Sloan Digital Sky Survey Telescope Technical Note 19990112
The plug-plates for the Sloan Digital Sky Survey are drilled with the 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 normal to the telescope telecentric surface, i.e., the conical bundle of light-rays is aligned with the axis of the hole.
The deformation of the plug-plate by the drilling mandrel and the plug-plate cartridge causes radial distortion of the plate that must be anticipated by the computer numerical controlled (CNC) drilling program so that the end of each fiber optic is positioned correctly on the focal surface by the plug-plate. Since the fiber end is flush with the sky-facing side of the plug-plate, it is the distortion of this surface that is most relevant. Finite element models (FEM), drl42 and pl124, were used to calculate this distortion for drilling and in the cartridge respectively.
The radial displacement of the sky-side of the plug-plate model is plotted during drilling and when deformed by the plug-plate cartridge for use (Figure 1). Also plotted is the difference of the these data. This is the amount to be subtracted from the radius of the focal surface coordinates to get the drilling coordinates. Also shown are 5th order polynomial fits to the data.
To investigate the accuracy of the FEMs, mid-plate measurements of four plug-plates that were drilled using the drilling fixture and measured flat were examined. The distortion correction made by the CNC program generator (gcodes10.c) was backed out of the data. Then, the distortion calculated for the mid-plate during drilling (drl42, mean of the layers d3 and d4) was removed. The linear trends in these data are interpreted as primarily due to the effect of temperature changes between drilling and measurement. The departures from linearity indicate agreement with the non-linear model predictions to better than 5 microns.
Figure 1: Plug-plate distortion. The radial displacement of the sky-side of the plug-plate model is plotted during drilling (drl42) and when deformed by the plug-plate cartridge for use (pl124). Also plotted is the difference of the these data (pl124-drl42). This is the amount to be subtracted from the focal surface radius to get the drilling coordinates. Also shown are 5th order polynomial fits to the data. Figure 2: Comparison of measurements with model. The data plotted are mid-plate measurements of four plug-plates that were drilled using the drilling fixture and measured flat. The distortion correction made by the CNC program generator (g codes10.c) was backed out of the data. Then, the distortion calculated for the mid-plate during drilling (drl42, mean of d3 and d4) was removed. The linear fits represent the effect of temperature changes between drilling and measurement. The departures from linearity indicate agreement with the model to better than 5 microns.
Figure 2: Comparison of measurements with model. The data plotted are mid-plate measurements of four plug-plates that were drilled using the drilling fixture and measured flat. The distortion correction made by the CNC program generator (g codes10.c) was backed out of the data. Then, the distortion calculated for the mid-plate during drilling (drl42, mean of d3 and d4) was removed. The linear fits represent the effect of temperature changes between drilling and measurement. The departures from linearity indicate agreement with the model to better than 5 microns.
Finite element models were used to calculate the radial distortion of plug-plates as a result of out of plane distortion imposed by the drilling fixture and the plug-plate cartridge. This distortion is compensated by the computer numerical controlled (CNC) program generator using the polynomial fit "pl124-drl42" from Figure 1. The accuracy of the drilling distortion calculation was checked against measurements and found to be better than 5 microns. Since the image scale is 60 µm/arcsecond, accuracy at this level is more than adequate. It is consistent with the fiber positioning error budget of 5 µm 2D rms that has been established for this item (unpublished).
Date created: 1/12/99 Last modified: 10/30/01 Copyright © 1999,2001 Walter A. Siegmund Walter A. Siegmund
