Plug-plate distortion
Sloan Digital Sky Survey Telescope Technical Note
19990112
Walter
Siegmund
Contents
Introduction
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.
Results
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.
Conclusions
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
siegmund@astro.washington.edu