Sloan Digital Sky Survey Telescope Technical Note 19990622
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.
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.
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
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.
Std. deviation
Minimum
Maximum
2.40
2.08
-11.0
8.4
2.54
2.53
-6.2
7.6
3.13
2.83
-10.7
14.2
2.86
-8.1
10.0
4.28
-4.4
13.7
2.59
2.11
-3.9
14.3
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
