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\title{Performance of Echidna fiber positioner for FMOS on Subaru} 

\author{Masayuki Akiyama\supit{a,b}, 
Scott Smedley\supit{c},
Peter Gillingham\supit{c},
Jurek Brzeski\supit{c},
Tony Farrell\supit{c},
Masahiko Kimura\supit{b},
Rolf Muller\supit{c},
Naoyuki Tamura\supit{b}, and
Naruhisa Takato\supit{b}
\skiplinehalf
\supit{a}Astronomical Institute, Tohoku University, Aramaki, Aoba-ku, Sendai, 980-8578, Japan; \\
\supit{b}Subaru Telescope, NAOJ, 650 North Aohoku Place, Hilo, HI, 96720, USA; \\
\supit{c}Anglo-Australian Observatory, PO Box 196, Epping, NSW 2117, Australia 
}

\authorinfo{Further author information: (Send correspondence to M.A.)\\M.A.: E-mail: akiyama@astr.tohoku.ac.jp}

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  \begin{document} 
  \maketitle 

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\begin{abstract}
Echidna is a fiber positioner designed and built by the Anglo-Australian Observatory 
using novel technology to position 400 fibers in the prime focus field of the 
Subaru telescope. The fibers feed two near infrared OH-suppression spectrographs,
the whole project being known as Fiber Multi Object Spectrograph (FMOS). 
In order to accommodate the large number of the fibers in the physically limited area, 
a new fiber positioning method is developed. Stand-alone tests of the positioner 
at sea level confirm its performance is fully satisfactory. Initial results and 
prospects of the on-sky commissioning tests of the positioner are also described.
\end{abstract}

\keywords{fiber positioner, piezoelectric actuators, Subaru telescope}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{INTRODUCTION}
\label{sec:intro}  

The Fiber Multi-Object Spectrograph (FMOS) is a next generation 
near-infrared spectrograph for the 8.2m Subaru telescope, being
able to obtain spectra of 400 objects simultaneously\cite{mai00,kim03}. 
Echidna is the fiber positioning system for the instrument and 
is attached to the prime-focus. The focus has 30$^{\prime}$ diameter 
FoV with the physical size of 150mm diameter. In order to position 
400 fibers in the limited area, a new fiber positioning method, 
tilting a fiber attached to a carbon-fiber ``spine'' sitting on a ball mount 
with a quadrant tube piezo actuator, was developed. See Fig.~\ref{Echidna_phot2}.
Once saw-tooth signal is applied to the piezo actuator, 
the spine tilts due to a slippage of the pivot ball against the
three point mount. 
The prototyping stage of the positioner is described in 
Gillingham et al.\cite{gil00} and in Moore et al.\cite{moo03}. 
The overall mechanical design is shown in Gilligham et al.\cite{gil03}, 
and its details are described in Brzeski et al.\cite{brz04}. 
See Fig. 4 of Ref.\citenum{brz04} for the input signal and the movement. 
The 400 fibers feed two cooled OH-suppression spectrographs, 
one developed in Kyoto university \cite{eto04,iwa06} and the other
build in UK \cite{lew03,dal06}. Both of them cover 900-1800nm.
In the fiber train, there is a collimated light coupling\cite{gra03,gra04},
in order to convert the fast F/2 ratio of the prime focus, and
to detach the positioner from the telescope. 

