Sloan Digital Sky Survey Telescope Technical Note 19980127
The Sloan Digital Sky Survey (SDSS) is a project by a diverse international collaboration to build and operate a facility to perform a very large imaging and spectrographic survey ( "Mining the Heavens: The Sloan Digital Sky Survey" by Gillian R. Knapp, Sky & Telescope, 94, p. 40., 1997.) The plug-plates of the SDSS project locate the optical-fiber plugs spatially and define the plug tilt with respect to the surface of best focus. The aluminum alloy 6061 plates are 795 mm (31.3") in diameter and 3.2 mm (0.125") thick. Approximately 670 holes are drilled in each plate. These include 640 science holes, 10 guide holes and 9 quality assurance holes. The balance are locating holes, light-trap holes and a sky brightness monitor hole.
For drilling, the plate is held by a drilling fixture that deforms it elastically so that its upper surface is convex. The center of the drilling region is about 10 mm higher than the edge. The holes are drilled parallel. In the telescope, the plate is deformed to match the concave surface of best focus. When this is done, the hole axes are aligned with the principal rays from the optics.
Once the plug-plate is assembled and installed on the telescope, guide stars imaged onto coherent fiber-optic bundles are used to determine the errors in telescope pointing, image scale and rotator angle. A low-bandwidth servo loop acts to minimize the position errors of the guide stars on the guide fiber bundles. (The telescope scale is adjusted by moving the primary axially and refocusing.) Consequently, it is important that the guide holes be drilled in the same operation and intermingled with the science holes to minimize any offset between the two hole patterns.
Plates uw0111 and uw0112 were drilled at the University of Washington (UW) Physics Instrument Shop. A vertical milling machine, a Dahlih MCV-2100, was used (Figure 1). Plates ke0111 and ke0112 were drilled by a commercial vendor, Karsten Engineering, Inc., Phoenix. A horizontal milling machine, a Dixi 420TPA, was used. Drilling on both machines was performed in one setup of the part.
Figure 1: Plug-plate drilling. The plug-plate is clamped in drilling fixture mounted on the Dahlih vertical milling machine at the University of Washington. Larry Stark, Instrument Maker, verifies the computer numerically controlled (CNC) program used to control the machine.
The plates took 60 to 195 minutes to drill. The time required was affected by factors such as operator confidence in the computer numerically controlled (CNC) program used to control the milling machine, mechanical problems and machine speed. The drilling time did not include the time required to set up the plate for drilling or to clean up afterwards. In production, we estimate that 20 minutes will be required between plates.
Prior to drilling, software was used to optimize the drilling order and to convert the list of hole types and coordinates into a CNC program. The science holes were drilled at 3000 rpm. A different spade drill bit was used to drill each plate. Each bit is specified to be ø0.0853 +0/-0.000,50" (ø2.1666 +0/-0.001 mm). The bits are made of carbide by Johnson Carbide Products, Inc., Saginaw, MI. The bits have a ø0.1250" shank. The tip extends 9.5 mm from the shank. The shank was fully inserted into the collet. A new bit was used for each plate. Drill runout was measured prior to drilling and was 6.4 µm or less.
Although both machines are in a temperature-controlled environments, excessive temperature fluctuations could affect hole locations. Consequently, the coolant temperature was monitored. The temperature range during drilling was 1 °C or less for each of the four plates. This corresponds to less than 7.9 µm thermal expansion on the radius, too small to be apparent in the plate measurements.
Before shipping the plates to Fermi National Accelerator Laboratory (FNAL) for measurement, the rear surface of each plate was sanded to remove burrs and to eliminate specular reflections from the front surface. Then the plates were vapor degreased and flushed with clean solvent. One plate, ke0111, appeared to have a small amount of aluminum powder contamination in a few holes. Otherwise, the plates were judged very clean upon inspection.
The plug-plates were measured at FNAL. A Giddings & Lewis-Sheffield Measurement, Inc., Apollo RS-50 coordinate measuring machine (CMM) with an accuracy specified at +/-2.5 µm (0.0001") was used for the measurements. The CMM was checked by Giddings & Lewis technicians within two months of the measurements and found to be within calibration.
The temperature of each plate was monitored during measurement by taping a thermocouple probe to the plate. The temperature was measured with an Omega 872A digital thermometer with a thermocouple. Thermally conductive grease was used. The maximum measurement temperature range for each of the four plates corresponds to 4.8 µm thermal expansion on the radius, too small to be apparent in the plate measurements.
Each plate took about 70 minutes to measure. The CMM extracts hole location, diameter and non-circularity from measurements at eight points equally spaced in angle at the same value of z. Since the hole diameters determined in this manner have been shown to be inconsistent with diameters determined using pin gauges, the hole diameter and non-circularity measurements were not used.
