Fiber Positioning System for the Sloan Digital Sky Survey
Sloan Digital Sky Survey Telescope Technical Note
19911019
Siriluk
Limmongkol, Russell
Owen, Charles Hull and
Walter
Siegmund
Abstract
A 600 fiber positioning system is being developed for the Digital
Sky Survey project of the Astrophysical Research Consortium. This
system couples to dual spectrographs mounted on an altitude-azimuth
2.5 m, f/5 telescope with a 3° field of view to be constructed
at Apache Point Observatory in southern New Mexico. Among other
approaches, we are studying plug-plates plugged manually
off-telescope. This technology has several advantages including
compatibility with focal plane characteristics, sampling uniformity,
and simplicity. We describe a strategy for minimizing interference
between fibers and for preventing obstruction of the plugging process
by the fibers. Finally, we discuss methods for plug-plate mounting
and support.
Introduction
The Digital Sky Survey (DSS) telescope will be built by the
Astrophysical Research Consortium (University of Chicago, University
of Washington, Institute for Advanced Studies, New Mexico State
University, Princeton University, Washington State University) and
will be located at Apache Point Observatory, near National Solar
Observatory in southern New Mexico. The telescope will be a dedicated
2.5 m diameter instrument with a wide (3°) well-corrected field.
It will have two instruments: a 6 x 5 charge coupled device (CCD)
imaging array for wide band photometry at four wavelengths, and a
pair of 300 fiber spectrographs. The focal plane assembly is designed
so that the telescope can be quickly changed from spectrographic to
imaging mode to take advantage of photometric conditions with good
image quality.
The goal of the survey is to obtain redshifts of ~10^6 galaxies
and ~10^5 quasars in a pi steradian region centered on the north
galactic pole. The imaging survey will be used to select targets for
the spectrographic survey and to determine accurate positions for
these objects. The result will be a data base that can be used to
investigate the large scale structure of the universe. A large and
uniform (or at least well-understood) sample of redshifts from a
representative volume of the universe is necessary to constrain
theories of the development of large scale structure. Other uses for
the survey include the study of various aspects of clusters of
galaxies, galaxies, quasars, quasar absorption line systems, etc. To
obtain such a large number of redshifts in a reasonable time, e.g. 5
years, the number of optical fibers used per field must be increased
beyond the current state of the art while maintaining high
efficiency.
Approach
The value of fiber fed spectrographs is well established
(Hill 1990). The current generation of
multi-fiber systems handle roughly 100 fibers. The proposed
instrument will be part of a new generation of multi-fiber
spectrographs with 400 to 600 fibers. These include, for example, a
400 fiber system for the Anglo-Australian Telescope expected to be
commissioned in 1994 (Gray and Taylor 1990).
These projects advance the state of the art and require development
of new techniques and hardware.
The simplest fiber positioning technology is the plug-plate. Holes
are drilled in a plate to match locations of the program objects in
the focal plane. Suitably terminated fibers are manually plugged into
the holes in a subsequent operation (Barden and
Massey 1990). Other technologies, such as the robot positioned
magnetic button approach, have been developed to allow for more
flexibility and to reduce operating costs (Hamilton
1990, Parry and Lewis 1990, Barden
and Rudeen 1990, Ingerson 1990).
The baseline approach that we have adopted for this project is the
plug-plate, plugged off the telescope. Approximately eight
plug-plate/fiber harness modules will be required for one night's
observing, and may be plugged in advance during the day.
Plug plates offer many advantages for the survey, including:
- Sampling of targets is more complete and more uniform than for
other technologies extrapolated to 600 fibers. This is because
fiber routing can occur away from the light path to the focal
surface. Because of the statistical nature of much of the
scientific program, it is important that sampling constraints be
very well understood.
- Fibers can be placed as close as 3 mm (50") between centers.
It is desirable for various studies of clusters of galaxies and
pairs of galaxy to be able to obtain spectra of targets that are
close together.