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=1.0\linewidth]{Echidna_phot2.eps}
\end{center}
\caption{
Left) drawing of one module of the fiber positioner from 
Fig. 4 of Ref\citenum{brz04}. One module has 20$\times$2 science-fibers and 
2 guide-bundles at both ends of the module. Science-fibers are 100$\mu$m diameter 
core fiber, and guide-bundles are bundles of 7 50$\mu$m-core fibers
with 80$\mu$m spacing, which corresponds to $0.96^{\prime\prime}$ at the focal plane. 
A fiber is attached to a carbon-fiber tubing, called  ``spine'', with a pivoting ball 
and a tungsten counter weight. The pivoting ball is sitting on a three-point mount 
with a ring magnet at the top of a quadrant tube piezo actuator. Spines for 
the science-fibers and the guide-bundles have the same structure.
Middle) close up view of the focal plane. 12 modules of the 40 science-fibers
cover the FoV. 400 science-fibers within the 
30$^{\prime}$ diameter FoV are connected to the spectrographs.
The spacing between neighboring spines is 7mm. Each spine is designed to
be able to reach the home positions the 6 neighboring spines.
Right) structure of the Echidna unit around the focal plane. The 
positions of the tips of the fibers are measured with the fiber camera 
of the Focal Plane Imager (FPI) on the XY gantry.
}
\label{Echidna_phot2}
\end{figure}

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.7\linewidth]{Echidna_phot3.eps}
\end{center}
\caption{
Left) Echidna unit on the testing jig (orange frame structure).
The bottom of the unit corresponds to the focal plane.
The black box on the table in front of the unit is the fiber 
connector assembly. Right) Echidna under installation into 
the prime-focus unit. The installation is done off the telescope 
in the prime-focus unit storage area and attached to the telescope, 
Echidna being enclosed in the unit.
}
\label{Echidna_phot3}
\end{figure}
 
In this paper, we describe the results of stand-alone and on-sky 
evaluations of the novel fiber positioning system. Most of the stand-alone 
tests were performed in the Hilo base facility at sea-level. They were 
done either on a custom tilting jig or in the prime-focus unit enclosed in a tilting
frame. The whole positioner unit on the tilting jig is shown in the
left panel of Fig.~\ref{Echidna_phot3}. The installation process to the
prime-focus unit is shown in the right panel. The stand-alone tests
confirmed the performance of the positioner was fully satisfactory. 
Measured mechanical properties of each component of the fiber
positioner unit are summarized in Section 2. Dynamical properties
of the positioner and the results of fiber positioning tests are
described in Section 3. After careful transfer to the Mauna Kea
summit facility, we confirmed that the performance did not degrade
in the low temperature and low humidity environment. On-sky commissioning
was conducted Dec. 2007, Jan. and May. 2008, and scheduled for
Jun. and Aug. 2008. The initial results of the commissioning and 
prospects are summarized in Section 4.

There are precise requirements for the accuracy of the fiber positioning.
In order to minimize the loss of the coupling efficiency 
due to the misalignment between a target and a fiber, the fiber must be
positioned within 20$\mu$m of the target. During the concept design study, 
the optimal core size of the science-fibers was determined to be $1.2^{\prime\prime}$, 
which corresponds to 100$\mu$m at the prime-focus, maximizing the expected 
SN ratios of faint galaxies in the background limited condition. In 
Fig.~\ref{misalignment}, the coupling efficiency of the 100$\mu$m fiber to
a stellar object is shown as a function of misalignment. For misalignment 
less than 20$\mu$m (=0.24$^{\prime\prime}$) the reduction of the coupling 
efficiency is less than 10\%, 
even under a good seeing condition with FWHM=$0.5^{\prime\prime}$.

Due to a number of physical effects (including the changing contact position
of the pivot ball with the three-point mounts) the repeatability of spine
movement is not precise.
In order to achieve the required positioning accuracy, we
need to iterate. After one movement, the positions of the tips of the
fibers are re-measured with the spine camera.
In order to position the 400 fibers within a reasonable time, 10-15 minutes,
the maximum number of iterations is $\sim$7. Each iteration process 
takes approximately 100 seconds. If the worst-case fiber movement has 40\% accuracy in 
each operation, 10$\mu$m positioning accuracy can be achieved with 7 iterations
for movement from the home position to the edge of the patrol field:
$0.4^7\times7200\mu$m $\sim$ 10$\mu$m.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.4\linewidth]{misalignment.eps}
\end{center}
\caption{
Plots of percentage energy encircled within a 100$\mu$m
diameter circle as a function of misalignment for three
different seeing conditions.
}
\label{misalignment}
\end{figure}

