Theodolite survey of dome from ao9 monument (origin=Reflector)
The dome position was surveyed from the ao9 monument
on 9aug01 starting at about 10pm. This shows the data moving the origin
to the center of the reflector (1.34 in east of AO9, .69 in south). See
survey (AO9 origin) for the results relative to AO9. The dome was moved
through the following positions:
Differences between the encoder
and reflector az and za positions-->platform offset from reflector
a za strip from 2 to 19.6 degrees in 1 degree za steps at an azimuth of
242.87 degrees (pointing at tower 8).
a za strip from 19.6 to 1.09 degree in 1 degree za steps at an azimuth
of 302.87 degrees.
an azimuth swing from an azimuth of 242.87 to 602.87 degrees in 30 degree
steps. The dome was at 19.6 degrees za.
an azimuth swing from an azimuth of 602.87 to 242.87 degrees in 60 degree
steps with the dome at 10 degrees za.
The pitch, roll, and focus errors versus az and
Fitting the pitch, roll, and focus.
the encoder and reflector az and za positions-->platform offset from
The dome and azimuth were positioned using the az, za
encoders with no model corrections included. The theodolite vertical is
determined by gravity while the theodolite azimuth is arbitrary. To calibrate
the theodolite azimuth I used:
The average was done over the two azimuth swings and then the correction
was added to the theodolite azimuth encoder values. The theodolite
positions were then translated to the center of the reflector (offset .69
in south, 1.34 in east of AO9). The offset was measured using the photogrametry
data and a survey of some of the optical targets. The position
differences (reflector - encoder) are shown in the plots:
The azimuth rotates about the main bearing. The bearing is
offset relative to AO9 where the theodolite was positioned. AO9 is then
offset from the center of the reflector. The combined offsets create
a 1 azimuth term in the differences of the measured azimuth positions (reflector
- encoder). The difference was computed as ReflectorZa-encoderZa (and similar
for az values). The peak of the sine wave has the Reflector angle
greater than the encoder angle. For this to occur the distance from the
center of the reflector to the dome must be greater than the distance from
the main bearing to the dome. So the platform is displaced along the direction
of the peak. To compute the horizontal distance I generated a circle and
then offset by .01 inch steps from 0 to 5 inches. I then computed the differences
in the two circles. The offset distance corresponding to 123 arc seconds
was 3.09 inches. Projecting this along the phase direction of 339 degrees
gives the offsets of the platform relative to the reflector:
The first figure is the azimuth differences plotted versus za (top) and
azimuth (bottom). These are great circle azimuth (the difference has been
multiplied by the sine of the zenith angle). The bottom plot contains a
sin fit to the 1az term for both of the spins. The offset, amplitude, and
phase of the peak are printed.
The second figure plots the zenith angle differences versus za (top) and
azimuth (bottom). The bottom plot also contains a fit to the 1az terms
of the swings. The the amplitude for the az swing at 19.5 degrees is 114
asecs instead of the 122 asecs for the other 3 fits.
The platform offset relative to the reflector will create
a pointing error. The
raw pointing errors that were used to build model13 (jan02) do not
agree with the measured translation:
|radial offset of platform
||dx offset (east positive)
||dy offset (north positive)
|| -1.11 inches
|| 2.88 inches
The pointing error is the direction you must move the telescope to correct
for the pointing offset. It is 180 degrees from the actual motion. The
pointing errors agree a lot better with the offset of the platform relative
to just AO9.
|pointing error amplitude,phase
||offset error ampltidue,phase
|za: 98 asecs, 185 degrees
||za: 122 asecs, 339 degrees
|az: 98 asecs, 94 degrees
||az: 122 asecs, 249 degrees
The pitch, roll, and focus errors versus az and
The directions of the pitch, roll, and focus errors
are defined as:
positive pitch error: the uphill portion of the dome is to high (far from
positive roll error: looking uphill, the right side of the dome is too
low (close to the dish)
positive focus error: the dome is too far away from the reflector.
The plots show the
pitch, roll, focus errors:
Figure 1 top is the pitch, roll, focus errors versus za. Black is pitch,
red is roll, and green is focus. The vertical access is degrees for pitch
and roll, and inches/10 for focus (.1 == 1 inch). The zastrips and azimuth
spins are plotted with different symbols. The measured radius of
curvature for the reflector was used (869.781 feet).
Figure 1 bottom is the same errors plotted versus azimuth angle.
Figures 2-4 plot the absolute value of the pitch, roll, and
focus errors versus azimuth and zenith angle. You can see the two za strips
plus the two azimuth swings. For pitch and roll 1 tick mark is .03 degrees.
For focus 1 tick mark in .3 inches. The angle is set so that 180 degrees
from pointing up is 50% of the maximum error. The za values of 19.6 and
10 at azimuth of 242.87 were repeated three times (twice with the azimuth
spin and once with the za strip). The points 19.6 and 10 za at azimuth
of 302.87 were repeated twice. These pitch values vary by about 8% max.
The roll value lie on top of each other. The focus error varies by up to
The last figure shows the motion of the platform about 1256.35 feet as
measured by the distomats while the survey was being taken. The maximum
motion was .2 inches so using 1256.35 feet as the average value will not
create large errors.
Fitting the pitch, roll, and focus. (top..)
The pitch, roll, and focus measurements were fit to
a cubic in (za-10) degrees and 1,2, and 3 az terms in azimuth. The figures
This data will be used to connect the pitch and roll
centered on the reflector to the pitch and roll as measured by the tilt
sensors. We can get a complete sampling of az, za with the tilt sensors
to help us with the model. We use the the reflector based data to
remove any offsets that the tilt sensors have.
Figure 1 has the pitch data (black) and the fit (red).
Figure 2 is the roll data (black) and the fit (red). This fit is pretty
Figure 3 is the focus data (black) and the fit (red). A different
fit was used for focus. It used (za-10) for the za variable. It was 3rd
order in (za-10) for the za part. The az terms had 1a,3az and sin(za-10)*[cos(3az)+sin(3az)].
The last figure shows the azimuth terms of the fits (1az,2az,3az) as well
as the fit coefficients. The rms for the fits are: pitch .013 degrees,
roll .0085 degrees, and focus .13 inches. The 1az term of .028 degrees
for pitch may be from the horizontal offset of the platform. This
offset should not give a roll term so i don't know where the .035 deg 1az
roll term is coming from. When the tilt sensors were run on 04aug01 the
1az term was .003 for these tiedown positions. The 3az term for pitch and
roll is similar to what we measured back in feb00 and what the tilt sensor
measured in 04aug01. The fit to focus is what will be used to compute the
focus error over the entire dish (since the tilt sensors don't measure
processing: survey/010809/reducR/doit.pro for initial analysis.