Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Performance of Echidna fiber positioner for FMOS on Subaru
Masayuki Akiyamaa,b , Scott Smedleyc , Peter Gillinghamc , Jurek Brzeskic , Tony Farrellc ,Masahiko Kimurab , Rolf Mullerc , Naoyuki Tamurab , and Naruhisa Takatoba Astronomical Institute, Tohoku University, Aramaki, Aoba-ku, Sendai, 980-8578, Japan;b Subaru Telescope, NAOJ, 650 North Aohoku Place, Hilo, HI, 96720, USA;c Anglo-Australian Observatory, PO Box 196, Epping, NSW 2117, Australia

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 OHsuppression spectrographs, the whole project being known as Fiber Multi Object Spectrograph (FMOS). In orderto accommodate the large number of the ﬁbers in the physically limited area, a new ﬁber positioning method isdeveloped. 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.
Keywords: ﬁber positioner, piezoelectric actuators, Subaru telescope

1. INTRODUCTION
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.1, 2 Echidna is the ﬁber positioning
system for the instrument and is attached to the prime-focus. The focus has 30 diameter FoV with the physicalsize 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, wasdeveloped. See Fig. 1. Once saw-tooth signal is applied to the piezo actuator, the spine tilts due to a slippage ofthe pivot ball against the three point mount. The prototyping stage of the positioner is described in Gillingham
et al.3 and in Moore et al.4 The overall mechanical design is shown in Gilligham et al.,5 and its details aredescribed in Brzeski et al.6 See Fig. 4 of Ref.6 for the input signal and the movement. The 400 ﬁbers feed twocooled OH-suppression spectrographs, one developed in Kyoto university7, 8 and the other build in UK.9, 10 Bothof them cover 900-1800nm. In the ﬁber train, there is a collimated light coupling,11, 12 in order to convert thefast F/2 ratio of the prime focus, and to detach the positioner from the telescope.
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. 2. The installation process to the prime-focus unit is shownin 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. andMay. 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 thecoupling eﬃciency due to the misalignment between a target and a ﬁber, the ﬁber must be positioned within
20µm of the target. During the concept design study, the optimal core size of the science-ﬁbers was determined
to be 1.2 , which corresponds to 100µm at the prime-focus, maximizing the expected SN ratios of faint galaxies
Further author information: (Send correspondence to M.A.)
M.A.: E-mail: akiyama@astr.tohoku.ac.jp

7018-106 V. 4 (p.1 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Furcation tube with 22 science fibres(including 2 spares)

Conduit
Custom made tube

Pivoting ballSingle fibre

Piezo actuator

Switchboard guide

Fiducial spine

Fiducial spine
Guide spine
Guide spine
40 SciencespinesFigure 1. Left) drawing of one module of the ﬁber positioner from Fig. 4 of Ref6. One module has 20×2 science-ﬁbers
and 2 guide-bundles at both ends of the module. Science-ﬁbers are 100µm diameter core ﬁber, and guide-bundles arebundles of 7 50µm-core ﬁbers with 80µm spacing, which corresponds to 0.96 at the focal plane. A ﬁber is attached toa carbon-ﬁber tubing, called “spine”, with a pivoting ball and a tungsten counter weight. The pivoting ball is sitting ona three-point mount with a ring magnet at the top of a quadrant tube piezo actuator. Spines for the science-ﬁbers andthe 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 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.

in the background limited condition. In Fig. 3, the coupling eﬃciency of the 100µm ﬁber to a stellar object isshown as a function of misalignment. For misalignment less than 20µm (=0.24 ) the reduction of the couplingeﬃciency is less than 10%, even under a good seeing condition with FWHM=0.5 .
Due to a number of physical eﬀects (including the changing contact position of the pivot ball with the threepoint 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 thespine camera. In order to position the 400 ﬁbers within a reasonable time, 10-15 minutes, the maximum numberof iterations is ∼7. Each iteration process takes approximately 100 seconds. If the worst-case ﬁber movement
has 40% accuracy in each operation, 10µm positioning accuracy can be achieved with 7 iterations for movementfrom the home position to the edge of the patrol ﬁeld: 0.47 × 7200µm ∼ 10µm.