\section{MECHANICAL PROPERTIES}

\subsection{Accuracy of the measurements of the fiber positions}

Accurate measurements of the fiber positions are critical to
the evaluations of the mechanical and dynamical properties of
the positioner. The positions are measured with the spine camera 
of the Focal Plane Imager (FPI). The camera covers the entire focal 
plane by moving with an XY gantry. Each fiber can be back-illuminated
individually by a illumination mechanism with a prism at the connector 
end of the fibers (inside the black box shown in the
left panel of Fig.~\ref{Echidna_phot3}). The spine camera has
768$\times$493 physical pixels with an 11$\mu$m$\times$13$\mu$m pixel size
and covers the 400 fibers with 59 FoVs (see Fig. 9 of Ref. \citenum{gil03}). 
The positions of the 400 fibers can be sequentially measured 
in approximately 100 seconds.

The spine-camera uses a telecentric lens to image the spine tips.
The distortion pattern of the spine-camera and the
non-orthogonality of the XY gantry were calibrated by measuring
a grid-pattern light-source attached at the focal plane instead
of the fiber modules. In details of the calibration source, see
Section 1.2.3 of Ref.\citenum{brz04}. In order to evaluate the
effect of gravity on the non-orthogonality, the calibrations
were done at various tilt angle and the rotator angle inside 
the prime focus unit. The distortion pattern of the spine-camera
was described well with a model including up to the third order
term; the residuals of the model is 1.3$\mu$m RMS with a maximum
error of 3.1$\mu$m. The residuals are shown in the left panel 
of Fig.~\ref{meserr}. The non-orthogonality of the XY gantry can
be described well with the mean parameters determined by
averaging the parameters measured at various tilt and rotator angles.
The residuals of the calibrations are 2.0$\mu$m RMS in the entire 
FoV, including both residuals of the distortion pattern and the
non-orthogonality models. The RMS represents the accuracy of the
fiber position measurements. The residuals do not have systematic
component as shown in the middle panel of Fig.~\ref{meserr}.

Additionally, repeatability of the measurements were checked 
by measuring the positions of the fibers multiple times using 
the spine-camera. The results are shown in the right panel of 
Fig.~\ref{meserr}. The differences of the measured positions
between two independent measurements have a scatter of 1$\mu$m 
RMS (p-p about $\pm$2$\mu$m) for each direction. If we measure
a position of a fiber in multiple times without moving the spine camera, 
the resultant scatter in each direction is $\sim$1$\mu$m RMS. 
Thus, the scatter of the positions in the multiple-measurements
is dominated by the accuracy of the centroid evaluation.

The above accuracy of the position measurements and the repeatability
are satisfactory to confirm the positions of the fibers.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=1.0\linewidth]{meserr.eps}
\end{center}
\caption{
Left) Residuals in one FoV of the spine-camera after removing
third order distortion. No systematic residual.
Middle) residuals in the entire focal plane after removing
the camera distortion model and the gantry XY movement
non-orthogonality model. 
Right) The differences of the measured positions of spine tips
in two measurements.
}
\label{meserr}
\end{figure}

\subsection{Length of the spines}

Due to the fast F/2 ratio of the prime-focus, careful control of the 
parfocality of the fibers is important. If a 100$\mu$m fibre is defocused
by 150$\mu$m, the reduction of the 
coupling efficiency will be 5\% under typical seeing condition. 
If an object at the edge of the patrol area of each fiber
is observed, then the tip of the fiber is 162$\mu$m off from
the focal plane. In order to minimize 
the further offset, the heights of the three point mounts from the base plate
of the Echidna unit and the lengths of the spines are carefully 
controlled during manufacturing (in details, see Section 1.1.3 and 1.1.4 
of Ref.\citenum{brz04}). 

