Fitting Plug-Plates To The Surface Of Best Focus
Sloan Digital Sky Survey Telescope Technical Note
19960805
Jessica Granderson
University of Washington
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.
Matching the Surface of Best Focus
In the first attempts to match the curvature of the plug-plates to
that of the best focal surface, the bending fixture was set upon 3
6.630mm metal supports that were affixed to a table top and spaced
120°apart. The sky side of the plate was facing up. The
adjustable parallel that served as the central constraint was also
affixed to the table top. The results indicated that a central
constraint of 27.36 mm (1.077") was slightly too large. See
previous
report . The difference between the shape of the plate and the
desired shape near zero radius indicates that a change of
approximately 0.25 mm, or 0.01" would yield a much better fit. (It
should be noted that in the previous report, the focal surface of
superceeded optical design kent005 was plotted as the desired shape.
In this report, the focal surface of the current design, kmg001 is
used. However, since the focal surface remained unchanged, the two
designs represent identical curves.)
The
bending
procedure was repeated using a central constraint of 27.04mm
(1.0645"). The deflection of the plate used in the initial bending
(uw0111) was measured, as well as that of a
second plate (ke0111). The results are plotted in
Figures 2 and 3,
respectively. The indicators used to measure the deflection of the
plate were zeroed with respect to the tooling balls that support
them, therefore measurements were also taken to determine the
deflection of the plate surface along which the tooling balls were
positioned (R = 323.85 mm) . These results can be found in
Figure 4.
Figure 1: The profilometer shown above was used to measure the
deflection of the plug-plate. The central constraint was placed
underneath the bending fixture, and 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: This plot shows the shape of plug-plate uw0111 and
kmg001, the desired shape of the plate. The 27.04mm central
constraint produced a significantly better fit than did a 27.36mm
constraint.
Figure 3: This plot shows the shape of plate ke0111 under the
27.04mm central constraint. Plate ke0111 deformed differently than
plate uw0111, resulting in a slightly closer match to the best focal
surface.
Figure 4: This figure indicates the deviation from flatness
exhibited by plate uw0111 along R = 323.85 mm. Three gauge blocks
were placed between the bending fixture and a surface block, and a
dial indicator was used to measure the displacement of the plate. The
data points plotted here represent the results of two trials, in
which the average displacement was subtracted from the measured
displacement at each of twelve angular positions.
Analysis
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.
As indicated in Figure 4, the deviation of
the plate from flatness at R= 323.85mm was approximately 0.127 mm, or
0.005". This variation in surface flatness is certainly large enough
to explain the scattering of the data points along a given radius.
For example, in both Figures 2 and
3, there is approximately a 0.1 mm scatter of
the data points at R=150 mm.
Conclusion
The results of the second set of plate bending trials confirm that
forcing the plate into a pre-determined slope along its outer edge,
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 indicate that using a 27.04mm central
constraint produces a curvature in the plug-plates that very closely
matches the surface of best focus. 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 0.047 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 closer the
allowed deviation of 0.025mm, at values of 0.029mm and 0.025mm,
respectively.
Date created: 8/06/96
Last modified: 8/14/96
Jessica Granderson