_{FP}$ is the measured field defocus and $\Delta x^{2}_{0}$
is the RSS of defocus without the affect of the field plates.

Figure 7: The encircled energy diameter of the PSF as a function of button
defocus, having accounted for the plate position and tilt in the new focus
budget. We can see that the worst case scenario with nominal seeing conditions
is $1.2"$ at $+150$ $\mu$m defocus.

The previous calculation assumes a symmetrical 2D gaussian profile for the
PSF. This assumption underestimates the energy in the wings of the profile,
and does not allow the full-width half-maximum (FWHM) to be well defined. As a
result, a Moffat function has been used for these calculations, which is
defined as

$f(x,y,\alpha,\beta)=2\left(\frac{\beta-1}{\pi\alpha^{2}}\right)\left[1+\frac{x^{2}+y^{2}}{\alpha^{2}}\right]^{-\beta}.$
(2)

where $\beta$ and $\alpha$ are seeing dependent parameters.

The result of modelling the PSF as a Moffat function with a FWHM of $0.8"$ and
a $\beta$ value of 3, then convolving it with typical seeing conditions at the
observatory is shown in figure 7. The worst case scenario is a FWHM of $1.2"$
at $+150$ $\mu$m defocus. The allowed angular travel range of the WRS system
when observing is $\pm 155^{\circ}$ rotation, and these results do not imply
that any orientations need to be avoided. However, the effect of the flexure
behaviour will need careful consideration, particularly as we receive results
from commissioning and first light.

###  2.3 Retractor interventions

After the positioner’s reassembly, remote testing began in the summer of 2021.
A handful of fibres had already been disabled in the Oxford laboratory,
however this list began to increase rapidly during operational testing at the
observatory. The reason for these failure modes was unclear, as there was no
indication that they were linked to any systematic failures or that they were
concentrated to a specific region of the plate. Included in the new list of
disabled fibres were a small number of guide fibres. These needed to be
brought back online, as each plate only has 8 available and at least 2 are
required for successful telescope guiding. A detailed description of the
retractors design and assembly process can be found in Schallig E. (2019)[12].

Figure 8: An image of the retractor repair process at AP3, of a guide fibre
retractor on plate A. Due to the limited distance the guide retractor could be
moved, the robot’s Y-gantry was used to safely support the retractor during
the repairs.

In January 2022, the retractor inspection and repairs process began at the
observatory after the flexure work was completed. An important aspect of this
process was to understand if the retractors would be easily accessible when on
the telescope. To check this, the orientation of the positioner on the rig was
changed to a rotation angle of $0^{\circ}$ and an elevation angle of
$90^{\circ}$ from zenith. This position corresponds to a standard telescope
maintenance position called Access Park 3 (AP3).

At AP3, we confirmed it is possible to extract both the field plates and the
retractors, provided that the covers can be removed appropriately, whilst also
leaving the shims under the field plate in position. The most effective way to
remove the retractors is in blocks of $\sim 20$, for additional maneuvering
space. It is necessary to do this when extracting retractors close to either
the motor or the bearing. The majority of the retractors have enough length in
their fibre cables to allow the retractors to be laid on a nearby work
surface. The exception is the guide fibre retractors, which have a reduced
freedom of movement. These retractors had to be repaired using a robot gantry
as the repair surface. This can be seen in figure 8.

After inspecting several retractors on plate A, it became clear that the
entire subsystem would need to be examined. While many of the retractors had
not failed, a large proportion of the pulley systems were not performing to
the standards expected. This is partially due to gradual improvements in the
quality control during assembly, as we increased our knowledge of how the
pulleys should behave. However, it is not clearly understood how the shock
affected the retractors. From assembly, we know that the retractors are quite
sensitive to how their axles are positioned in the covers and aluminium plate.
It is possible that the shock disrupted many of the retractors this way, or
changed the operation of those which were deemed functional, yet were on the
border of acceptable performance.

In total, it took approximately 5 weeks to fully complete the inspection and
repairs of all 336 retractors. Many of which were not a direct result of
retractor failures. As each fibre is fed into a metal button, it is surrounded
by a thick tubing called a ferrule, which runs through the length of the
button and ensures that the prism rests a set distance away from the front of
the button. Several fibres were found to have loose ferrules which had to be
re-attached carefully by-hand, as well as some magnets coming loose from their
buttons. It is important to note that recovering fibres with loose ferrules
can be completed at AP3 without extracting any retractors.

