Fiber-optic plug rotation
Sloan Digital Sky Survey Telescope Technical Note
19980815
Walter
Siegmund
Contents
Introduction
Guiding of the SDSS 2.5-m telescope during spectrographic
observations is performed using coherent optical fiber bundles. These
are plugged into plug-plate holes drilled at the predicted locations
of suitable guide stars in the field of view. Ten guide stars are
used to provide redundancy and diagnostic information. The star
images at the output ends of the guide bundles are transferred to the
guider CCD using a 1:1 reimaging lens. The offset of the star images
from the center of the guide bundles is calculated.
Measurements
A pointer made from a paper clip was bent around a fiber optic
plug. Fiber 16 of harness #353 was used. Plug-plate uw0111 was used.
The selection of fiber and plug-plate were arbitrary. Hot-melt glue
was used to secure the pointer to the plug. A transparent protractor
with a clearance hole for the plug was used to measure the angle
indicated by the pointer. A transparent scale was affixed to the
plug-plate using hot-melt glue along the y axis and served as both an
angle and Cartesian coordinate system zero point.
The origin of the coordinate system was the location that the
ø3.2 mm red tubing emerges from the anchor block projected
vertically to the plug-plate. The emergent direction defines the +y
axis. The anchor block machine screw is in the +x half-space. (In
Figure 2, +x is right and +y is up.) The center of the anchor block
was 305 mm above the plug-plate. A circle R165 mm centered at the
origin indicated the plugging region for the fiber. The diameter of
the plugged holes is ø2.169 mm. These are the dimensions that
are specified for the survey.
I plugged 49 holes and recorded the location
and plug angle for each hole. The first 18 measurements were made
with the tubing emerging toward the center of the plug-plate. The
rest of the measurements were made with the tubing emerging away from
the center of the plug-plate.
The results for a particular hole varies by 40° to 50°
peak-valley depending on the torque applied to the plug during the
plugging process. No effort was made to minimize this. I believe that
the results should be similar to those likely to be found during the
operation of the survey. Data were obtained in two setups of the
harness with respect to the plug-plate. However, no attempt was made
to investigate the effect of interference by other fibers. However,
it is likely that the interference of other fibers did occur and is
responsible for the larger variation than would be predicted from the
range reported above for a single hole. In particular, any departure
from the ideal elastic curve from the tubing anchor point to the hole
appears to affect the rotation angle of the plug.
Figure 1: The plug angle indicated
by a pointer made from a paper-clip was read from transparent
protractor. The pointer was attached to the plug using hot-melt
glue.
Figure 2: Harness #353 was mounted
above plug-plate uw0111. The center of the anchor block was 305 mm
above the plate. The plugging region on the plug-plate was
indicated by a R165 mm circle. Its center was directly below the
location where the ø3.2 mm red tubing emerges from the
anchor block. The tubing emerges in the +y direction at the origin
of the coordinate system used to measure the plugging
locations.
Analysis
The data were examined with a 3-D stereo data visualization
program (Rotater
3.5). An offset was noted between data obtained in the two
setups described above. However, it was not sufficient to change
the results significantly.
A linear or possibly quadratic dependence of the plug angle
with the x-coordinate of the hole location was identified in the
data (Figure 3). Since a quadratic dependence is unlikely to be
physical, the linear dependence was removed. No structure of the
residual plug angle appeared significant when these data were
examined in 3-D.
Figure 3: The plug rotation angle has a
standard deviation of 54° (201° peak-valley). The plug
rotation angle depends on the x-coordinate of the plugged location
(0.46°/mm).
Figure 4: With the linear fit of
Figure 3 removed, the standard deviation is 31° (154°
peak-valley).
Figure 5: With the linear fit of
Figure 3 removed, no trend in y is apparent.
Conclusions
The plug-angle has a standard deviation of 54° (201°
peak-valley). The plug rotation angle depends on the x-coordinate of
the plugged location. The slope is 0.46°/mm. With this trend
removed, the standard deviation is 31° (154°
peak-valley).
How large can the rotation error be? I calculated 56 sets of
normally distributed rotation errors for the ten guide bundles. For a
unit pointing error in x, I calculated the x and y offsets that would
be detected by each guide bundle. Then, it was a simple matter to
calculate the mean x and y offsets for the ten guide bundles (Figure
6), i.e., the pointing correction computed by the guider. I ignore,
for the moment, the issue of scale and image rotator errors.
As the standard deviation of the rotation errors increases, the
computed pointing correction in x decreases. The x offset from each
guide bundle is proportional to the cosine of the bundle rotation
error. This is never larger than 1 and can be negative for
sufficiently large rotation errors. The behavior of the correction in
y is quite different. With no rotation errors, it should always be
zero since the pointing error is only in x. On average it is zero.
However, the envelope about zero grows slowly as the standard
deviation of the rotation error increases. The outliers that define
the envelope occur when all or nearly all of the rotation errors
happen to have the same sign.
Since other errors and noise will be present and speed is
important, it is reasonable to require that the magnitude of the y
correction be less than half that of the x correction, i.e., an error
reduction of roughly a factor of two or more per iteration. This is
satisfied if the standard deviation of the bundle rotation errors is
less than 50°.
Since this is slightly less than the measured rotation error, it
may be necessary to either compensate for the rotation error that is
proportional to the x-coordinate of the plugged location or to reduce
the error, e.g., by providing a mechanical means of constraining the
rotation error of the plugged bundle. With the former approach, once
the pointing error has been minimized, it is still necessary to
determine the rotation angles of the bundles by offsetting the
telescope a small amount to reduce the errors in the guide and scale
parameters. The latter approach eliminates this step and the software
to accomplish this. This is offset by somewhat more complex plate and
bundle fabrication and more difficult plugging. Also, the target
exclusion region around each guide star will be enlarged.
Scale and rotator errors should have little impact on the above
discussion, unless their magnitude is such that the guide star images
cannot be placed on the guide fibers. If scale and rotator
corrections are solved for simultaneously with the x and y pointing
corrections, noise in the centroid locations may be coupled in a more
complicated way to the corrections thereby rendering the system
somewhat less robust.
Figure 6: The means of the x and y offsets
measured for the guide bundles are plotted for a unit pointing error
in x. Bundle rotation errors are normally distributed with a standard
deviation of sigma.
Acknowledgment
It is a pleasure to thank Russell Owen who helped develop the
measurement technique.
Date created: 8/15/98
Last modified: 1/26/98
Copyright © 1998, 1999, Walter A. Siegmund
Walter A. Siegmund
siegmund@astro.washington.edu