In order to check the parfocality of the tips of the fibers, 
a CCD camera with a high-magnification lens was attached to the FPI and a relative
measurement of the best focus position was calculated.
Results 
for all 400 science fibers and all 14 guide bundles are shown in 
Fig.~\ref{focalplane} with black dots and light-blue circles, 
respectively. The red solid line represents the curvature of 
the focal plane. The vertical position of the solid line was 
determined so that the RMS of the deviation of the science spines 
from the focal plane is minimum. All but two of 
the science fibers are within $\pm$100$\mu$m of the best focus position. 
The RMS of the deviation is 33$\mu$m for the science fibers.
For the guide-bundles, all but two spines have
length within $\pm150\mu$m of the focus position.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.4\linewidth]{focalplane.eps}
\end{center}
\caption{
Results of the parfocality measurements. The black dots and
blue circles represents the measurements for the science-fibers
and the guide-bundles, respectively. The red solid
line represent the best focus position, and the thin sold lines
indicate $\pm100\mu$m and $\pm150\mu$m from the best focus.
}
\label{focalplane}
\end{figure}

\subsection{Flexure of the spines}

In order to examine the amount of flexures of the spines,
we measured the movements of the tips of the fibers with changing
tilt angle between 0 degrees and 60 degrees. The results are shown 
in Fig.~\ref{ELchange2}. Black dots and light-blue circles represent
the offsets of the science-fibers and guide-bundles, respectively,
between two measurements before and after changing the tilt angle.
The offsets reflect the variation in flexure between the two tilt
angles due to gravity. The direction of gravity is 
in the X-direction in these panels. The change of the tilt angle is
shown at the top of each panel.

The average of the absolute size of the offsets are 
$30 \mu$m and $20 \mu$m respectively, for the tilt angle changes of
0$\leftrightarrow$30degree (left and middle panels) and 
30$\leftrightarrow$60degree (right panels).
There is a $\pm$10$\mu$m scatter around the average offsets.
Several spines show very large offsets; slippages of the pivot
ball of the spines during the change of the tilt angle are 
thought to cause the large offsets of these spines.
In Fig.~\ref{spine_deflection}, the distribution of the
relative deflection of the spines from the mean deflection
during the tilt angle change of 0 to 60 degree 
is shown as a histogram. Measurements in 4 different rotation
angles are shown in different lines. 

Because the offsets between the guide-bundles and the guide
stars will be removed by correcting the tracking of the telescope
during real observations, the average flexure of the spines 
will be cancelled. However, the difference between 
the flexure of the science-fiber and the guide-bundle spines 
will cause misalignment between the science-fiber and targets.
The measured variations of flexure is sufficiently small
to keep the targets within $10\mu$m accuracy during an 
integration with 30 degree elevation change. 

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.95\linewidth]{ELchange2.eps}
\end{center}
\caption{
Variation of the positions of the tips of the 
science-fibers (black dots) and the guide-bundles (light-blue circles)
following the change of the tilt angle. The tilt angle changes
are indicated at top of the each panel. In these measurements,
X-axis corresponds to the direction of gravity.
Several spines show very large offset due to slippages of their
pivot ball during the tilt movement.
}
\label{ELchange2}
\end{figure}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.3\linewidth]{spine_deflection.eps}
\end{center}
\caption{
The magnitude of relative deflection between the tilt angle
of 0 degrees to 60 degrees. Measurements at 4 different rotation
angles are shown with different line types.
}
\label{spine_deflection}
\end{figure}