Since completing these repairs, there have been a small number fibres which
have failed during the calibration process. This is not entirely unexpected,
and we have still succeeded in reducing the total number of disabled fibres,
and preventing the potential failure modes of many more. When isolating the
recently disabled fibres to the retractor repairs alone, we do not observe any
patterns with previous list of disabled fibres.

##  3 Metrology measurements

Due to the modifications made to the positioner, the metrology measurements
and calibration procedures completed in Oxford and described in Hughes et
al.[4] had to be repeated. This includes re-measuring the base z-height of the
field plates, evaluating the park heights of every tier 3 fibre, and new tasks
such as measuring the maps and park heights as a function of position.

Many of the methods used previously have been altered to improve their
efficiency, whilst adapting to the reduced positioner access as it changes
orientation.

###  3.1 Field plate maps

Figure 9: The DTI gauge used to measure the z-height of the field plates, for
a range of orientations of the positioner. The gauge has been mounted in place
of the theta counterweight system, meaning that every measurement must be made
at a fixed orientation. The gauge is zeroed at coordinates (0, 0, 37) mm on
the field plate.

The field plate maps were measured using a dial gauge mounted to each robot,
the exact set up can be seen in figure 9. The position of the gauge is in
place of the new theta counterweight system, therefore it is offset from the
grippers $x$ position by $\pm 55$ mm depending on the robots orientation. This
means that the movement of the robots across the field plate must be
restricted to prevent a collision between the robot gripper unit and the
retractors.

Maps must be measured for each plate using both robots. The robots are driven
to the same set of coordinate points to maintain consistency. To measure a
complete map, the robot must take the majority of the measurements at
$-90^{\circ}$ rotation, and the remaining points at $+90^{\circ}$ rotation.

Figure 10: The field plate z-height as a function of position for
$\left(\emph{left}\right)$ Morta and $\left(\emph{right}\right)$ Nona. All
measurements were made using a DTI gauge attached to each robot, for a
consistent set of coordinates across the plate. As a result these measurements
are relative to the robot gantries.

A rotational offset was measured at (0,0) between the two theta angles, $\pm
90^{\circ}$, so that they can be shifted into the same frame. This method was
verified by measuring a series of points at both orientations that the robot
could reach. The result was consistent with the offset measured at the origin,
allowing us to use this as a global offset between the two rotational frames.

The base map was set to be the same as the zero-point used for the flexure
metrology, at ZD $40^{\circ}$ with a rotation angle of $0^{\circ}$. The final
base maps for the positioner are shown in figure 10.

There has been a significant change in the Z-map prior to the positioner being
shipped to the observatory. This is expected due to the change in distribution
of the field plate shims, and also the affect of having the reinforcement
strut attached to the centre of the retractor support disc. We see that the
difference between Nona and Morta, in figure 10, is consistent for both
plates.

###  3.2 Park heights

The method for measuring the park heights has remained unchanged from Hughes
et al.[4], as this is still the most effective procedure available. Using the
dial gauge for this process is not possible due to the restrictions on the
robots movement whilst it is mounted. As the fibres must be moved before the
height of the porch can be found, using the grippers directly to measure the
values requires the least physical intervention.

Figure 11: The complete set of park height measurements for plate A, for both
Nona and Morta, for all tier 3 fibres.

At ZD $40^{\circ}$, measurements for the complete set of park heights were
made for every fibre, across both plates and using both robots. This is shown
in figure 11. The distribution of the park heights remains relatively
unchanged compared the values in Oxford, showing the same trend discussed in
Hughes et al.[4]. The retractors position has a small tolerance, therefore we
do not expect each fibres park height to have shifted significantly, despite
the inspection and re-installation of the entire sub-system.

###  3.3 Elevation and rotation mapping

To ensure that the fibres are being picked up and placed accurately during
observations, we must understand how the field plates and park heights change
as a function of elevation and rotation. By using a dial gauge to map the
plates, this procedure can be completed at a range of positions with relative
ease by driving the robots remotely. The set of plate maps covering the full
range of allowed rotations and elevations is shown in figure 12.

