Theodolite survey of dome from ao9 monument (origin=AO9)
The dome position was surveyed from the ao9 monument
on 9aug01 starting at about 10pm. This page shows the results using AO9
as the origin. See ao9
survery (reflector as origin) for the results relative to the center
of the reflector. The dome was moved through the following positions:
Differences between the encoder
and theodolite az and za positions-->platform offset from AO9.
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 theodolite az and za positions-->platform offset
from AO9. (top..)
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. The correction was then
added to the theodolite azimuth encoder values. The position
differences (theodolite - encoder) are shown in the plots:
The azimuth rotates about the main bearing. The bearing is
offset relative to the AO9 monument where the theodolite was positioned.
This offset causes a 1 azimuth term in the differences of the measured
azimuth positions. The difference was computed as TheodoliteZa-encoderZa
(and similar for az values). The peak of the sine wave has the theodolite
angle greater than the encoder angle. For this to occur the distance from
AO9 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 88 arc seconds was
2.23 inches. Projecting this along the phase direction of 6 degrees gives
the offsets of the platform relative to AO9:
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 80
asecs instead of the 88 for the other 3 fits. Looking at the fit, the peak
to peak excursion is closer to an amplitude of 88 asecs so the sine wave
probably got messed up a bit.
The platform offset will create a pointing error. The
raw pointing errors that were used to build model13 (jan02) agree with
the measured translation:
|radial offset of platform
||dx offset (east positive)
||dy offset (north positive)
|| .2 inches
|| 2.2 inches
The pointing error is the direction you must move the telescope to correct
for the pointing offset. It is 180 degrees from the direction of the motion
and the amplitudes are within 10%.
|pointing error amplitude,phase
||offset error ampltidue,phase
|za: 98 asecs, 185 degrees
||za: 88 asecs, 5 degrees
|az: 98 asecs, 94 degrees
||az: 88 asecs, 277 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.
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 so the platform was relatively
stable during the measurements.
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
The fit data will eventually be used to connect the
pitch and roll of the theodolite 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 theodolite data to remove any offsets
that the tilt sensors have.
Figure 1 has the pitch data (black) and the fit (red). The fit is good
except for the bump at za of 8 degrees, 1 degree, and za >= 19.
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 pitch fits are: pitch .013 degrees,
roll .0085 degrees, and focus .1 inches. The 1az term of .02 degrees
for pitch and roll may be from the horizontal offset of the platform. 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 focus).
processing: survey/010809/reduc/doit.pro for initial analysis.
Do some more tilt sensor azimuth swings to make sure that the platform
is not tilted. The tiedown encoders were changed back in sep01 (lightning)
and we should verify that the tiedowns were set back to the same values.