\subsection{Fiber position stability}

We examined the stability of fiber positions by measuring
the positions at a 2 hours intervals. The vibration during the
measurements was comparable that observed at the top ring of
the telescope. No systematic shifts were observed in the
measurements at tilt angles of 0 and 30 degrees. The results
at tilt angle of 60 degree are shown in Fig.~\ref{Timechange_60}.
In this measurements, systematic offset of 2$\mu$m was observed
in the first 2 hours. The offset is still sufficiently small
compared with the required positioning accuracy.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.6\linewidth]{Timechange_60.eps}
\end{center}
\caption{
Fiber position stability measured at tilt angle of 60 degree.
Left) Position difference in the first two hours,
Right) Position difference between the two and four hours.
}
\label{Timechange_60}
\end{figure}

\section{DYNAMICAL PROPERTIES}

\subsection{Step-size with large step numbers}

The movements of the tips of the spines happen in 
``steps'', following the input saw-tooth signal to the quadrant
tube piezo (see Fig. 4 of Ref~\citenum{brz04}). There are two 
operation modes; the coarse and the fine modes with 140V 70Hz 
and 55V 15Hz saw-tooth signals, respectively. The size of
each step is measured with the spine-camera at three
tilt angles, 0, 30, and 60 degrees. The measured step sizes
are shown in Fig.~\ref{Stepdiff_Xplus} for $X+$ movement. 
Black dots and light blue circles represent the science-fiber 
and the guide-bundle spines, respectively. The upper and lower
panels are for the coarse and for the fine modes. The horizontal 
axis is the measured step size at tilt angle of 0 degree. The
average step sizes are 40$\mu$m for coarse mode and 10$\mu$m
for fine mode. As a result, the movement in coarse mode
is 19 times faster than the movement in fine mode; it will
take 2.5s and 47s to move 7mm distance in the coarse and fine
modes, respectively. The step sizes have factor of 2 scatter 
around the average step size from spines to spines.

The vertical axis of the figure shows the difference of the
step size for each spine between different tilt angles; 
30 and 0 degrees for the left panels, and 60 and 0 degrees for
the right panels. No systematic increase or decrease
of the step sizes is observed. The variation in step size for each
spine is less than 40\% for most of the spines in these
tilt angles. Therefore, in order to achieve the 40\% 
accuracy for the movement, we need to calculate the
required step number for each spine using the step size
of each spine, but we do not need to consider the 
variation of the step size of each spine due to the
change of the elevation angle.

In a few months timescale, there is no significant
change in the step size. The long term stability of the
step size will be checked in future, but it should
be noted that we can calibrate the step sizes of all spines
in a few hours.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.6\linewidth]{Stepdiff_Xplus.eps}
\end{center}
\caption{
Step sizes measured in the X$+$ movement.
Upper panels) for coarse mode operation. Left and right
panels are for tilt angle 0 degree vs. 30 degree and 0
degree vs. 60 degree, respectively.
Lower panels) for fine mode operation. Left and right
panels are for tilt angle 0 degree vs. 30 degree and 0
degree vs. 60 degree, respectively.
}
\label{Stepdiff_Xplus}
\end{figure}

\subsection{Accuracy of open-loop ``tweaking''}

The positions of targets in the FoV will change with
time after the initial configuration due to
differential atmospheric diffraction within the 30$^{\prime}$
FoV and due to the shift of the distortion pattern on
the focal plane. The former effect is calculated to be
1.24$^{\prime\prime}$ from zenith to elevation of 60 degree
between the top and the bottom of the 30$^{\prime}$ FoV. 
The cause and details of the latter effect are described
in Section 4.2; the size is estimated to be 
0.25$^{\prime\prime}$ with a rotation angle change of 
13 degrees. The variation of the target positions with time
limits the maximum integration time after a fiber configuration. 
If fine-mode step size is 
stable, the maximum integration can be extended -
we can tweak the positions of the fibers in open-loop 
during integration. ie. "blindly" move spines a small amount
without using the FPI and spine camera for position-feedback.