Figure 12: The plate B Nona z-height maps, for a set of elevation and rotation
angles which span the range of the orientations that will be used on-sky.
These plots show the change in height of the field plate relative to the base
map measured at ZD $40^{\circ}$. The individual plots are the difference
between the plate maps at rotation angles $+120^{\circ}$, $+60^{\circ}$,
$-60^{\circ}$ and ZD angles $0^{\circ}$, $15^{\circ}$, $30^{\circ}$,
$40^{\circ}$, $50^{\circ}$, and $65^{\circ}$. The colour represents the change
in $z$-height of the plate from the map at ZD $40^{\circ}$.

Due to the reduced physical access to the positioner as it changes position,
both on the testing rig and on the telescope, we devised a method of
extrapolating the z-maps to the park positions in order to predict how they
will evolve.

We begin by defining a function which describes our base plate map
$f\left(x,y\right)$. For the complete set of park measurements we have another
function called $M\left(X,Y\right)$. The plate map is extrapolated to estimate
the plate map at the same position the park heights were measured, $f(X,Y)$.
For every park position, we find the difference $\Delta M$, between our
extrapolated base map and the park heights, where

$\Delta M(X,Y)=f\left(X,Y\right)-M\left(X,Y\right).$ (3)

We then apply $\Delta M$ to the new plate map measured for the change in
position, which has also been extrapolated to the park positions. This gives a
new set of predicted park heights $F\left(X,Y\right)$ that we can then compare
to a subset of park heights measured using the gripper jaws at the new
position, where

$F\left(X,Y\right)=f_{new}\left(X,Y\right)+\Delta M\left(X,Y\right),$ (4)

and $f_{new}\left(X,Y\right)$ is the new extrapolated plate map.

For a comparison, direct measurements of the guide retractor porches were made
for the same set of positions as the new maps. With plate A, this does not
require moving any fibres. However, for plate B the guide retractors are
populated, so the tier 3 fibres need to be moved out onto the plate to clear
the porches for measurements. The guide fibres were chosen due to their even
spacing along the perimeter, and the reduced number of fibres that need to be
moved.

Figure 13: Plots of predicted park heights for Nona on plate A, calculated
using the plate maps measured at each ZD angle and the offset between the park
heights and plate map at ZD $40^{\circ}$. These predictions were calculated
for ZD angles $0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $40^{\circ}$,
$50^{\circ}$, and $65^{\circ}$.The red points represent the tier 3 guide
retractor heights, which were measured directly using the robot gripper jaws
for comparison. Figure 14: Plots of predicted park heights for Nona on plate
A, calculated using the plate maps measured at each rotation angle and the
offset between the park heights and plate map rotation angle $0^{\circ}$.
These predictions were calculated for rotation angles $+120^{\circ}$,
$+60^{\circ}$, $-60^{\circ}$, and $-120^{\circ}$. The red points represent the
tier 3 guide retractor heights, which were measured directly using the robot
gripper jaws for comparison.

The change in rotation and ZD are evaluated separately. By understanding how
these two movements evolve independently, we can apply their predictions as
transformations to the plate maps and park heights. Once WEAVE is on-sky,
comparisons can be made to our current models and eventually will be
implemented within the positioner’s software. The predictions for each
elevation angle are shown in figure 13.

For the rotational movement, we chose to set the positions to $+120^{\circ}$,
$+60^{\circ}$, $-60^{\circ}$, and $-120^{\circ}$. Figure 14 shows our
predictions for the park heights on plate A, using the appropriate Z-map for
each rotation, and compares it to the set of guide retractor heights found
with the robot gripper jaws directly.

For both the elevation and rotation predictions, there remains an uncertainty
on the scale of $\sim 40\mu$m. This uncertainty is estimated from the
difference between the measured guide retractor heights and the predictions at
each rotation and ZD angle. The residuals we observe appear to be periodic,
and we are in the process of generating a routine that will reduce their
magnitude to less than $20$ $\mu$m. During observations, the positioner’s
software will select the closest map to the position of the telescope when
each field is configured. The predicted heights for each fibre can then be
read directly from the corresponding map file. This will require additional
maps to be taken once the positioner has been mounted onto the telescope, as
well as validating this approach when combining both rotations and ZD
predictions.

##  4 Calibration procedures

With the positioner’s updated metrology, the fibre movement processes must be
re-calibrated. This includes calculating the new focus height and rotation
centres for all three cameras on each robot.

###  4.1 Robot calibration

We begin by setting the zero point of the encoders for both robots. This is
done by either finding the centre spot, or by placing a fibre by hand over the
central spot and moving the robot so that the fibres position can be found
using the positioner’s centroiding software. With the robots in position the
encoder values are re-zeroed.

