Sloan Digital Sky Survey Telescope Technical Note 19950215-01
The very demanding goal of 50 milliarcseconds root-mean-square (mas RMS) for the astrometric precision of the Sloan Digital Sky Survey implies that focus and collimation motions of the secondary must be very smooth.
The Apache Point Observatory 3.5-m telescope secondary is a hot-gas-fusion borosilicate lightweight (25% of solid) mirror. The secondary is supported axially by three three-point whiffletrees, a total of nine points. The transverse support is provided by a linear bearing inside flex-pivot gimbal located at the center-of-gravity of the mirror, i.e., inside the mirror. Each axial whiffletree is driven by a linear actuator consisting of a 200 step/revolution motor, a 60:1 harmonic speed reducer and a 1.574 threads/mm (40 threads/inch) ground lead screw. The nominal displacement per step is 53 nm. Focus motion occurs when all three motors rotate equal amounts. Differential rotation provides tilt motions.
The Apache Point Observatory 3.5-m telescope secondary is a hot-gas-fusion borosilicate lightweight (25% of solid) mirror. The secondary is supported axially by three three-point whiffletrees, a total of nine points. The transverse support is provided by a linear bearing inside flex-pivot gimbal located at the center-of-gravity of the mirror, i.e., inside the mirror. Each axial whiffletree is driven by a linear actuator consisting of a 200 step/revolution motor, a 60:1 harmonic speed reducer and a 1.574 threads/mm (40 threads/inch) ground lead screw. The nominal linear step is 53 nm.
On January 18-21, 1995, motions of the secondary were measured by two electronic indicators located on a diameter about 10 mm from the outer diameter of the mirror back-plate (Figure 1). A typical result is shown in Figure 2. The mirror was moved in ten increments of 530 nm each (10 steps) away from the primary followed by 10 increments toward the primary. The increment size would be sufficient to correct a 0.5 micron blur, i.e., at the limit of detectability of a focus monitor. The differential motion across the 830 mm diameter of the mirror is 310 nm RMS. This amounts to 370 nrad RMS of mirror tilt or 24 mas RMS on the sky. (The effect on the sky is reduced by the back focal distance divided by the final focal length, i.e., 0.21 for the 3.5-m and 0.35 for the 2.5-m. There is an additional small correction because the secondary does not tilt about its vertex.)
Other tests included focusing in different increments and varying the rate of motion. Also, we moved actuators 1 and 2 (lower left and lower right viewed from the back) in opposite directions equal amounts. This motion should not cause the linear bearing at the center to translate. Consequently, friction in this bearing should not have any effect. Also, we made measurements with the indicators sensing the motion of the whiffletrees near actuators 1 and 2. Such measurements should be less sensitive to the effect of friction in the linear bearing, particularly if the stiffness of the whiffletrees was low. We found that friction in the linear bearing did not appear to have a significant effect.
Fig. 1. Mounting of an electronic indicator. The indicator is supported by a magnetic base attached to the secondary frame. The indicator contacts the back surface of the secondary near its edge. The three stepper-motor linear actuators are visible behind the mirror.
Fig. 2. Focus motion of the secondary. The outputs of two electronic indicators located on a diameter near the edge of the mirror are plotted. The mirror was moved ten 530 nm steps away from the primary followed by ten 530 nm steps toward the primary. The difference in motion across the diameter, i.e., tilt, was 310 nm RMS or 24 mas RMS referred to the sky.
About September 1994, the whiffletrees were replaced because measurements had indicated that their stiffness was low. Consequently, with the indicators located as shown in Figure 1, the rectangular tubing supporting the magnetic base was struck lightly with a clenched fist (Figure 3). The impulse was parallel to the secondary optical axis. Two such sets of data were obtained and analyzed. The power spectral density of the resulting data suggests that the secondary assembly is quite stiff with little power present below 18 Hz (Figure 4). The feature at 8 Hz is likely real but is either well damped or not efficiently excited by the impulse.
Fig. 3. Impulse response of the secondary assembly. The data are from the configuration shown in Figure 1. The secondary assembly was excited by lightly striking the tubular steel frame near the magnetic base with a clenched fist.
Fig. 4. Natural frequencies of the secondary assembly. The power spectral density of the data shown in Figure 3 is plotted (red). A second similar set of data was obtained and analyzed (blue).
The secondary tilt during focus motions will need to be reduced by a factor of 4 to 5 if it is not to limit the astrometric accuracy of the SDSS survey. Otherwise, it will be necessary to plan observations so that refocusing is not required. In the case of the 3.5-m telescope, the observed tilt has little impact. It will contribute negligible pointing error and image degradation.
We suspect that the performance of the linear actuators may be improved by changing the lubrication of the lead screw. Most lubricants become very viscous at low temperatures. The measurements reported above were performed at temperatures near 0¡C. Consequently, the friction between the nut and the lead screw may have been quite high. This, in combination with the compliance of the harmonic speed reducer, may degrade the performance of the actuator. We expect to change to a silicone lubricant with more constant viscosity over the temperature range and repeat these measurements.
The natural frequencies of the 3.5-m secondary assembly are of interest because it has been proposed to remove low frequency wavefront tilt and tracking errors by tilting the secondary using piezoelectric actuators that are mounted in series with the secondary lead-screw actuators. The bandwidth of this system will be limited by the presence of natural resonances. Our measurements indicate that these resonances are mostly above 18 Hz.