In order to evaluate the accuracy of the open-loop
tweaking, the stability of the step size of the fine 
mode was measured with numbers of steps of 1, 5, and 10.
The results are shown in Fig.~\ref{finestepsize}. 
The horizontal axis is the average step size of 10
measurements for each step number. The vertical axis
shows the differences of the step size in one measurement
from the average value normalized to the average
step size. For most of the spines, the variation of step 
size is as small as 20\% for 1-step and 10-steps movement.
The variation is even smaller for the 5-steps movement.
It should be noted that the measurement of the 1-step movement
can be significantly affected by the random error of the 
measurements of spine positions.
The results suggest that $\sim0.5^{\prime\prime}$ open-loop
tweaking can be done with $0.1^{\prime\prime}$ accuracy.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.9\linewidth]{finestepsize.eps}
\end{center}
\caption{
Left) Average spine step size with 1-step fine-mode movement vs.
the difference between one measurement and the mean result,
i.e. 0.2 corresponds to 20\% stepsize variation in one
measurement. Middle) for 5-step movement. Right) for 10-step
movement.
}
\label{finestepsize}
\end{figure}

\subsection{Fiber configuration results}

The positioning of all 400 science fibers and all 14 guide bundles
occurs simultaneously. Firstly, 
all fibers are moved in an X-direction (positive or negative) using an
appropriate (calculated) number of steps for each fiber. The same
process is repeated for the Y-direction. Then
the positions of all fibers are measured with the spine-camera
on the FPI. Initially, all fibers are moved in
coarse mode. If the average distance to target is
less than a threshold value, all of the spines are moved
in fine mode during the remaining iteration. The instrument control 
software (ICS) automatically does the iteration process, based 
on the fiber allocation data made from a pre-prepared target list. 
It takes $\sim$13 minutes to complete 7 iterations; the required
configuration time is dominated by the overhead required in moving
the FPI to measure the positions of the fibers.

Intensive configuration tests have been performed inside the prime-focus
unit at various tilt angles and rotation angles. Two results of
the configuration tests are shown in Fig. 10. The top panels show
the distribution of the initial distance to the target. The 
horizontal axis uses a logarithmic scale. The following panels
show the distributions after each iteration - the bottom panel
showing the result after 7 iterations. For the first configuration
test shown on the left, the spines are moved in coarse 
mode until the third iteration, then 4 iterations in fine mode are
performed. In both left and right cases, most of the spines reach 
within 10$\mu$m from the targets after 6 iterations, and about
10 spines do not reach their targets within 10$\mu$m even after
7 iterations. 

In order to reveal the cause of the large residuals for about
10 spines, we checked the paths of their movement. Fig.~\ref{Configpath}
shows examples of 6 spines. For each spine, the left panel shows the wide view
covering the patrol area, i.e. radius of 7mm, of each spine and
the right panel shows the close-up view around its target position
marked with large circle indicating 10$\mu$m from the target.
Starting from the position marked with the blue circle, each spine
moved to the red circle going through the positions marked with
open circles after each iteration. Although there are a few spines,
for example No.361 and No.467 in the figure, that stop moving
at a certain point, the paths of other spines suggest that these
spines once reach their target position but they are kicked off from
the position due to the neighboring spines or due to
the vibration caused by the movements of the other spines. For
most cases there is no neighbouring spine being positioned on a target
close to these spines.

In summary, with a tilt angle $<$60 degree, 95\% of the spines
reach target position within 12$\mu$m after 7 iterations. Typically, about 10
fibers have difficulty reaching the target positions. At a tilt angle of 60 
degrees with some rotation angles, the performance degrades; 90\% of the
spines reach target position after 7 iterations. The degraded
positioning accuracy is because some spines have difficulty
moving against gravity. 