After being reset, the $Z$ height of the robot is adjusted so that the fibre
is in focus with the gripper camera. We then calculate the axis of rotation
for all three cameras on each robot. This procedure has been refined, after
finding that our original method did not evaluate this number to a high enough
accuracy.

A fibre is placed on the rotation centre of the gripper camera by hand as
accurately as possible, and the gripper camera measures its position. The view
is switched to the upper camera, and the fibre is located in its field of
view. This value will be different to that of the gripper camera. The upper
camera is then moved to a sequence of four points, which form the corners of a
square around the position of the fibre. At each point the camera is kept
still whilst the fibres position is re-measured. The difference in the fibres
position between all corners is calculated. This is used to set the plate
scale of the camera, until the measured position at all four points agree with
one another. The rotation centre of the upper camera is then set in pixels, so
that it agrees with the position of the fibre as measured by the gripper
camera.

After setting the camera parameters, a base-grid of the field plate is
measured. Both field plates have a series of points etched into their surface,
called the grid, which can then be imaged using the camera’s attached to each
robot. The position of the grid points are measured using a centroiding
software, which are then used to remove the offset, rotation, scaling and non-
perpendicularity of the axes when placing fibres on the field plate. Further
details on the grid measurements and software can be found in Schallig E.
(2019)[12].

The process of measuring the fibre’s position with each camera and the four-
points is repeated, along with another base-grid from the robots park
position, to ensure that the measurements are self-consistent. For this entire
process, the robot should be kept at the a constant $\theta$ angle, the same
as its park position, since it was found that changing the robots orientation
gave inconsistent values. This is likely due to the relative tilt of the robot
axes.

It is crucial to ensure that the robots optical system agrees on the fibre’s
position for both foci. For the gripper focus this should be to within $\pm 1$
$\mu$m. However, for the upper focus this can be within $\pm 5$ $\mu$m. The
upper focus can have a lower tolerance as it is mostly used when searching for
misplaced fibres. As long as the fibre is within the field of view, then this
feature will be functional. Almost all fibre movements and many of the
calibration procedures are made using measurements that are relative to the
gripper focus, therefore the tolerances must be as small as possible.

From this point, we can begin running scans of the field plate grids across
the same set of orientations as the field plate maps. The first grid tests
were ran for the ZD $40^{\circ}$ zero point position for both plates. As
before with the field plate maps, we change the rotation and elevation angles
independently, so that a complete set of grids can be measured for each
position. These will be used as the default in software, which will then be
replaced when the grids are measured during the field configuration process
on-sky.

###  4.2 Fibre placement offsets

The fibre placement offsets can be divided into four main components; The
grasp offsets, the plate release offsets, the park release offsets, and the
unpark release offsets. These describe all the stages in a fibres movement
cycle.

The grasp offset is the change in the position of the fibre once the gripper
jaws have closed around the button vane. Specifically, this is the change in
position of the fibres centroid, relative to its button vane. Factors that can
affect this include the shape of the vane due to the manufacturing process,
the location of the prism relative to the front of the button, and the height
at which the fibre is being picked up from.

Figure 15: The Move $\left(top\right)$, Park $\left(middle\right)$, and Unpark
$\left(bottom\right)$ offsets for 250 fibres on plate A. Here, the cyan
markers indicate the offset in the $x$ direction, and magenta markers
represent the $y$ direction offset. These measurements have been made using a
gripper force of 30 N. The blue and red points represent the $x$ and $y$
direction offsets after the gripper force has been increased to 50 N.

The park release offset is found by measuring the shift in position of the
fibre when it is released onto its porch, referred to as its park position.
This is then used to adjust the positioning of the robot over the porch when
it goes to place the fibre back to its resting position. The unpark release
offset follows a similar process, except it is the movement of the fibre that
has been carried from its park position and placed onto the field plate.

The plate release offset, referred to as _Move_ in figure 15, is the change in
position of the fibre when it has been carried from one position on the field
plate to another. The reason for these different offsets is that the relative
tilt angle of the plate to the robots, and each retractor porch to the robot
is different. Whilst these angles are relatively small, they have a
significant impact on the fibres coordinate shift.

