Plug-plate hole tilt reexamined
Sloan Digital Sky Survey Telescope Technical Note
19990622
Walter
Siegmund
Contents
Introduction
The two Sloan Digital Sky Survey (SDSS) spectrographs are coupled
to images formed by the SDSS 2.5-m telescope by 640 optical fibers.
Clearly, the ends of optic fibers that couple images from the
telescope focal surface to a spectrograph must be located on the
surface of best focus at the location of each image. It may be less
obvious that the axis of each fiber must be accurately aligned with
the conical bundle of light-rays coming from the telescope pupil.
This is to minimize the f-ratio degradation in fibers coupling
a telescope focal surface to a spectrograph and thereby maximize the
light intercepted by the spectrograph collimator. The telecentric
surface is defined to be that surface that is normal to the central
ray of each image. With this definition, the alignment criterion can
be restated as follows: the axis of each fiber must be normal to the
telecentric surface.
The plug-plates for the Sloan Digital Sky Survey are drilled with
each plate elastically deformed over a convex mandrel and with the
sky-facing side away from the mandrel. The holes are drilled with
their axes parallel to the z-axis of the machine (the plate is
deformed in z from the x-y plane). For use, the plates are deformed
by the plug-plate cartridge so that the sky-facing side is concave
and matches the surface of best focus of the telescope. As a
consequence of this process, the hole axes are nearly normal to the
telescope telecentric surface. Clearance between the fiber ferule and
hole are controlled so that fiber alignment is well-constrained by
the hole axis
In SDSS Telescope Technical Notes 19941206 (Full-scale Plug-plate
Drilling Tests I: UW), 19950130 (Full-scale Plug-plate Drilling Tests
II: Karsten) and 19950209 (Full-scale Plug-plate Drilling Tests III:
D-Velco), I reported the results of the measurements of holes drilled
in this manner. The tilt of the holes was compared to that of the
telecentric surface of the contemporaneous spectrographic optical
design, kent005.
In April of 1995, kent005 was modified slightly to kmg001 to
reduce the lateral color in the spectrographic images and make the
spectrographic corrector easier to manufacture (SDSST TN19961022,
2.5-m telescope spectrographic optical design). This is the current
optical design. The telecentric surface was changed somewhat between
designs. In particular, the slope of the telecentric surface as
compared with the surface of best focus is now about 5 mrad steeper
in the outer portion of the field of view (Figure 1). This makes the
comparison of the tilt data from the earlier measurements with the
kent005 model reported earlier obsolete and is corrected below.
Figure 1: Difference of the slopes
of the telecentric and best focus surfaces (dyp) for the optical
designs kent005 and kmg001. Put another way, this is angle that
the direction cosine of the central ray makes with the normal to
the focal surface and is the angle that the fiber hole must be
drilled into a plate which conforms to the focal surface.
Results
The plug-plates were measured at Fermi National Accelerator
Laboratory (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 plates were measured flat on the CMM. The CMM extracts hole
location, diameter and non-circularity from measurements at eight
points equally spaced in angle at the same value of z. These
parameters were recorded at three different heights; -2.5375, -1.5875
and -0.3810 mm (-0.1000", -0.0622" and -0.0148"). 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 tilt of each hole as a function of its radial location on the
plate is plotted along with the ideal tilt from optical design kmg001
(Figures 2 through 7). The ideal tilt dyp = -2.492e-1*r +
18.41e-7*r3 + 4.027e-12*r5 -
5.952e-17*r7. The difference of the measured hole tilt
from the ideal hole tilt was calculated for each hole. Statistical
measures of these tilt errors are noted on each plot.
Figure 2: Hole tilts for uw0100. The
tilt of each hole in plate uw0100 is plotted along with the ideal
tilt from optical design kmg001. The statistics for the tilt
errors are listed.
Figure 3: Hole tilts for uw0102.
Figure 4: Hole tilts for ke0100.
Figure 5: Hole tilts for ke0102.
Figure 6: Hole tilts for dv0100.
Figure 7: Hole tilts for dv0102.
The RMS errors from SDSS Telescope Technical Notes 19941206,
19950130 and 19950209 are summarized below (Table 1). They are to be
compared with the current results (Table 2). The maximum and minimum
errors are not to be taken too seriously since often these are due to
a single outlier.
Table 1: Summary of hole tilt errors
(mrad) with respect to kent005.
Plate
|
RMS
|
uw0100
|
2.6
|
uw0102
|
2.1
|
ke0100
|
3.3
|
ke0102
|
2.5
|
dv0100
|
2.3
|
dv0102
|
2.4
|
Table 2: Summary of hole tilt errors
(mrad) with respect to kmg001.
Plate
|
RMS
|
Std. deviation
|
Minimum
|
Maximum
|
uw0100
|
2.40
|
2.08
|
-11.0
|
8.4
|
uw0102
|
2.54
|
2.53
|
-6.2
|
7.6
|
ke0100
|
3.13
|
2.83
|
-10.7
|
14.2
|
ke0102
|
3.13
|
2.86
|
-8.1
|
10.0
|
dv0100
|
4.28
|
2.54
|
-4.4
|
13.7
|
dv0102
|
2.59
|
2.11
|
-3.9
|
14.3
|
Conclusions
Measurements of the tilts of holes in plates drilled in December
of 1994 have been reanalyzed and compared to the ideal hole tilt of
the current optical design kmg001. While the results are a little
worse than the comparison with the earlier optical design, kent005,
they are better than required.
The fiber alignment error budget includes 10 mrad RMS for
principal ray misalignment due to errors in the deformation in the
plug-plate. This item has two components. One is the deformation
during drilling and the other is deformation in the plug-plate
cartridge. The tilt error associated with drilling deformation (these
measurements) uses little of the budget. The tilt error associated
with deformation in the cartridge should be similar to these
measurements but should be measured as time and resources permit.
The fiber alignment error budget includes 2 mrad RMS tilt error
for hole drilling per se (prior to deformation). Since we have no
plans to measure this separately, it is inconsequential when added in
quadrature, and is included in these measurements, it would simplify
matters to drop it from the budget.
Note that plug/hole alignment is allocated separately in the
budget at 5 mrad RMS. This item is associated with the clearance
needed for reliable plug insertion.
Date created: 6/22/99
Last modified: 8/30/99
Copyright © 1999, Walter A. Siegmund
Walter A. Siegmund
siegmund@astro.washington.edu