The figures show the theodolite and corrected tilt sensor data for the theodolite positions.For each of the 60 theodolite measurements, all tilt sensor points within 3 degrees az encoder and .05 degrees za encoder of theodolite point were averaged. 3 and .05 were chosen by trying all az distance < 5 deg and all za dist < 1 and using the pair that minimized the residuals. The az swing at 19.6 degrees was note used since it was not within .05 degrees of the tilt sensor swing (at 19.5). The theodolite 1az term was removed from the theodolite data and the 1az term was removed from the tilt sensor data. A linear fit to za enc. was done to the differences: dif(i)= A0 + A1*za*(theod(i)tilt(i)) for pitch and roll separately. The corrected tilt sensor data was then: tsCor(az,za)=ts(az,za) + ((A0)+A1*za) + theod1Azterm(az)
 Fig 1 is the pitch  (constant + linearTime) term for each swing over plotted. The 1 an 3 azimuth terms stick out.
 Fig 2 plots the roll for each azimuth swing. The dashed lines are the individual fits. The fit values are listed below.
 Fig 3 has the pitch residuals for each swing and the average at the bottom.
 Fig 4 plots the roll residuals for the individual swings and the average residual at the bottom. There is a strong 6az terms for az 0180 and then it decreases for az 180360. There also appears to be a 3az*sin(za) term for az 0180 (see fig 2 for the za to color mapping).
 Fig 5 plots the pitch coefficients versus za. The top plot has plots (c0 (a+b*za)) versus za. With a.0258 and b.0037 degP/degza. Moving down the page has sin(azph) amplitude, sin(azph) phase, sin(3azph) amplitude, and sin(3azph) phase. Except for the constant term, there is not much za dependence. The constant term fit of a+b*za gives a=.0258. The 2d fit had a constant term of .011. The is not surprising since the many za terms in the 2d fit can modify the y intercept.
 Fig 6 is the same plots for Roll. The fit to the constant term give a y intercept of .06 while the 2d fit had .1 . The 3az roll amplitude drops by .007 degrees from 10 deg za out to za of 19.5.
Amplitude 
(deg) 
Amplitude 
(deg) 
Amplitude 
(deg) 
Amplitude 
(deg) 

1. tiltSensor 








2. Theod. at AO9 








2b. theod. focus error 





3. TheodEncPlatEnc
from az swings Gives platform offset dx=.2 east,2.2north(in) 

(186)




4. pointings errors:za,gcAz 








5.Pitch,roll or dome
Using center of reflector. 








5b. reflector based focus error 





6.ReflectorEncplatformEnc
platform is: dx:1.14 west,2.89 north(in) 




A 1 azimuth term in pitch and roll can be caused
by tilting the platform. A horizontal translation of the platform can create
a 1 az term in pitch but should not affect the roll. This is because the
elevation rails are curved in the pitch direction but are flat in the roll
direction (spinning in azimuth or za does not change the roll angle of
the dome).
We have an inconsistancy. The pitch 1az term
is explained by a horizontal offset, but there is an identical roll error.
If both of these were caused by a platform tilt, then the tilt sensors
should have measured it. The tilt sensor data was taken on 04aug01 while
the survey was on 09aug01. Maybe the platform moved. Even if this is so,
the difference in encoder values shows that there is a horizontal
offset that should give a pitch error close to what we measure. So where
is the 1az roll error coming from ??
Some other values....
tilt sensor Floor offsets:  pitch:.141,roll:.672 degrees. 
hor offset platform from AO9  .2 inches east, 2.2 inches north 
Theod 1az term:  pitch: ampl:.021 deg, peak@az=196.64
Roll : ampl:.025 deg, peak@az=272.56 
tiltSens 1az term:  pitch: ampl:.002 deg, peak(not measured).
roll : ampl:.002 deg, peak(not measured). 
convert tiltSens to Theod:  tscorpitch=9.78186.99575*za + tsrawPitch+theodPitch1Az
tscorRoll = .3524 .02124*za + tsrawRoll + theodRoll1Az 
Residuals (TheodtiltsenCor) 47 pnts  pitch:.008, roll:.009 degrees 
2dfit smoothing:  1 degree az, .05 degrees za 
tiltsensor input data: 5450 points.
sample at 5hz 
za strips 219.5 at az:(62.87+60*n) n=0..4 at .01deg/sec,(down/up)
azwings at za=2,4,6..18,19.5 at .2 deg/sec 
residuals(tiltSenCor  2d fit)  pitch: .0052 degrees
roll : .0038 degrees. 
residuals(theod  2dfit)  pitch: .0054 degrees
roll : .0084 degrees. 
The main coefficints to the 2d fit are:
term  pitch  roll 
constant  0.011280838  0.10458930 
Asin(azph)  A:0.02141,ph:106.57  A:0.02479,ph:181.027 
Asin(3azph)  A:0.02168,ph:304.570  A:0.04892,ph:133.993 
To evaluate the 2d fit in idl:
@phil
@tsinit
prfit2dio,prfit2d,'/home/phil/idl/data/prAug01.coef',io='read'
prfit2deval,azDeg[],zaDeg[],prfit2d,pitchCor,rollCor
pitchCor[],rollCor[] will be the pitch, roll errors in degrees
for the az,za positions.
home_~phil