Sloan Digital Sky Survey Telescope Technical Note 19980815
Walter Siegmund
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.
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.
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.
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. Siegmundsiegmund@astro.washington.edu