2. MECHANICAL PROPERTIES
2.1 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-illuminatedindividually 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. 2). The spine camera has 768×493 physical pixels with an 11µm×13µm pixel sizeand covers the 400 ﬁbers with 59 FoVs (see Fig. 9 of Ref. 5). The positions of the 400 ﬁbers can be sequentiallymeasured 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 attachedat the focal plane instead of the ﬁber modules. In details of the calibration source, see Section 1.2.3 of Ref.6. Inorder 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 wellwith a model including up to the third order term; the residuals of the model is 1.3µm RMS with a maximum

7018-106 V. 4 (p.2 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 2. 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 tothe telescope, Echidna being enclosed in the unit.
100
95

collection efficiency %90

seeing FWHM 0.5 arcsec

85
80
75
70
65

seeing FWHM 0.75 arcsec

60
55
50

seeing FWHM 1.0 arcsec

45
40
0

5

10

15

20

misalignment
micronmisalignmentum

Figure 3. Plots of percentage energy encircled within a 100µm diameter circle as a function of misalignment for three
diﬀerent seeing conditions.

error of 3.1µm. The residuals are shown in the left panel of Fig. 4. The non-orthogonality of the XY gantry canbe described well with the mean parameters determined by averaging the parameters measured at various tilt androtator angles. The residuals of the calibrations are 2.0µm 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. 4.
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. 4. The diﬀerences of the measured
positions between two independent measurements have a scatter of 1µm RMS (p-p about ±2µm) for eachdirection. If we measure a position of a ﬁber in multiple times without moving the spine camera, the resultant
scatter in each direction is ∼1µm RMS. Thus, the scatter of the positions in the multiple-measurements isdominated by the accuracy of the centroid evaluation.
The above accuracy of the position measurements and the repeatability are satisfactory to conﬁrm thepositions of the ﬁbers.

7018-106 V. 4 (p.3 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 4. 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.
200

deviation from the mean value (micron)

150
100
50

#125

0
-50
#126

-100
-150

#146
#202

-200
0

10

20

30

40

50

60

70

80

radius from field center (micron)Figure 5. Results of the parfocality measurements. The black dots and blue circles represents the measurements for thescience-ﬁbers and the guide-bundles, respectively. The red solid line represent the best focus position, and the thin soldlines indicate ±100µm and ±150µm from the best focus.

2.2 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 100µm ﬁbre is defocused by 150µm, 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 162µm
oﬀ from the focal plane. In order to minimize the further oﬀset, the heights of the three point mounts from thebase plate of the Echidna unit and the lengths of the spines are carefully controlled during manufacturing (indetails, see Section 1.1.3 and 1.1.4 of Ref.6).
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. 5 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 sothat the RMS of the deviation of the science spines from the focal plane is minimum. All but two of the scienceﬁbers are within ±100µm of the best focus position. The RMS of the deviation is 33µm for the science ﬁbers.
For the guide-bundles, all but two spines have length within ±150µm of the focus position.

7018-106 V. 4 (p.4 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 6. 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 ballduring the tilt movement.

2.3 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. 6. Black dots and lightblue 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 isshown at the top of each panel.
The average of the absolute size of the oﬀsets are 30µm and 20µm respectively, for the tilt angle changesof 0↔30degree (left and middle panels) and 30↔60degree (right panels). There is a ±10µm scatter around theaverage oﬀsets. Several spines show very large oﬀsets; slippages of the pivot ball of the spines during the changeof the tilt angle are thought to cause the large oﬀsets of these spines. In Fig. 7, the distribution of the relativedeﬂection of the spines from the mean deﬂection during the tilt angle change of 0 to 60 degree is shown as ahistogram. 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 trackingof the telescope during real observations, the average ﬂexure of the spines will be cancelled. However, thediﬀerence 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
10µm accuracy during an integration with 30 degree elevation change.

2.4 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 areshown in Fig. 8. In this measurements, systematic oﬀset of 2µm was observed in the ﬁrst 2 hours. The oﬀset isstill suﬃciently small compared with the required positioning accuracy.

7018-106 V. 4 (p.5 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 7. 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.

Figure 8. 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.

3. DYNAMICAL PROPERTIES
3.1 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 6). 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 threetilt angles, 0, 30, and 60 degrees. The measured step sizes are shown in Fig. 9 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 40µm for coarse mode and 10µm for ﬁne mode. As a result, the movement incoarse mode is 19 times faster than the movement in ﬁne mode; it will take 2.5s and 47s to move 7mm distancein 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 decreaseof 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 thevariation 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

7018-106 V. 4 (p.6 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 9. Step sizes measured in the X+ movement. Upper panels) for coarse mode operation. Left and right panels arefor tilt angle 0 degree vs. 30 degree and 0 degree vs. 60 degree, respectively. Lower panels) for ﬁne mode operation. Leftand right panels are for tilt angle 0 degree vs. 30 degree and 0 degree vs. 60 degree, respectively.

hours.