- Feasibility of this approach at the 600 fiber level can be
assured more readily than for the alternative technologies. For
other technologies, feasibility can be demonstrated only with
elaborate prototypes and simulations.
- Fibers can be aligned with the principal ray over the entire
field. Fiber misalignment increases the output f-ratio causing
light to miss the spectrograph collimator thereby reducing
efficiency.
- The flexibility of other systems is not an advantage for this
project since astrometry must be accurate and target selection
must be automated for it to succeed.
Fiber Plug-Plate Mockup
A full-scale mockup of the plug-plate/fiber assembly was used to
demonstrate that 600 fibers could be manually plugged and unplugged
and to measure the time necessary for this operation (Figure 1). The
mockup was intended only to investigate questions of access to the
fibers and the management of fibers behind the focal plane.
Figure 1. In this mockup of the proposed fiber plug-plate
systems, the aluminum disk contains 600 Ø1.5 mm holes
drilled at galaxy locations from APM data. Half of the 600 fibers
in the final system are represented by nylon tubing terminated in
Ø1.5 mm dowel pins. The "fibers" are brought to the plate
from the left in flat ribbons of 20 each. Each ribbon is assigned
to a rectangular tile on the plate. Plugging order is indicated by
drawing lines between holes.
Each plug-plate contains 600 Ø1.5 mm holes. The plates are
3.2 mm thick aluminum sheet 0.84 m in diameter. Fibers are
represented by Ø3.2 mm nylon tubing. Plugs were made by
pressing Ø1.5 mm dowel pins into the ends of the tubing,
leaving about 3.2 mm of each pin exposed. No particular care was
taken to make the plug/hole interaction realistic since we are
studying this separately. The mean clearance between the plug and
hole was 50 microns. The mockup has fibers (tubes) for only half the
plate, since we expect that first one half of the plate will be
plugged and then the other half. The fibers are brought to the plate
from the left in flat ribbons. The ribbons are anchored 0.25 m above
the plate with 0.38 m left free.
Automatic Plate Measuring (APM) machine data were used to generate
hole locations. These data are for a 5°x5° region
containing the central region of the Horologium supercluster at
around 18000 km/s, which is the nearest big supercluster in the
survey. It is one of the main features visible in the brighter galaxy
maps. This region was chosen because the galaxy distribution is very
non-uniform, making this a difficult case. From the objects in the
data set, the brightest 600 galaxies in a circle corresponding to a
plug-plate were selected. The holes were drilled at the nominal scale
of the 2.5 m telescope: 60 microns/arc-sec.
For plugging, the plug-plate is divided into tiles, one for each
ribbon of fibers. The tiles are arranged in horizontal strips. The
ribbon anchors were positioned about 0.18 m to the left of the right
edge of the corresponding tile. Since the tiles boundaries shift
depending on the distribution of targets, it may be necessary to move
the ribbon anchors for each plate. Lines are drawn between the holes
on the plate to indicate the plugging order within a tile.
For our time trials we used 15 ribbons, each containing 20 fibers.
The corresponding tiles were arranged in 2 horizontal strips, with 8
tiles in the inner strip and 7 tiles in the outer strip. Within each
strip we used vertical tile boundaries. This arrangement appears to
be quite reasonable, but we are also examining variations, including
fewer tiles and reducing the number of holes in the tiles at the ends
of the outer strips. Figure 2 shows half of one of the plug-plates
used for time trials.
Figure 2. This is a plot of the target pattern used for
several of the time tests. The 300 targets in this half of the
field are divided into two strips separated by a horizontal
boundary. The strips are further divided into tiles of 20 targets,
separated by vertical boundaries. Within each tile, the targets
are connected with straight lines from top to bottom. These lines
were transferred to the aluminum plate to indicate plugging order.
The target distribution is from near the center of the Horologium
supercluster and is quite non-uniform.
The order of plugging must be chosen so that each hole is
accessible and visible when it is to be plugged. The algorithm
depends on the hand used for plugging; the following discussion
assumes right-handed plugging. Most of the rules are straightforward.