In previous offset measurements, each fibre completed 50 moves on the field
plate, which were randomly distributed within it’s patrol range[4]. We learnt
that when the positioner is in its zenith position, the release offsets do not
change as a function of position on the field plate. This must also be
verified for a range of elevations.

We can see the distribution of the mean offsets for each fibre at ZD
$40^{\circ}$ in figure 15, which have been measured for 250 fibres. These
measurements are relative to the grasp offset calculated for each fibre. This
procedure is still ongoing, as the initial measurements, shown by the magenta
($y$ direction offset) and cyan markers ($x$ direction offset), had large
random errors. To reduce the magnitude of the offsets, the gripper force was
increased from 30 N to 50 N. The offsets measured after this increase are
represented by the red ($y$ direction offset) and blue ($x$ direction offset)
markers in the figure 15. From this plot, we can see that increasing the
gripper force has significantly reduced the magnitude of the offsets random
errors. However, we still observe some unusual behaviour in the offsets $y$
direction which requires closer inspection. The reduction of these errors also
allows for more anomalous points to be identified and investigated further.

##  5 Conclusion

The new top-end of WEAVE has successfully been installed, and all its
components have now been aligned. The observatory is in the process of
conducting operational tests, and the commissioning period is due to begin by
August 2022.

Figure 16: The new top-end of the WHT, positioned at AP3

The positioner exhibited significant flexure behaviour with respect to the WRS
interface plate, which was outside the tolerance of defocus across each fibres
button. Several sets of measurements were taken with both a laser tracker and
multiple DTI’s to trace the source of the flexure, which was identified to be
the tumbler beam and the top plates attached to it. After installing a clamp,
aluminium stiffening structures, and two pistons that connect to the RSD, the
magnitude of the flexure behaviour was reduced to a maximum displacement of
200 $\mu$m. In addition, both plates now follow the same function of
displacement with elevation.

Despite these measures, we still observe a movement of the positioner with
respect to the WRS interface, as the rotation angle is changed. When
calculating the affect of the defocus on the PSF, the worst case scenario was
found to be $1.2"$ at $+150$ $\mu$m defocus.

After the maintenance and flexure work was completed, all 336 retractors
installed in the positioner were extracted, inspected, and repaired if
necessary. This process took approximately 5 weeks to complete, and resulted
in many disabled fibres, including guide fibres, being brought back online.
There have been some retractor failures since this work, however this is to be
expected. The setup of each retractor can easily be disturbed, and the act of
removing and re-installing them is enough to do so.

After re-assembling the positioner, the metrology of the field plates was re-
measured using a DTI attached to each robot. Maps were taken for a series of
elevation and rotation angles to cover the full range of orientations that
will be used during observations. Predictive models were generated for the
park heights of every fibre across the set of orientations for the positioner,
using the complete set of park measurements and the plate map at ZD
$40^{\circ}$ as its basis. These predictions will be adjusted when on-sky, and
currently serve as a starting point when performing the other calibration
procedures. They have residuals of order $\pm 40$ $\mu$m, prior to further
analysis.

The robots rotation centre was carefully measured for all three camera’s so
that they are in agreement to within a few micrometers. For the gripper
camera, this measurement has a much smaller tolerance, as all the fibre
movements are made with respect to its measurement of the fibre’s position.
The new procedure for calculating this axis has proven to be accurate enough
that it may be used during configuration testing.

Finally, the Move, Park, and Unpark offsets of 250 fibres have been measured
on plate A, and this process is still ongoing. It was found that increasing
the robots gripper force from its default value of 30 N to 50 N, caused a
substantial reduction in the random errors observed. Some unusual behaviour is
still seen in the offsets $y$ direction, which will be investigated further
after the remaining offset measurements are made. At this stage, the complete
set of offsets have been measured for plate A, and are now being conducted for
plate B.

