Sloan Digital Sky Survey Telescope Technical Note 19940520
The SDSS 2.5-m mirror was cast of Ohara E-6 borosilicated glass by Hextek Corp. It consists of a face-plate and a back-plate connected by a ribs in a honeycomb pattern. The mirror was cast with cylindrical skirt at both the inside and outside diameters connecting the face and back-plates. After the mirror was damaged during initial generation, the inner skirt was removed along with inner portions of the face and back-plates and ribs.
On May 3, 1994 at the Optical Sciences Center at the University of Arizona, measurements of cell depths and locations of the back-plate holes were made. At this time, the generation of the back plate was complete (on April 24), but the transverse support holes had not been enlarged, nor had any of the holes in the back plate been chamfered. The inner and outer diameters of the back plate were finished with a ~5 mm chamfer.
For convenience in referencing a particular cell in the mirror, cell names have been established as shown in Figure 1. The coordinate system for measurements of the back-plate is shown as well. (The coordinate system for measurements of the face-plate is reflected about the y axis with respect to the back-plate system)
Figure 1: Cell labels and coordinate system for the 2.5-m primary mirror. The view is from the back with the chip (an obvious feature) at the bottom of the drawing (as shown).
The depths of the cells along 6 radii were measured ( Table 1 ). These were measured from the back of the face plate to the back of the back plate using a special purpose measurement tool. All measurements were made at the centers of the back plate holes. Debris from grinding and water was present in the cells and may have affected measurements although an effort was made to prevent this. Also, the measurement tool probe tip has a radius of curvature of 6 mm. Thus, it samples only a small region on the back of the face-plate, a surface that is fairly rough.
x (m) y (m) z (m) 0.000 0.768 0.2540 0.000 0.960 0.2675 0.000 1.152 0.2916 0.665 0.384 0.2540 0.831 0.480 0.2695 0.998 0.576 0.2858 0.665 -0.384 0.2540 0.831 -0.480 0.2695 0.998 -0.576 0.2891 0.000 -0.768 0.2525 0.000 -0.960 0.2687 0.000 -1.152 0.2852 -0.665 -0.384 0.2545 -0.831 -0.480 0.2695 -0.998 -0.576 0.2873 -0.665 0.384 0.2540 -0.831 0.480 0.2708 -0.998 0.576 0.2865
The design radius of curvature of the mirror face-plate is 11.25 m, so the back of the face-plate should have a radius of 11.275 m (the face-plate design thickness was 25 mm). An even second order polynomial least squares fit to the cell depth data (Figure 2) gives R = 1/2a = 10.9 m, where R is the radius of curvature of the back of the face-plate and a is the coefficient from the fit. This is within 3% of the design value. The coefficient b is the depth of an imaginary cell at the center of the mirror. It is 2.7 mm larger than the design value.
The back-plate of the mirror is flat to better than 1 mm. This was measured using a straight-edge across a couple of cords by Charlie Hull about October 30, 1996.
Figure 2: The cell depth measurements are plotted as a function of radius. A second order even polynomial least squares fit to these data is shown.
The design radius of curvature and mean cell depth was removed from these data and the residual values plotted against x and y (Figure 3 and Figure 4). The residuals were within 2 mm of the mean except for one outlier at 4.5 mm.
Figure 3: Residual cell depths after removing the design radius of curvature of the back-plate and the mean cell depth. These are plotted against x.
Figure 4: Residual cell depths after removing the design radius of curvature of the back-plate and the mean cell depth. These are plotted against y.
The back of the mirror was compared to a full size design drawing of the mirror (composed of E-sized plots taped together). After moving the drawing to match the mirror, a rubbing was done to indicate the actual locations of the 76 mm diameter holes in the back plate and the outer and inner diameters of the back plate. Because of the way the mirror was fabricated, it is believed that the locations of the ribs is highly correlated with the locations of the holes. This has been spot checked, as well.
The errors in the locations of the centers of the 76 mm holes (relative to the design drawing) were estimated to an accuracy of about 1 mm. Some breakage occurred about some holes at the back plate so some judgement was required to determine the error. For most holes, enough of the hole was undamaged that it was straightforward to determine the error.
The errors for the 12 smallest outer partial cells and the 6 inner partial cells tend to be much larger than for the rest of the cells. Consequently, these data were not included in a least squares fit to determine the mean scale factor and rotation of the hole pattern. The scale factor was found to be 1.00305. Since the nominal center-to-center cell spacing is 192 mm, upon multiplying by the scale facter it becomes 192.6 mm. The design hole locations must be multiplied by this factor to better match the mirror. The rotation was -0.092 degrees. Although the template was rotated to match the mirror before doing the rubbing, this was not done perfectly. This is the error in the rotation angle. The residual location errors after removing scale and rotation are plotted below (Figure 5, Figure 6, Figure 7 and Figure 8). The maximum residual error was about 4 mm. Data for the 12 smallest outer partial cells and the 6 inner partial cells were not plotted.
Figure 5: Residual back-plate hole location error in x after removing the mean scale of the hole pattern and the rotation. These are plotted against x.
Figure 6: Residual back-plate hole location error in y after removing the mean scale of the hole pattern and the rotation. These are plotted against x.
Figure 7: Residual back-plate hole location error in x after removing the mean scale of the hole pattern and the rotation. These are plotted against y.
Figure 8: Residual back-plate hole location error in y after removing the mean scale of the hole pattern and the rotation. These are plotted against y.
Last modified: 10/30/96 Copyright © 1996, Walter A. Siegmund Walter A. Siegmund
siegmund@astro.washington.edu