First one half of the plate is plugged, then the whole assembly is
rotated 180° and the other half is plugged. Strips are plugged
from back to front, and tiles within a strip are plugged from right
to left. The fibers of each ribbon are plugged from back to
front.
Within a tile, a number of algorithms for plugging order were
examined, including a horizontal raster pattern where the holes were
sorted in order from top to bottom (as shown in figure 2), a diagonal
raster pattern where the holes were sorted from the upper left to the
lower right, and a combined algorithm where most holes are sorted top
to bottom, but holes within 20 mm of each other are sorted along the
diagonal. The first algorithm resulted in some holes that were
difficult to plug without forceps. The second algorithm caused some
fibers to interfere with each other above the plate, resulting in
poor retention. Subjectively, the last algorithm was judged best;
there was little need for forceps and all fibers were well
retained.
The mockup has a number of shortcomings. We did not include any
clips to hold the unplugged fibers out of the way during plugging. In
some timing trials one person held unplugged fibers out of the way of
the person doing the plugging. In a practical system, some means of
organizing and protecting the fibers during plugging must be
provided. It would be useful to illuminate the holes from below the
plate to improve visibility. The height, angle and lighting of the
work surface could all be improved.
The mean of 5 time trials involving 4 people was 15.2 minutes for
300 fibers. This corresponds to a mean plugging time of 3.0
seconds/fiber. The standard deviation was 0.32 seconds. No plugged
fibers came loose during the plugging process, even though this was
not a goal of the experiment. It was never necessary to untangle or
re-route fibers. We should point out that the individuals doing the
plugging were novices and were not selected for manual dexterity.
The survey will require the use of approximately 3000 plates
covering a total of 21000 deg^2. Assuming 6 seconds/fiber for a
plug/unplug cycle, surely conservative in view of the mockup
shortcomings mentioned above, a total of 1.8 person-years will be
needed for the plugging/unplugging activity for 3000 plates (21000
deg^2, roughly the amount needed for the survey). The corresponding
cost for this activity is $54k assuming a salary plus overhead and
benefits of $30k/year. This offers little incentive for attempting to
replace manual labor with a robot.
Plug-Plates And Focal Plane
The optical design for the DSS telescope is a fast, simple optical
system with a nearly flat focal plane and low distortion. However,
focal plane curvature is such that the ends of the optical fibers
feeding the spectrographs must be placed on the best focal surface
rather than simply a plane. A graph of the best focal surface for
spectroscopy as a function of linear distance from the center of the
field is shown in Figure 3. Unfortunately, the principal ray is not
normal to this surface.
Figure 3. The best focal surface, the surface normal to
the principal ray and the shape of an ideal mandrel are shown. The
mandrel is the shape that the plate should have for drilling if
all holes are drilled with their axes parallel to each other and
if the plate is deformed to match the best focal surface in the
telescope. Thus, the mandrel curve is the difference between the
other two curves.
Ideally, the end of each fiber should be located on the best focal
surface and oriented with its axis parallel to the principal ray. To
achieve this, we propose the following. For drilling, the plate is
bent convex, and the holes are drilled with their axes parallel to
each other. In the telescope, the plate is deformed so that its
surface matches the best focal surface. It turns out that this can be
done with adequate accuracy with the application of a fairly simple
set of bending forces to the plate. If the proper deformation is
chosen for drilling, the holes will be aligned with the principal ray
in the telescope. These relationships are illustrated in Figure 3.
The ideal mandrel is the shape that the plate should have for
drilling and is the difference between the focal surface and surface
normal to the principal ray. The advantage of this approach is that
hole angles and locations can be controlled very well, yet it only
requires a simple 3-axis drilling machine.