3.2 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 FoV and due to the shift of the distortion pattern on the focal plane. The
former eﬀect is calculated to be 1.24 from zenith to elevation of 60 degree between the top and the bottom of the30 FoV. The cause and details of the latter eﬀect are described in Section 4.2; the size is estimated to be 0.25
with a rotation angle change of 13 degrees. The variation of the target relative 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, i.e. ”blindly” movespines 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. 10. The horizontal axis is
the average step size of 10 measurements for each step number. The vertical axis shows the diﬀerences of thestep 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 forthe 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 ∼ 0.5 open-loop
tweaking can be done with 0.1 accuracy.

3.3 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 spinecamera on the FPI. Initially, all ﬁbers are moved in coarse mode. If the average distance to target is less than

7018-106 V. 4 (p.7 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 10. 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.

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 froma pre-prepared target list. It takes ∼13 minutes to complete 7 iterations; the required conﬁguration time isdominated 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 10µm fromthe targets after 6 iterations, and about 10 spines do not reach their targets within 10µm 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. 12 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 10µm from the target. Starting from the position marked with the blue circle, eachspine 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, thepaths of other spines suggest that these spines once reach their target position but they are kicked oﬀ from theposition 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 12µm 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.

4. ON SKY COMMISSIONING RESULTS AND PROSPECTS
4.1 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 (∼ 5◦ 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.

7018-106 V. 4 (p.8 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Logarithmic Distance from target (micron)

Logarithmic Distance from target (micron)Figure 11. 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 10µm and 10mm, respectively. The number of spines
as a function of distance from their targets are shown in the histograms.

Figure 12. Positioning record of spine residuals larger than 10µm in a positioning test. Left panels are 14mm×14mm fovand right panels are 120µm×120µm 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 10µm from the target.

7018-106 V. 4 (p.9 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

ngc2682.hdr

E

+180

N

-175
+95
+90

-90

-85

+5
+0
Residuals (1 arcsec, 80 microns)

Figure 13. Left) Measured position of the center of the distortion pattern on the focal plane. During the observation, thecorrector itself was on the optical axis of the primary mirror. 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 thedistortion pattern and the shift of the distortion pattern. Measured in NGC2682. The targets are selected from UCAC2
astrometry catalog.14 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.

4.2 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 × 1.0 FoV with 0.1 pixel−1 image scale.
The camera is a non-cooled video-rate CCD with no fore lens system. The camera can detect R = 15.5mag stars
with averaging 30 frames under relatively bad weather condition; >1.0 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.,13 there is a oﬀset between the optical axis of the primary mirror and therotator 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. 13; the center ofthe distortion pattern moves along a circle with 4.3mm diameter on the focal plane. The center of rotation isconsistent with the measured position of the axis of the instrument rotator on the focal plane marked with across.
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 rightpanel of Fig. 13. The RMS of the residuals is 0.3 .

4.3 Acquiring stars with the guide-bundles
After the initial reﬁnement of the telescope distortion pattern, we tried acquiring bright stars with the guidebundles 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 radius area. We
expect more than a few stars can be covered even in high-galactic latitude ﬁelds above the magnitude limit of7018-106 V. 4 (p.10 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Figure 14. Guide ﬁber bundle image taken during the May 2008 commissioning run. 10 stars are acquired with the guidebundle. Each bundle consists of 7×50µm diameter ﬁbers. The positions of the 7 ﬁbers of the 14 bundles are marked withcircles.

the guide camera (R = 16 − 18mag). 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. 14. Based on an astrometry
catalog in the ﬁeld, 10 guide-bundle spines are conﬁgured to 10 guide stars. After rastering the telescope, the 10stars 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 formost of the guide-bundles.

4.4 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 modelingand the cataloged positions of stars. Then, “rastering” of the telescope in a grid pattern around the estimatedposition 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 witha breakdown of the overall error residual into its constituent components: the telescope distortion pattern, theaccuracy of the ﬁber positioning, and the typical uncertainties of the astronomical object catalog. In order toachieve the ﬁber positioning accuracy of 0.24 for most of the ﬁbers as introduced in Introduction, we need to
improve the distortion pattern modeling less than 0.05 RMS accuracy.

ACKNOWLEDGMENTS
The authors would like to thank all members of the FMOS project, especially, Prof. Toshinori Maihara and Prof.
Fumihide Iwamuro. The authors also thank the members of Subaru telescope for their support to the testing of
the Echidna unit in the Hilo base and on the telescope, and the members of Anglo-Australian Observatory for
their support to complete the instrument.

7018-106 V. 4 (p.11 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within themargin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.

Distortion pattern modeling
Positioning accuracy
Accuracy of input catalog
Total accuracy

Desired( )(µm)
RMS Worst
0.05
0.15
0.14
12.0
0.05
0.15
0.25

Current( )(µm)
RMS Worst
0.3
0.9
0.14
12.0
0.05
0.15
0.9

Table 1. Summary of the desired and current positioning accuracy of the instrument.

