The figures show the reflector and corrected tilt sensor data for the reflector positions.For each of the 60 reflector measurements, all tilt sensor points within 3 degrees az encoder and .05 degrees za encoder of reflector 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 not used since it was not within .05 degrees of the tilt sensor swing (at 19.5). The reflector 1az term was removed from the reflector data and the 1az term was removed from the tilt sensor data (it was close to 0 for the tilt sensors). A linear fit to za enc. was done to the differences: dif(i)= A0 + A1*za*(refl(i)-tilt(i)) for pitch and roll separately. The corrected tilt sensor data was then: tsCor(az,za)=ts(az,za) + ((A0)+A1*za) + refl1Azterm(az)
- Fig 1 is the pitch - (constant + linearTime) term for each swing over plotted. The 1 and 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 0-180 and then it decreases for az 180-360. There also appears to be a 3az*sin(za) term for az 0-180 (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=.0244 and b=.0033 degP/degza. Moving down the page has sin(az-ph) amplitude, sin(az-ph) phase, sin(3az-ph) amplitude, and sin(3az-ph) phase. Except for the constant term, there is not much za dependence. The constant term fit of a+b*za gives a=.0244. The 2-d fit had a constant term of .006. The difference is not surprising since there are 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 gives a y intercept of -.06 while the 2d fit had -.1 . The 3az roll amplitude drops by .005 degrees from 10 deg za out to za of 19.5.
Amplitude |
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Amplitude |
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Amplitude |
(deg) |
Amplitude |
(deg) |
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1. tiltSensor |
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2. Theod. (AO9 origin) |
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2b. theod. focus error (AO9 origin) |
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3. TheodEnc-PlatEnc (AO9 origin)
from az swings Gives platform offset dx=.2 east,2.2north(in) |
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(186)
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4. pointings errors:za,gcAz |
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5.Pitch,roll (Reflector origin)
Using center of reflector. |
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5b. focus error (reflector origin) |
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6.ReflectorEnc-platformEnc
platform is: dx:1.14 west,2.89 north(in) |
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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 |
hor offset reflector from AO9 | 1.34 inches east, .5inches south |
convert tiltSens to Theod: | tscorpitch=9.78055-.99616*za + tsrawPitch+reflPitch1Az
tscorRoll = .3522 -.02122*za + tsrawRoll + reflRoll1Az |
Residuals (refl-tiltsenCor) 47 pnts | pitch:.008, roll:.009 degrees |
2d-fit smoothing: | 1 degree az, .05 degrees za |
tiltsensor input data: 5450 points.
sample at 5hz |
za strips 2-19.5 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(refl - 2dfit) | pitch: .0055 degrees
roll : .0085 degrees. |
The main coefficints to the 2d fit are:
term | pitch | roll |
constant | 0.011280838 | -0.10467 |
Asin(az-ph) | A:0.02141,ph:73.0 | A:0.035,ph:156.8 |
Asin(3az-ph) | A:0.02168,ph:304.570 | A:0.04892,ph:133.993 |
To evaluate the 2d fit in idl:
@phil
@tsinit
prfit2dio,prfit2d
prfit2deval,azDeg[],zaDeg[],prfit2d,pitchCor,rollCor
pitchCor[],rollCor[] will be the pitch, roll errors in degrees
for the az,za positions.
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