An axis symmetric solid element model was used to investigate this
scheme. This approach, in effect, reduces a 3-dimensional axis
symmetric problem with axis symmetric loading to a two dimensional
problem. Solid elements are used. In two dimensions, these are
rectangular, but represent three-dimensional annuli with rectangular
cross-sections. The mesh is 89 elements wide by 5 high. The material
is aluminum 2024, 3.18 mm thick and 419 mm in radius. To match the
focal plane shape, displacement constraints were applied at 343 mm
and 384 mm radius to force the plate to match the focal plate slope
at the edge of the field. A further displacement constraint was
applied at radii of 0, 50, or 100 mm to force the plate sag to match
that of the best focal surface. Without the latter constraint, the
plate sags about 0.5 mm too much at the center. To match the shape of
the ideal drilling mandril, similar constraints are used. However,
only radii of 0 and 50 mm for the central constraint were
examined.
The best match to the best focal surface occurred with the central
constraint applied at a radius of 100 mm (Figure 4). For this case,
the best focal surface is matched to an accuracy of 50 microns peak
to valley. With the constraint applied at the center, the best focal
surface is matched to an accuracy of 250 microns peak to valley. With
no constraint at the center (not shown), the mismatch was 830 microns
peak to valley. Table I gives the RMS fit error of the deformed plate
to the best focal surface. Model plg41-3 (central constraint applied
at a radius of 100 mm) satisfies the error budget of 25 microns that
we have established for this item.
Figure 4. The fit of three models to the best focal
surface is plotted. The central constraint was applied at three
different locations; r = 0 mm, r = 50 mm, and r = 100 mm. The fit
with the constraint applied at a 100 mm radius is excellent.
Table I Quality of fit to the best focal surface
Model Central constraint Mean surface Fit error
Name radius (mm) (microns) (RMS)
plg31 0 -65 83
plg41 50 -16 46
plg41-3 100 4.7 7.9
These results are fairly insensitive to variations in the plate
thickness, but not variations in the constraints. Figure 5 shows
results for three models. Plg32 is the baseline case. In plg33, the
thickness of the plate was increased 10%. Assuming that the telescope
is focused on a probe at 70% of the radius, the maximum focus error
is almost unchanged. Changes in the plate thickness would have a
larger effect if the bending were done with forces rather than
displacements. In plg31, the displacement of the outer constraint was
increased with respect to the inner constraint 10%. This increases
the slope at the edge of the focal plane by the same amount. In this
case, the shape of fit error curve changes by 100 microns indicating
that we have to control displacements quite a bit better than
10%.
Figure 5. Fit error sensitivity to two parameters is
plotted. Plg32 is the baseline case. In plg31, the displacement of
the outer edge constraint is increased 10% with respect to the
inner edge constraint. In plg33, the plate thickness is increased
10%.
Figure 6 shows results for two attempts to deform the plate to
match the shape of the ideal mandrel. The constraints were basically
the same as before. The pair of edge constraints were chosen to match
the shape of the ideal mandrel at the field edge. The central
constraint was set to produce the overall sag of the ideal mandrel.
In one case, the central constraint was applied at the plate center.
In the other case, it was applied at a radius of 50 mm. The area
weighted principle ray angle error was 12 mrad RMS for the first case
and 6.7 mrad RMS for the second. We have established an error budget
of 10 mrad RMS for this item, so the first case exceeds the error
budget somewhat.
Figure 6. The predicted error in hole alignment with the
principle ray is plotted for two models. In plg34, the central
force is applied at the center of the plate. In plg44, the force
is applied at a radius of 50 mm. The curves are labeled with the
radius of the central constraint. For r = 0, the area weighted
hole misalignment is 12 mrad RMS. For r = 50 mm, the error is 6.7
mrad RMS.
For the model of plg34, the maximum tensile stress is 389 MPa (56
kpsi) at the plate center. Since the yield strength of aluminum alloy
2024 T3 is only 340 MPa (50 kpsi), this is a problem. For plg44, the
maximum stress is 107 MPa (16 kpsi), well below the yield strength of
the material. Thus it appears that some attempt to distribute the
central force will be necessary.
