Sloan Digital Sky Survey Telescope Technical Note 19961230
Jessica Granderson University of Washington
The plug-plates of SDSS project are responsible for locating the optical-fiber plugs spatially and for defining the plug tilt with respect to the surface of best focus. The plates are 795 mm (31.3") in diameter and 3.2 mm (0.125") thick. Approximately 670 holes are drilled in each plate. For drilling, the plate is held by a drilling fixture that deforms it elastically so that its upper surface is convex. The hole axes are drilled parallel. In the telescope, the plate is deformed to match the surface of best focus. When this is done, the hole axes are aligned with the principal rays from the optics.
Previous attempts to match the SDSS plug-plates to the surface of best focus were conducted using only the bending fixture. The analyses performed indicated that by adding a central constraint to the plug-plate deformation process, the plates could be made to match the surface of best focus within an acceptable range of error. Since the time that the last tests were performed, the cartridge that will hold the plug-plates and the bending fixture on the telescope has been fabricated. Inside of the cartridge is a thin rod that serves as the central constraint. The height of the rod, and thus the magnitude of the central constraint can be adjusted using a threaded nut. A second series of tests has been performed in order to determine the accuracy with which the plug-plates can be deformed using the cartridge.
A set of five indicators supported by tooling balls was used to measure the deflection of two plates (uw0111 and ke0111). Data was taken at five points along the radius of the plate, at four different angular locations. The deformation was recorded and plotted against a curve of the focal surface, kmg001. The results are shown in Figure 3 and Figure 4. The central constraint was adjusted to displace the plate centers approximately 0.72mm and 0.68mm from their unconstrained positions for plates uw0111 and ke0111, respectively.
Figure 1: Pictured here is the cartridge, with bending fixture and plug-plate installed. The profilometer atop the plug-plate was used to measure the deflection of the plug-plate. The central constraint is located underneath the bending fixture. Data was taken at five points along the radius, using the five indicators pictured. The profilometer is supported by tooling balls, and calibrated on a granite straight edge that is flat to 1 micron. The right tooling ball provides a sixth measuring point.
Figure 2: A close-up view of the mechanism that is used to impose the central constraint.
Figure 3: This plot shows the shape of plug-plate uw0111 versus kmg001, the desired shape of the plate.
Figure 4: This plot shows the shape of plate ke0111 versus kmg001. Plate ke0111 deformed differently than plate uw0111, resulting in a slightly closer match to the best focal surface.
It can be seen from the graphs that by bending the plates and adding a central support, the curvature of the plug-plates can be made to match the surface of best focus quite closely. The two plates tested deformed into two different shapes. Since they were fabricated by two different groups, the 3.175mm aluminum plates differed in thickness by approximately 0.076mm. This difference in thickness is the most likely cause of the difference in deformation of the two plates. The ke0111 plug-plate was the thicker of the two, and correspondingly it did not vary as much in deflection along the inner radius.
While the average deformation of the two plug-plates tested provided quite a close matches to the desired focal surface, there is a large degree of scatter among data points taken at a given radius at different points about the plates. The plug-plates deformed into a saddle-like shape; the deflection at 0° and 180° was approximately 0.10mm less than the deflection at 90° and 270°. The total variance between largest and smallest deflections at a given radius was approximately 0.19mm. This is far greater than the amount of scatter seen in previous bending tests, which was approximately 0.04mm.
The results of this set of plate bending trials confirm that the cartridge, into which the plug-plates and bending fixture are to be installed, provides a suitable mechanism for imposing the central constraint upon the plug-plates. The average deflection of both plates tested could be well matched to that of the surface of best focus. The experimental data indicate that the magnitude of the constraint should be 0.72mm or 0.68mm, depending upon whether plate uw0111 or ke0111 is to be used. Variations in the thickness of the plate, such as those that appear when different manufacturers are used, do affect the shape of the plate.
The slightly thicker plate, ke0111, matched the desired curve most closely with a standard deviation of 0.025 mm; the thinner plate, uw0111, was fit with a deviation of 0.035 mm. The tolerated deviance of the plates from the target curve is 0.025 mm. An area-weighted standard deviation was also calculated, to account for the radial spread in data points that is obscured in a point by point, unwieghted calculation. The area weighted deviation for plates uw0111 and ke0111 were worse than the allowed deviation of 0.025mm, at 0.043mm and 0.031mm, respectively. The deviation would have been much the same had the central constraint had not been adjusted between plates.
The most probable cause for the increase in scatter between data points at a given radius, is out-of-flatness of the mating surfaces of the bending rings. Previous deflection tests were conducted using a different set of bending rings, which could account for the better results that were obtained. In machining the second set of rings, more variance of the ring surfaces may have been introduced.
Date created: 12/30/96 Last modified: 12/31/96 Jessica Granderson
