Deformation Of Plug-Plates To Match The Surface Of
Best Focus
Sloan Digital Sky Survey Telescope Technical Note
19960708
Jessica Granderson
Contents
Introduction
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.
Plate bending
The bending fixture consists of two rings with outer diameters
approximately equal to that of the plate. In order to deform the
plate, the inner surfaces of the rings between which the plate is
clamped are slightly angled, rather than planar. See
Figures 1,
2 and 3.
Figure 1: View of the bending fixture and plug-plate as seen from
above. The green and black lines represent the bending fixture and
plug-plate, respectively.
Figure 2: Cross-section of the bending fixture and plug-plate.
Incoming rays of light are seen in light blue; the top and bottom
rings of the bending fixture are shown in blue and green,
respectively.
Figure 3: A closer view of the plug-plate while installed in the
bending fixture shows the angled clamping surfaces of the top and
bottom rings. Also pictured are a set of ridges on the top ring
intended to block scattered light paths.
A finite element analysis was performed to compare the curvature
of the plate to the slope of the focal surface, given the constraints
imposed on the plate by the bending fixture. See
Figure 4. A further displacement
constraint can be added at the center of the plate to force the plate
sag to match that of the best focal surface, once the the plate has
been bent to the desired curvature.
To verify the design, a plate was inserted into a prototype and
the subsequent deformation of the plate was compared to the desired
shape. See Figure 5. For each of four
angles, the displacement of the plate with respect to its outermost
exposed edge was measured at five points along the radius. In order
to match the sag of the plate to that of the focal surface, gauge
blocks were inserted between the surface supporting the clamping
device, and the center of the underside of the plate. The shape of
the plate after two trials using different gauge block sizes can be
seen in Figures 6 and
7 .
Figure 4: The results of the finite element analysis
corresponding to the constraints imposed upon the plate by the
bending fixture, are plotted with the best focal surface.
Figure 5: This plot shows the curvature of the plate with no
central support at five points along the radius, at four different
locations on the plate. The desired shape of the plate is shown in
red, and the average displacement of the plate is shown in blue.
Figure 6: This plot shows the shape of the plate after an initial
attempt to match the displacement of the plate's center to that of
the best focal surface. In this case a 1.1" gauge block pushed the
center of the plate slightly higher than desired.
Figure 7: The sag of the plug-plate was still too severe after
decreasing the size of the gauge block to 1.077".
Analysis
It can be seen from the graphs that after bending the plate and
adding a central suport, the curvature of the plate was quite near
that of the desired Kent005 curve. Close examination of the Kent005
curve and the plate curvature toward the outermost data points
reveals that with no central support, the slope of the plate is
slightly greater than that of the Kent005 curve. Upon adding a
central support, however, the slope of the plate decreases to a value
slightly less than that of the Kent005 curve.
Conclusions
From the results of the initial plate bending trials it appears
that forcing the plate into a pre-determined slope along the outer
edge of the plate, and applying an additional displacement constraint
at the center of the plate, is a practical method by which to deform
the plug-plates. The experimental data suggest that decreasing the
size of the gauge block used as a central constraint would
significantly improve the fit of the plug-plate to the shape of the
Kent005 curve. Given that the slope of the unsupported plate is
greater than desired, while the slope of the supported plat is less
than desired, alteration of the extent to which the plate sag is
adjusted after bending, is expected to produce a notable improvement
in the shape of the plug-plates.
Date created: 7/08/96
Last modified: 7/19/96
Jessica Granderson