The locations, x and y, of each hole, were measured at the z = -1.58 mm (middle of plate). The desired hole locations (the drilling machine coordinates) were subtracted from these values to get hole location errors.
During operation, guide stars on ø8.25 arc-second coherent fiber-optic bundles will be used to determine the values of a1, b1, dx and dy (see below) and the telescope image scale, pointing and rotator angle will be adjusted accordingly. The errors in these coefficients, as long as they are small enough that the guide stars can be acquired, do not affect the ability of the telescope to center the targets in the science fibers. Only the residual errors, after these effects are removed, are important.
To remove these effects, the functions f(x) = dx + b1*y + (a1 + a3*r^2 + a5*r^4)*x and g(x) = dy - b1*x + (a1 + a3*r^2 + a5*r^4)*y were fit to the x and y errors respectively of the science holes. The coefficient a1 includes the effect of thermal expansion between drilling and measurement and the lowest order effect of bending the plate for drilling. The coefficients dx and dy are the offset of the plate center between drilling and measurement. The coefficient b1 is the rotation of the plate between drilling and measurement.
The coefficients a3 and a5 account for higher order effects due to the drilling fixture. Unlike the other coefficients, these cannot be determined separately for each plate during operation of the telescope without measuring each plate. Since this is not envisioned, these coefficients were set to the mean of the coefficients found separately from least squares solutions for the two UW plates (a3 = 1.46E-05 µm/mm^3, and a5 = -8.29E-11 µm/mm^5). Once the coefficients were determined, the residual errors in x and y were calculated (Table 1).
Table 1: Hole location fit.
Plate dx RMS dy RMS (µm) (µm) uw0111 8.4 4.5 uw0112 10.6 5.3 ke0111 7.2 11.6 ke0112 6.7 11.0
Figure 2: Hole location error in x is plotted v. drilling order. The outliers for plate uw0112 are the most non-circular holes and are likely due to remnant burrs or contamination. Standard deviations after trend removal are given. For clarity, 40 µm has been subtracted from the data for uw0112.
The residual errors in one axis are dominated by a positive trend with hole number on both machines (Figure 2). With a linear trend in hole number removed, the residual error in x is 4.4 µm RMS for both uw0111 and uw0112 and 6.2 and 6.5 µm RMS for ke0111 and ke0112 respectively. The residual errors in the other axis do not show this correlation. In the case of the UW machine, the spindle housing is heated by bearing friction and electrical dissipation in the spindle motor. The resulting thermal expansion of the the spindle housing increases the separation of the spindle and the vertical ways of the machine. Measurements of the spindle housing temperature and the displacement of the spindle housing are consistent with this explanation.
No higher order correlations of the residual error in r with r are apparent. This indicates that the model of plate distortion on the drilling fixture is adequate.
The errors in both x and y are well-correlated between pairs of holes adjacent in the drilling sequence. The standard deviation of the differences of the residual errors of adjacent holes is 4 µm or less for each axis for the four plates. These numbers represent the small-scale (20 mm) repositioning error of the machines and drill bit wander.
The plug-hole clearance must be specified so that nearly all holes can be plugged given the distribution of hole and plug diameters. However, excessive plug-hole clearance increases fiber location error unnecessarily since the moment applied to the plug by the protective fiber tubing causes the plug to tilt so that the plug tip is pushed against one side of the hole thereby decentering the fiber in the hole. This same tilt causes misalignment of the fiber axis with the principal ray. Consequently, it is desirable that the hole diameters be as uniform as possible so that the plug-hole clearance can be small.
The holes in uw0111 and uw0112 were gauged with pin gauges (Table 2). Each hole was assigned the diameter of the largest gauge that could be inserted in the hole. The project goal for hole diameter is 2.167 +0.010/-0.000 mm and was satisfied by nearly all the holes (Figure 3).
Table 2: Pin gauge diameters. Diameter(mm) Diameter(inches) 2.167 0.0853 2.169 0.0854 2.172 0.0855 2.174 0.0856
Figure 3: Hole size distribution for plate uw0111. If the fit of the largest pin gauge was judged loose, it was assigned to the right-most bin.
The drill bits used to drill these holes were measured. Plate uw0111 was drilled with a bit measuring ø2.1576 mm. Plate uw0112 was drilled with a bit measuring ø2.1582mm. These numbers are somewhat smaller than the ø2.1666+0/-0.0013 mm (0.0853+0/-0.00005") specified. The bits used to drill ke0111 and ke0112 were not measured.
