SDSS 2.5m telescope focal surface scale adjustment
Sloan Digital Sky Survey Telescope Technical Note
19971020
Steve Kent and Walter Siegmund
Contents
Introduction
The 2.5 m optics have the capability for piston motion of both the
primary and secondary mirrors. Thus it is possible to move the
primary and secondary simultaneously such that focus is maintained,
but the scale factor at the focal plane is changed. This allows
aluminum plug-plates, that have a much different coefficient of
thermal expansion than the borosilicate optics, to be predrilled and
used over a range of ambient temperatures.
What are the equations relating the mirror motions to each other
and to the scale factor? How much mirror motion is necessary to
compensate for the ambient temperature range over three months?
"Zoom equations" for the 2.5m telescope
Define the following quantities:
Z = Displacement of primary along the optical axis from some nominal
position in mm.
S = Displacement of secondary along the optical axis from some
nominal position in mm.
DF = fraction change in scale factor
M = magnification factor of the secondary
D2 = nominal distance of secondary mirror vertex from the prime focus
For the 2.5 m optical design, D2 = 1980.47 mm and M = 2.22.
The primary and secondary motions are related by the equation:
S = Z * M^2 / (1. + M^2) = 0.83*Z
The sense is that the primary and secondary both move towards or
away from the focal plane. The fractional change in scale is given
by
DF = ((M - 1) / (1. + M^2)) * (Z/D2) = Z / 9614
The sense is such that the scale factor increases (more arcsec/mm)
if the primary moves closer to the focal plane.
To good accuracy, these equations should work equally well for
both imaging and spectroscopy. They were tested by running ray traces
on the spectroscopic design.
Drilling plug-plates and adjusting the telescope
zoom
The plug-plates will be drilled for the mean temperature of the
month that they are expected to be used. Records are available of the
extreme maximum and minimum temperature of each month for Sunspot, NM
for a 20 year period from 1954 to 1974 ("A
Twenty-Year Summary of Sacramento Peak Weather: August 1954 Through
July 1974", Sloan Digital Sky Survey Telescope Technical Note
19970822). The mean temperature of each month is taken to be the mean
of the extreme high and extreme low for that month. Note: this
is not the normal definition of the mean temperature, but it is
appropriate since it minimizes the maximum departure that must be
accommodated. Subsequently, the average monthly mean was calculated
by averaging the monthly means month by month over the 20 year period
and plotted (Figure 1). It is this temperature, adjusted for the
daytime temperature swing, that will be used to drill plates.
The maximum positive and negative departures from the monthly mean
were calculated for each month over the 20 year period. Subsequently,
the 20-year extremes were found month by month by taking the most
extreme values of the monthly departures over the 20 year period.
These were plotted as well (Figure 1).
The results show that the most extreme departure from the monthly
mean (as defined above) occurs in January. It is due to the -23
°F record low in 1962. With this event removed from the data,
the largest range is 74 °F and occurs in April. For intervals
longer than a month, it is necessary to consider the time rate of
change of the monthly mean temperature (Figure 2). April and May have
gradients near 9 °F/month while October has a gradient of just
less than -9 °F/month. The largest three-month range occurs in
February-April and is 86 °F. The range for all year, still
removing the January 1962 record low, is 103 °F.
Figure 1: Mean temperatures and maximum
departures. The means of the extreme maximum and minimum temperatures
for each month are calculated. These are averaged month by month over
20 years and the result plotted. The maximum positive and negative
departures from the monthly mean for each month are also plotted. The
negative departure for January would be -38 °F if the record
1962 low temperature were deleted from the data.
Figure 2: Rate of change of the mean
temperature per month.
Since the plug-plates are not used during the daytime, the maximum
nighttime temperature is clearly more relevant than the maximum
temperature. Extreme maximum temperatures invariably occur during
clear days with strong solar heating. Consequently, it is quite
plausible that the maximum nighttime temperatures are 15 °F less
than the daytime high temperatures. Also, the mean temperature should
be reduced by about 8°F for plug-plate drilling (Table 1). With
this adjustment, the largest three-month range occurs in
February-April and is 71 °F. The range for all year, still
removing the January 1962 record low, is 88 °F.
The expansion coefficient for aluminum alloy 6061 is 24.3
microns/m-°C while that for borosilicate glass E6 is 2.8
microns/m-°C. The expansion coefficient difference is 21.5
microns/m-°C. Combining this number with the scale factor
equation from the previous section gives a coefficient of 0.207
mm/°C for primary motion. The primary motion range needed for
three months is 8.2 mm and for all year is 10.1 mm. The secondary
motion range needed for three months is 6.8 mm and for all year is
8.4 mm.
Table 1: Estimated mean monthly
nighttime temperatures. These are from the mean curve of Figure 1
reduced by 8 °F to adjust for the daytime temperature swing.
Plug-plates intended for use in the given month should be drilled
according to this table.
|
month
|
°F
|
°C
|
|
Jan
|
20.3
|
-6.5
|
|
Feb
|
21.7
|
-5.7
|
|
Mar
|
26.3
|
-3.2
|
|
Apr
|
35.1
|
1.7
|
|
May
|
43.9
|
6.6
|
|
Jun
|
53.1
|
11.7
|
|
Jul
|
55.1
|
12.8
|
|
Aug
|
52.4
|
11.3
|
|
Sep
|
46.5
|
8
|
|
Oct
|
37.8
|
3.2
|
|
Nov
|
27.8
|
-2.3
|
|
Dec
|
23.9
|
-4.5
|
Conclusions
For the primary mirror, the axial motion range needed to adjust
the focal surface scale to compensate for differential thermal
expansion between the optics and the plug-plates is 8.2 mm for the
worst case 3 month temperature range. It is 10.1 mm for the worst
case range over the entire year. The secondary motion range needed
for three months is 6.8 mm and for all year is 8.4 mm.
Additional motion range of the secondary is necessary to
compensate for telescope flexure (about 0.5 mm), differential
expansion of the truss and the optics (about 0.8 mm), and departures
from the nominal spacing during assembly (about 1 mm). The nominal
design range of both the primary and secondary is 13 mm and appears
to be more than adequate. Plug-plates intended for use in a
particular month should be drilled for the temperature given in Table
1.
Date created: 10/20/1997
Last modified: 10/20/1997
siegmund@astro.washington.edu