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.5\linewidth]{Configres.eps}
\end{center}
\caption{
Results of 7-iteration positioning tests from home position to a random position.
The horizontal axis shows logarithmic distance from target in microns. Thus 1 and 4
means 10$\mu$m and 10mm, respectively. The number of spines as a function of
distance from their targets are shown in the histograms.
}
\label{Configres07}
\end{figure}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.6\linewidth]{Configpath.eps}
\end{center}
\caption{
Positioning record of spine residuals larger than 10$\mu$m in a positioning test.
Left panels are 14mm$\times$14mm fov and right panels are 120$\mu$m$\times$120$\mu$m
fov. The blue points indicate starting position and the red points indicate the
final position after 7 iterations. The large circles in the right panels 
indicate 10$\mu$m from the target.
}
\label{Configpath}
\end{figure}

\section{ON SKY COMMISSIONING RESULTS AND PROSPECTS}

\subsection{Echidna performance at summit and on-sky commissioning}

After a thorough evaluation of the fiber positioner at sea level, we brought the
Echidna unit to the summit of Mauna Kea and checked 
the performance again in the low temperature ($\sim5 ^{\circ}$C), 
low humidity environment. No degradation of the positioing performance
was observed. After installing into the prime-focus unit,
Echidna was attached to the top of the telescope. So far, we
have conducted on-sky commissioning tests of Echidna on 3 separate occassions -
Dec. 2007, Jan. 2008, and May 2008. The results are summarized
in the following two subsections.

\subsection{Distortion pattern measurements with the sky-camera}

The first step of commissioning was the evaluation of the telescope
distortion pattern using the sky-camera mounted on the FPI. The sky-camera
images the focal plane with $1.3^{\prime}\times1.0^{\prime}$ FoV 
with $0.1^{\prime\prime}$ pixel$^{-1}$ image scale. The camera is
a non-cooled video-rate CCD with no fore lens system. The camera can
detect $R=15.5$mag stars under relatively bad weather
condition; $>$1.0$^{\prime\prime}$ FWHM seeing condition with thin cirrus. 
An OG570 filter is installed in front of the camera to block light shorter 
than 570nm. Considering the sensitivity curve of the CCD camera, the
effective wavelength of the camera is 700nm for objects with flat spectra. 

As described in Kimura et al.\cite{kim06},
there is a offset between the optical axis of the primary mirror 
and the rotator axis of the instrument rotator. This causes
the center of the distortion pattern to move along a circle
following the variation of the rotator angle relative to the
focal plane of the instrument.

In order to evaluate the distortion pattern and the shift of
the center of the pattern against the focal plane, we observed
fields with many stars, i.e. open clusters and galactic plane,
with the sky-camera. Using measurements taken at various
rotator angles, the shift was determined as shown in the left panel
of Fig.~\ref{plot_dist_cen};
the center of the distortion pattern moves along a circle with
4.3mm diameter on the focal plane. The center of rotation 
is consistent with the measured position of the axis of the
instrument rotator on the focal plane marked with a cross.

Using the measured distortion pattern and the shift of the
center of the pattern against the focal plane, positions of
stars on the focal plane can be modelled. The residuals of the
current model are shown in the right panel of Fig.~\ref{plot_dist_cen}.
The RMS of the residuals is $0.5^{\prime\prime}$.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.8\linewidth]{plot_dist_cen.eps}
\end{center}
\caption{
Left) Measured position of the center of the distortion 
pattern on the focal plane. During the observation, the corrector
itself was on the optical axis of the primary mirror. 
% was at ($+3.7$mm, $-3.8$mm) 
It should be noted that the fibers rotate with the
instrument rotator, but the optical axis and the 
distortion pattern do not.
Right) Residual distortion pattern after
removing the distortion pattern and the shift of the
distortion pattern. Measured in NGC2682. The targets
are selected from UCAC2 astrometry catalog\cite{zac04}. The positional 
errors are about 20mas for the stars in the 10 to 14 magnitude
range, with about 70mas at the limiting magnitude of $R$ about
16 mag.
}
\label{plot_dist_cen}
\end{figure}