Of course, if the plate is drilled from the convex side of the
plate, it can be supported by a physical mandrel having the ideal
shape. However, the ability to produce the proper shape with a simple
set of constraints allows the plate to be drilled from the concave
side as well. This is desirable for some schemes where the holes are
counterbored to provide an axial locating shoulder for the plugs. For
example, this would be necessary to provide adequate positioning of
the fibers on the best focal surface if the simple focal plane
support system corresponding to model plg31 were used.
Table II gives the forces required for each model. The forces are
given in newtons/radian. The tabular values should be multiplied by
2№ to get the total force on each annulus. The forces are modest but
will have to be considered in the design of the bending fixtures.
Table II Forces applied to models in N/rad
Model Central Inner edge Outer edge
Name Constraint force force
plg31 34.69 -976.0 941.3
plg32 26.99 -810.0 783.0
plg33 40.42 -1032. 991.4
plg41-3 52.41 -1021. 968.2
plg34 -293.7 1193. -898.9
plg44 -357.3 1370. -1013.
Conclusions
We have demonstrated that it is feasible to manually plug 600
fibers in clearance holes drilled in an aluminum plate. The fibers
can be arranged and plugged so that stresses on the fibers and plugs
are low and bend radii are acceptable. Separately, we have
investigated a scheme of bending plates for drilling and in the
telescope so that both the best focal surface and the principal ray
angle are matched to a particular telescope optical design. The
result appears to be feasible and to meet our requirements. We have
not yet adequately addressed the implementation of this scheme.
Much work remains to be done in other areas as well. In
particular, we continue to study various plug-plate materials, plug
designs, and plug retention schemes. We are collaborating with our
colleagues at Fermi National Accelerator Laboratory in a study of
plug-plate drilling accuracy and costs. The integration of these
various ideas into a system that is reliable and that allows quick
interchange of plug-plates remains a major design challenge.
Acknowledgements
We are grateful to Steve Schectman, Sam Barden, John Hill, and
Peter Gray for generously sharing with us their experience. Steve
Schectman suggested to us the idea of drawing lines on the plug-plate
to indicate plugging order. Our colleagues at Fermi National
Accelerator Laboratory, especially Steve Bracker, Charles Matthews,
and Chris Stoughton, have made many helpful suggestions, provided
plug-plates for our tests, and have contributed practical advice on
plug-plate manufacture. The FNAL metrology lab is providing
invaluable feedback on the plug-plate manufacturing process. The APM
galaxy data were supplied by Will Sutherland and Steve Maddox of
Oxford. Jim Gunn and Robert Lupton of Princeton University and Ed
Mannery of the University of Washington were generous with their
comments and suggestions.
References
- J.M. Hill, Fiber Optics in
Astronomy, ed. S. M. Barden, PASP conference series 3, p.
77, 1990.
- P.M. Gray, and K. Taylor,
Instrumentation in Astronomy VII, ed. D.L. Crawford,
Proc. SPIE 1235, p. 709, 1990.
- S.C. Barden, and P. Massey, Fiber
Optics in Astronomy, ed. S. M. Barden, PASP conference
series 3, p. 140, 1990.
- D. Hamilton, Instrumentation Astronomy
VII, ed. D.L. Crawford, Proc. SPIE 1235, p. 673, 1990.
- I.R. Parry and I.J. Lewis,
Instrumentation in Astronomy VII, ed. D.L. Crawford,
Proc. SPIE 1235, p. 681, 1990.
- S.C. Barden, and A. Rudeen,
Instrumentation in Astronomy VII, ed. D.L. Crawford,
Proc. SPIE 1235, p. 729, 1990.
- T.E. Ingerson, Fiber Optics in
Astronomy, ed. S. M. Barden, PASP conference series 3, p.
99, 1990.
A paper similar in content to this note is
published as "Fiber Positioning System for the Digital Sky Survey",
S. Limmongkol, R. Owen, W. A. Siegmund, and C. L. Hull, in Fiber
Optics in Astronomy II, ed. Peter Gray, 1992, p. 127.
Date created: 10/19/91
Last modified: 6/16/99
Copyright © 1999, Walter A. Siegmund
Walter A. Siegmund
siegmund@astro.washington.edu