REFERENCES[1] Maihara, T., Ohta, K., Tamura, N., Ohtani, H., Akiyama, M., et al., “Fiber multi-object spectrograph(fmos) for the subaru telescope,” in [Optical and IR instrumentation and detectors], Iye, M. and Moorwood,A., eds., Proc. SPIE 4008, 1111–1118 (2000).
[2] Kimura, M., Maihara, T., Ohta, K., Iwamuro, F., Eto, S., Iino., M., Mochida, D., Shima, T., Karoji,
H., Noumaru, J., Akiyama, M., et al., “Fibre-multi-object spectrograph (fmos) for subaru telescope,” in[Instrument Design and Performance for Optical/Infrared Ground-based Telescopes], Iye, M. and Moorwood,A., eds., Proc. SPIE 4841, 974–984 (2003).
[3] Gilligham, P., Miziarsky, S., Akiyama, M., and V.Klocke, “Echidna - a multi-ﬁber positioner for the subaru
telescope,” in [Optical and IR instrumentation and detectors], Iye, M. and Moorwood, A., eds., Proc. SPIE
4008, 1395–1403 (2000).
[4] Moore, A., Gillingham, P., Griesbach, J., and Akiyama, M., “Spine development for the echidna ﬁber
positioner,” in [Instrument Design and Performance for Optical/Infrared Ground-based Telescopes], Iye, M.
and Moorwood, A., eds., Proc. SPIE 4841, 1429–1439 (2003).
[5] Gilligham, P., Moore, A., Akiyama, M., et al., “The ﬁbre multi-object spectrograph (fmos) project: theanglo-australian observatory role,” in [Instrument Design and Performance for Optical/Infrared Groundbased Telescopes], Iye, M. and Moorwood, A., eds., Proc. SPIE 4841, 985–996 (2003).
[6] Brzeski, J., Gillingham, P., Correll, D., et al., “Echidna - the engineering challenges,” in [Ground-based
Instrumentation for Astronomy], Moorwood, A. and Iye, M., eds., Proc. SPIE 5492, 1228–1242 (2004).
[7] Eto, S., Maihara, T., Ohta, K., et al., “The ﬁber multi-object spectrograph (fmos) for the subaru telescopeiii,” in [Ground-based Instrumentation for Astronomy], Moorwood, A. and Iye, M., eds., Proc. SPIE 5492,
1314–1318 (2004).
[8] Iwamuro, F., Maihara, T., Ohta, K., Eto, S., Sakai, M., Akiyama, M., et al., “Fmos - the ﬁber multiple-object
spectrograph iv: current status of ohs-based spectrograph,” in [Ground-based and Airborne Instrumentation
for Astronomy], McLean, I. and Iye, M., eds., Proc. SPIE 6269, 431 (2006).
[9] Lewis, I., Dalton, G., Holmes, A., et al., “Developments on the uk fmos project for the subaru telescope,” in[Instrument Design and Performance for Optical/Infrared Ground-based Telescopes], Iye, M. and Moorwood,A., eds., Proc. SPIE 4841, 1108–1114 (2003).
[10] Dalton, G., Lewis, I., Bonﬁeld, D., et al., “The uk fmos spectrograph,” in [Ground-based and Airborne
Instrumentation for Astronomy], McLean, I. and Iye, M., eds., Proc. SPIE 6269, 136 (2006).
[11] Murry, G., Woodhouse, G., Froud, T., et al., “An ultraprecision ﬁber connector for fmos,” in [iber-based
Component Fabrication, Testing, and Connectorization], Pruneri, V., Dahlgren, R., and Gregory, M., eds.,
Proc. SPIE 4943, 184–194 (2003).
[12] Murry, G., Luke, P., Robertson, D., and Tamura, N., “A connectorized ﬁber downlink for fmos,” Proc.
SPIE 5492, 1383–1394 (2004).
[13] Kimura, M., Maihara, T., Iwamuro, F., Eto, S., Akiyama, M., et al., “Fmos: The ﬁber multi-object
spectrograph v results of early pir engineering run,” in [Ground-based and Airborne Instrumentation for
Astronomy], McLean, I. and Iye, M., eds., Proc. SPIE 6269, 132 (2006).
[14] Zacharias, N., Urban, S., Zacharias, M., Wycoﬀ, G., Hall, D., Monet, D., and Raﬀerty, T., “The second us
naval observatory ccd astrograph catalog (ucac2),” A.J. 127, 3043–3059 (2004).

7018-106 V. 4 (p.12 of 12) / Color: No / Format: A4 / Date: 6/9/2008 6:42:41 PM
SPIE USE: ____ DB Check, ____ Prod Check, Notes: