Fiber Positioning System for the Sloan Digital Sky Survey

Sloan Digital Sky Survey Telescope Technical Note 19911019

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

1. J.M. Hill, Fiber Optics in Astronomy, ed. S. M. Barden, PASP conference series 3, p. 77, 1990.
2. P.M. Gray, and K. Taylor, Instrumentation in Astronomy VII, ed. D.L. Crawford, Proc. SPIE 1235, p. 709, 1990.
3. S.C. Barden, and P. Massey, Fiber Optics in Astronomy, ed. S. M. Barden, PASP conference series 3, p. 140, 1990.
4. D. Hamilton, Instrumentation Astronomy VII, ed. D.L. Crawford, Proc. SPIE 1235, p. 673, 1990.
5. I.R. Parry and I.J. Lewis, Instrumentation in Astronomy VII, ed. D.L. Crawford, Proc. SPIE 1235, p. 681, 1990.
6. S.C. Barden, and A. Rudeen, Instrumentation in Astronomy VII, ed. D.L. Crawford, Proc. SPIE 1235, p. 729, 1990.
7. 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