As described in the introduction, the holes are drilled tilted with respect to the normal to the plate surface. The tilt of holes were measured on six plates drilled prior to plate uw0111. For these plates, the holes were measured at three different depths. The radial components of the hole location at the top and bottom of the each hole in combination with the separation of the two measurements were used to calculate the tilt of each hole. The hole tilt as a function of radius is compared to the ideal tilt from the optical design and to the finite element model of the plug-plate in its drilling fixture. The RMS error from the ideal tilt ranged from 2.1 to 3.3 mrad for the six plates. Plate ke0100 had the largest RMS error (Figure 4).
Figure 4: Hole tilt is plotted as a function of radius for uw0102 (open circles). The filled squares are the optimal tilts from the optical design. The filled diamonds are the tilts calculated from the finite element model. The RMS error is calculated with respect to the kent005 curve. The standard deviation is that of residuals to a 7th-order odd-polynomial fit (as shown).
The ends of the fibers must be located so that they intercept the images formed by the telescope where they are in sharpest focus, i.e., on the surface of best focus. The results of finite element modeling suggested the feasibility of deforming the plug-plates elastically so that the plug-plate surface matches the surface of best focus. The plug-plates are clamped near their circumference between a pair of slightly conical bending rings that impose the proper slope at the field edge. A ø3.2 mm rod at the center of the cartridge pushes on the back of the plug-plate. It constrains the center of the plug-plate to have the correct axial displacement with respect to the edge. The bending rings, central constraint, fibers and slit assemblies are supported by an aluminum casting. It is quite stiff and controls the spatial relationship between the bending rings and central constraint.
A set of five indicators mounted on a bar supported by tooling balls was used to measure the deflection of two plates (uw0111 and ke0111) at five points along the radius of the plate and at four different angular locations. The deformation was recorded and plotted with the surface of best focus from the telescope optical design. For uw0111, the area-weighted deviation of the surface of best focus was 43 µm RMS (Figure 5). For ke0111, it was 37 µm RMS.
Figure 5: Measurements along four radii of plate uw0111 compared with the surface of best focus from optical design kmg001.
The SDSS telescope has a final f-ratio of 5 and a focal surface scale of 60 µm/arc-sec. Errors in the lateral position of the ø180 µm science fibers cause decentering of targets. Errors in the axial position cause image blur. Misalignment of the fiber axis with the principal ray increases focal ratio degradation. These effects reduce survey efficiency because fewer photons are detected by the spectrograph.
Residual hole location errors are dominated by a linear trend in hole number of the residual error in x. The error budget that we proposed in SDSS Technical Note 19930430 allows 9 µm root-mean-square (RMS). The 2-d position errors measured, 9.5, 11.9, 13.6 and 12.9 µm RMS for uw0111, uw0112, ke0111 and ke0112 respectively, are not quite consistent with this goal. However, if the linear trend in hole number of the residual error were corrected or compensated, the results would be consistent with the budgeted amount. One option, under consideration for the Dahlih machine is to implement an available temperature control system for the spindle lubricant.
The measurements of hole diameters suggest a large-diameter tail in the distribution that exceed our specified range. Since only 1 or 2% of the holes are affected, this appears to be inconsequential.
The hole tilt measurements indicate excellent performance. The holes on the worst plate have an RMS error of 3.3 mrad, much better than the 6 mrad allotted.
The plates match the surface of best focus to 43 and 37 µm area-weighted RMS for uw0111 and ke0111 respectively. These do not meet our goal of 25 µm RMS. It appears that the error is largely due to departures from planarity of the bending rings. Correcting this appears to be straightforward and should improve the match to the focal surface since so much of the area of the plug-plate is in close proximity to the bending rings.
We are grateful to our colleagues at FNAL, Paul Mantsch, Robert Riley, Barb Sizemore and Charles Matthews for their help with the measurement of the plates and their interest in and assistance with various aspects of plug-plate drilling. Jim Gunn at Princeton University was a continuous source of inspiration and encouragement. It is a pleasure to thank Ron Musgrave, Larry Stark, Dan Skow, Siriluk Limmongkol and Jeff Morgan at the UW for their interest and comments.
A paper similar in content to this note is published as "Performance of the Fiber Positioning System for the Sloan Digital Sky Survey", W. A. Siegmund, R. E. Owen, J. Granderson, C. L. Hull, R. F. Leger, E. Mannery and P. Waddell, in Fiber Optics in Astronomy III, ed. S. Arribas, E. Mediavilla and F. Watson, A.S.P. Conference Series, 152, (San Francisco, Astronomical Society of the Pacific) 1998, p. 92.
Date created: 1/29/98 Last modified: 4/16/99 Copyright © 1998, Walter A. Siegmund Walter A. Siegmund