\subsection{Acquiring stars with the guide-bundles}

After the initial refinement of the telescope distortion pattern, we tried 
acquiring bright stars with the guide-bundles in order to determine
the offset between the spine-camera coordinate and the sky-camera
coordinate. There are 14 guide-bundles
at the right and left edge of the field of view, each covering
$78^{\prime\prime}$ radius area. We expect more than a few stars
can be covered even in high-galactic latitude fields above the magnitude limit of
the guide camera ($R=16-18$mag). The output light from the fiber 
bundles are imaged onto a Hamamatsu water-cooled CCD camera. This
camera also has an OG570 filter in front of it.

The result of the acquisition of bright stars with the guide-bundles
is shown in Fig.~\ref{AGimage2}. Based on an astrometry catalog in 
the field, 10 guide-bundle spines are configured to 10 guide stars.
After rastering the telescope, the 10 stars were imaged within the 
FoV of the guide-bundles.
Due to the residual of the telescope 
distortion model, there is a offset between each guide-bundle spine 
and its guide star and the fiber at the edge is illuminated for
most of the guide-bundles.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.4\linewidth]{AGimage2.eps}
\end{center}
\caption{
Guide fiber bundle image taken during the May 2008 commissioning run. 
10 stars are acquired with the guide bundle. 
Each bundle consists of 7$\times$50$\mu$m diameter
fibers. The positions of the 7 fibers of 
the 14 bundles are marked with circles.
}
\label{AGimage2}
\end{figure}

\subsection{Measuring the distortion pattern using the science fibers}

The next commissioning observations are scheduled in Jun., Aug., and Oct.
in 2008. In order to determine the distortion pattern more accurately, 
we will use science fibers to map the residual pattern of the current
distortion modelling. Initially, fibers will be positioned on
targets based on the current distortion modeling and the cataloged 
positions of stars. Then, ``rastering'' of the telescope in a grid pattern
around the estimated position will enable us to take data with the two spectrographs at
each position. Reducing the rastering data, we expect to be able to accurately measure
the acquisition error for each science fiber and it's associated target star.
With this method, we can sample
400 points inside FoV at once. Furthermore, we can refine the
telescope distortion pattern in the observing wavelength directly.

Finally, in Table 1,
we summarize the desired and current accuracy of the 
fiber positioner instrument with a breakdown of the overall error residual into its
constituent components: the telescope distortion
pattern, the accuracy of the fiber positioning, and the typical uncertainties
of the astronomical object catalog. In order to achieve the fiber positioning
accuracy of 0.24$^{\prime\prime}$ for most of the fibers as introduced in 
Introduction, we need to improve the distortion pattern modeling 
less than $0.05^{\prime\prime}$ RMS accuracy.

\begin{table}[tbp]
\begin{center}
\begin{tabular}{lcccccc}\hline
                                  & \multicolumn{3}{c}{Desired}       & \multicolumn{3}{c}{Current}    \\ \hline
                                  & \multicolumn{2}{c}{($^{\prime\prime}$)} & ($\mu$m) & \multicolumn{2}{c}{($^{\prime\prime}$)} & ($\mu$m) \\
                                  & rms    & worst      &          & rms   & worst       &          \\
Distortion pattern modeling       & 0.05   & 0.15       &          & 0.4   & 1.2         &          \\
Positioning accuracy              &        & 0.14       & 12.0     &       & 0.14        & 12.0     \\ 
Accuracy of input catalog         & 0.05   & 0.15       &          & 0.05  & 0.15        &          \\ \hline
Total accuracy                    &        & 0.25       &          &       & 1.2         &          \\ \hline
\end{tabular}
\end{center}
\caption{
Summary of the desired and current positioning accuracy of the instrument.
}
\label{summary}
\end{table}

\acknowledgments 

The authors would like to thank all members of Subaru telescope for
their support to the testing of the Echidna unit 
and to the on-telescope commissioning. 

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