Sloan Digital Sky Survey Telescope Technical Note 19980823
The SDSS 2.5-m primary mirror is supported in a manner similar to the Apache Point Observatory 3.5-m telescope primary.1 Separate systems support the axial and transverse components of the 2.5-m mirror weight vector. The axial support is provided by 48 air pistons. The pistons have the same diameter thereby applying equal forces with the same air pressure. The 48 pistons are divided into three groups of 16 each. Each group supports a 120° sector of the mirror. The portion of the weight of the mirror that is not supported by the air pistons is sensed by load cells located near the center of each 120° sector. Each load cell controls the air pressure to the pistons in its sector so that the force on the load cell is about 10 N. This force is too small to cause significant distortion of the mirror.
The transverse support is provided by 18 air pistons, supported by cantilevers from the mirror cell, that act on the mirror local center of gravity surface when the mirror is lowered into place. Each piston pushes on a steel force spreader that, in turn, pushes on four nickel-iron alloy blocks bonded to the mirror ribs. All transverse air pistons are the same diameter. A single load cell senses the unsupported mirror weight and controls the air pressure to the transverse support pistons. The remaining rotational and lateral degrees of freedom are constrained by two links to the mirror cell. With the mirror pointed at the horizon, these are located near the top and bottom edge of the mirror. They are attached to the back of the mirror and act horizontally.
During figuring and testing, slurry skirts, pressure seals and tangent rods were attached to the mirror to control contamination, allow pressurization of the inside of the mirror to prevent tool pressure-induced dimpling, and to constrain the mirror on its supports. It is believed that that one of the seals or skirts applied forces at one or more points along either the inside or outside edge of the mirror. Upon removal, the mirror relaxed and a small amount of astigmatism appeared. Testing by the optician2, after the slurry skirts, pressure seals and tangent rods were removed, indicated that the Zernike coefficient of surface astigmatism, R22 was approximately 230 nm (R22(r/r0)2cos2ø), i.e., four measurements of the mirror at three different angles relative to the axial supports ranged from 190 to 280 nm.
The calculations and measurements by the optician suggest that four forces with a magnitude of approximately 15 N equally spaced on the circumference alternating positive and negative will correct the measured astigmatism. I present calculations using the finite element method that extend these results.
In Astigmatism correction for the 2.5-m primary mirror: I. axial supports (SDSST Technical Note 19980805), rings of 12 actuators at two different radii were analysed. These rings are at approximately the same radii as the existing primary axial support pneumatic pistons. The results of that analysis suggested that attaching force actuators to the outer edge of the mirror might be effective. (Figure 1).
The finite element model is described in 2.5-m primary mirror transverse support system (SDSST Technical Note 19980713). One-quarter of the mirror was modeled. Symmetric boundary conditions were applied on the x=0 and y=0 planes. Forces given by the expression f = 10*cos2ø N were applied to the nodes corresponding to the green circles of the Figure.
Figure 1: CAD drawing showing the 2.5-m primary mirror and the locations of actuators (green circles) These actuators apply forces (10*cos2ø N) to correct astigmatism.
Figure 2: Surface deflection in meters calculated for astigmatism forces applied to the green circles shown in Figure 1. (The 9 colors in the legend do not correspond to the 9 colors in the plot. However, the maximum and minimum are annotated on the plot and the color order is green, yellow, red, orange, olive, turquoise, cyan, purple, magenta).
Figure 3: Residual surface deflection in meters for Figure 4 with astigmatism removed.
The results of the calculation is shown in Figures 2. The expression uz = a1 + a2*r2*cos(2ø) + a3*r2*sin(2ø) was fit to the results and the residual deflections at each node were calculated. These were plotted in Figures 3. The parameters for the astigmatism fit is given in Table 1. A coefficient (as defined in the Table) of 143 nm/m2 corresponds to the Zernike coefficient found by the optician. Consequently, a force amplitude of 11.0 N is required.
Table 1: Surface error fit parameters for astigmatism forces applied to the locations of Figure 1. pria11 uz = a1 + a2*r2*cos(2ø) + a3*r2*sin(2ø) i ai sigma 1 149.2 nm 0.161 nm 2 129.6 nm/m2 0.126 nm/m2 3 0.3 nm/m2 0.213 nm/m2 Initial error (RMS) 180 nm Residual error (RMS) 3.9 nm
pria11
uz = a1 + a2*r2*cos(2ø) + a3*r2*sin(2ø)
i
ai
sigma
1
149.2 nm
0.161 nm
2
129.6 nm/m2
0.126 nm/m2
3
0.3 nm/m2
0.213 nm/m2
Initial error (RMS)
180 nm
Residual error (RMS)
3.9 nm
The performance of actuators that apply astigmatism correcting forces to the outer edge of the 2.5-m primary mirror was examined. The force amplitude that is required is approximately 11.0 N to correct the astigmatism reported by the optician. The results are excellent. The resulting deformation departs from pure astigmatism by only 4.3 nm RMS.
1. W.A. Siegmund, E.J. Mannery, J. Radochia and P.E. Gillett, "Design of the Apache Point Observatory 3.5-m telescope II. deformation analysis of the primary mirror", Proc. S.P.I.E. 628, pp.377-389, 1986.
2. "Fabrication of the 2.5 m primary mirror for the Sloan Digital Sky Survey Telescope, Final report", Optical Sciences Center, University of Arizona, Nov. 4, 1997.
Date created: 8/25/98 Last modified: 8/25/98 Copyright © 1998, Walter A. Siegmund Walter A. Siegmund