###### Acknowledgements.

This work was supported by the Science and Technology Facilities Council and
St. Cross College, Oxford. The author would like to give special
acknowledgement to SPIE for their support in funding their attendance to this
conference. Funding for the WEAVE facility has been provided by UKRI STFC, the
University of Oxford, NOVA, NWO, Instituto de Astrofísica de Canarias (IAC),
the Isaac Newton Group partners (STFC, NWO, and Spain, led by the IAC), INAF,
CNRS-INSU, the Observatoire de Paris, Région Île-de-France, CONCYT through
INAOE, Konkoly Observatory of the Hungarian Academy of Sciences, Max-Planck-
Institut für Astronomie (MPIA Heidelberg), Lund University, the Leibniz
Institute for Astrophysics Potsdam (AIP), the Swedish Research Council, the
European Commission, and the University of Pennsylvania. The WEAVE Survey
Consortium consists of the ING, its three partners, represented by UKRI STFC,
NWO, and the IAC, NOVA, INAF, GEPI, INAOE, and individual WEAVE Participants.
The WEAVE website can be found at
https://ingconfluence.ing.iac.es/confluence//display/WEAV/The+WEAVE+Project
and the full list of granting agencies and grants supporting WEAVE can be
found at
https://ingconfluence.ing.iac.es/confluence/display/WEAV/WEAVE+Acknowledgements.

## References

  * [1] Balcells, M., Benn, C. R., Carter, D., Dalton, G. B., Trager, S. C., Feltzing, S., Verheijen, M. A., Jarvis, M., Percival, W., Abrams, D. C., et al., “Design drivers for a wide-field multi-object spectrograph for the William Herschel Telescope,” in [Ground-based and Airborne Instrumentation for Astronomy III ], 7735, 2659–2673, SPIE (2010).
  * [2] Dalton, G., Trager, S. C., Abrams, D. C., Carter, D., Bonifacio, P., Aguerri, J. A. L., MacIntosh, M., Evans, C., Lewis, I., Navarro, R., et al., “WEAVE: the next generation wide-field spectroscopy facility for the william herschel telescope,” in [Ground-based and Airborne Instrumentation for Astronomy IV ], 8446, 220–231, SPIE (2012).
  * [3] Dalton, G., “Integration and early testing of weave: the next-generation spectroscopy facility for the william herschel telescope,” in [Ground-based and Airborne Instrumentation for Astronomy VIII ], Proc. SPIE 11447 (2020).
  * [4] Hughes, S., “Final assembly, metrology, and testing of the WEAVE fibre positioner,” in [Ground-based and Airborne Instrumentation for Astronomy VIII ], Proc. SPIE 11447 (2020).
  * [5] Dalton, G., “Final design and progress of weave: the next generation wide-field spectroscopy facility for the william herschel telescope,” in [Ground-based and Airborne Instrumentation for Astronomy VI ], Proc. SPIE 9908 (2016).
  * [6] Tomàs, A., Canchado, M., Casalta, J. M., Dalmases, F., Maroto, O., Martín-Nuño, C., Romero, A., Aguerri, J. A. L., Herreros, J. M., Delgado, J. M., et al., “The WEAVE prime focus correction: from design to integration,” in [Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation III ], 10706, 27–35, SPIE (2018).
  * [7] Rogers, K., Stuik, R., Steele, I. A., Pragt, J., Middleton, K. F., Bates, S., Kragt, J., Tromp, N., Lesman, D., Lhomé, E., et al., “The design of the weave spectrograph,” in [Ground-based and Airborne Instrumentation for Astronomy V ], 9147, 2043–2057, SPIE (2014).
  * [8] Sayède, F., Younes, Y., Fasola, G., Dorent, S., Abrams, D. C., Aguerri, J. A. L., Bonifacio, P., Carrasco, E., Dalton, G., Dee, K., et al., “First results of tests on the weave fibres,” in [Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II ], 9912, 674–686, SPIE (2016).
  * [9] Lhomé, E., Agócs, T., Abrams, D. C., Dee, K. M., Middleton, K. F., Tosh, I. A., Jaskó, A., Connor, P., Cochrane, D., Gers, L., et al., “Manufacturing process for the WEAVE prime focus corrector optics for the 4.2 m william hershel telescope,” in [Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II ], 9912, 1290–1305, SPIE (2016).
  * [10] Astobiza, A. S. V., Llano, G. M., Uriarte, I., Fernández, D., Urrutia, R., Múgica, A., Campo, R., Ariño, J., de Bilbao, L., Kosmalska, A., et al., “New prime focus rotator system for the WHT,” in [Ground-based and Airborne Telescopes VIII ], 146, SPIE (2020).
  * [11] Jin, S. et al., “The weave survey: Design, overview and simulated implementation,” Monthly Notices of the Royal Astronomical Society in preparation (2022).
  * [12] Schallig, E., Metrology, calibration, integration and testing of the WEAVE fibre positioner, PhD thesis, University of Oxford (2019).