links to plots:
radial errors arrow plot and fractional change.
image of survey 2 radial errors.
error along each north/south column.
median and rms normal errors along a north/south column of targets.
of the target positions (survey2-survey1) vs position on dish.
of the target position motion vs position on dish.
change in the measurement errors vs position on the dish.
of radial error ratio Surv2/Surv1.
Results survey1 and survey2 (M_SUR1,M_SUR2)
All 38000 targets were measured on mar01 (M_SUR1).
After this the dish was adjusted. In oct-nov01 another set of pictures
were taken (M_SUR2). These were measured and analyzed by the vstars software
that came with the photogrametry equipment. The results became available
in oct03. Lynn baker then fit a sphere to the targets and came up with
a radial error for each target. For the plots below, I took the two
data sets and used only the common targets from both surveys (37752 common
The targets have an x,y,z position using the center
of the dish as the origin, x positive is east, y positive in north, and
z positive is up. There is an associated measurement error computed
by the vstars software. The two plots below show how the coordinate position
of individual targets moved between the first and second surveys.
The coordinate positions of the targets.. How they've
changed survey1 to survey2. (top)
Fig 1 (1mb). Motion
of the targets (survey2-survey1) vs position on dish. The top
plot is versus x (east,west), the middle plot is versus y (north,south),
and the bottom plot is versus z. For each plot the x,y,z differences are
plotted in color: deltaX black, deltaY red, deltaZ blue. To keep the size
of the file manageable i sorted the data by x,y,z smoothed by 5 and then
decimated by 5. This reduced the scatter in the data, but the trends remained.
The x coordinate of the targets moved by an average of 1.2 inches ramping
from +.5 inches to +2 inches as you move west to east.
Fig 2 (1.8mb). Magnitude
of the target position motion vs position on dish. This is the
fig 1 data combined to just plot the magnitude of the target motion sqrt(deltax^2+deltay^2
+deltaz^2). It has not been smoothed so the scatter is that of the original
Fig 3 (1.7mb). The
change in the measurement errors vs position on the dish. For each
target the measurement error ( SigMeas=sqrt(sigx^2+sigy^2+sigz^2))
was computed for survey 1 and survey 2. Then the difference in the measurement
error (sigMeasSurvey2 - sigMeasSurvey1) was plotted versus the x, y, and
z coordinate of the targets. For most of the data, the errors were smaller
on the second survey. The exceptions are points with z less than 10 feet
(za le 9 degrees) and 50 feet north of the center were the errors have
increased. This might be showing us the degradation of the targets with
The radial errors are the residuals from fitting a sphere
to all of the measured targets. The sign convention is: positive means
the target is too far from the center of curvature, negative is too close
to the center of curvature.
The normal errors (radial direction) of the targets. (top)
The color bar at the top extends from -5 mm (blue) thru 0 error (green)
to +5 mm (red). The black spots are missing targets. I interpolated
the x, y projected target positions onto a grid of 3,1.5 feet using
a tophat function with a radius of 3.4 feet. Some grid points have averaged
together more than 1 target. The blue spots in the lower right stand out.
They correspond to areas that were over corrected (see fig 5). The
red ring at a radius of 200 feet stands out clearly (the moat??). Some
of the red horizontal lines that go across the entire dish are probably
the new east west cables that were installed during the upgrade. They are
probably stretching causing them to sink lower.
Fig 4 (.4 mb). Survey2
radial errors arrow plot and fractional change. This only includes
data with radial errors gt than 2 mm. The top of the plot is north,
the left of the plot is west. There are many things coded in this plot:
You can see patches of black (+20,-10) where the correction was not enough.
There is also a circle on the right at za=20 where is wasn't corrected
enough (this may be above the moat). All of the arrows that point at -120
degrees (to the left) were turned the wrong way.
The length of the arrow is proportional to the error (2mm per division).
The arrows are clipped at 10 mm.
The angle of the arrow is computed from -Err2/Err1. 0 Degrees is
perfect, -60 degrees is no motion, + 60 degrees too far times 1, -120 is
turned the wrong way...
Color Red has not been corrected enough (also points to the left),
black has been corrected too much. Green is ge 10mm (and clipped) blue
is le 10mm (and clipped).
Fig 5 (.04mb) Histogram
of radial error ratio Surv2/Surv1 (.ps) (.pdf).This
is a histogram of the radial error Surv2/Surv1 using all the data.. The
y axis is fraction of all targets (rather than number of targets). The
histogram was binned to .02 mm. The jumps at -1,1,2 are flagged with what
they are caused by. I'm not sure why there is a jump at 0 (maybe this is
just a binning problem??). The histogram is centered at .1 so on
average the correction was not enough by about 10%.
Fig 6 (.2mb) Image of survey2 radial errors.The
image includes all the survey 2 points, not just the points common between
survey1 and survey2.
The panels are 3 by 6.25 feet and are mounted with the
long direction east-west. Targets are positioned at the corner of
each target. As you look down on the dish, the targets make columns running
north/south spaced every 6.25 feet (161 columns in total). Every
25 feet a column of targets sits atop of one of the main support cables.
Normal errors moving along the north/south cable direction.
I arranged the targets in columns of constant X
by sorting the 38000 targets in X (east/west) and then I found
the locations where they jumped by 6.25 feet. Each of these columns
was then sorted in Y (north/south).
Fig 7 This shows the
normal error along each north/south column (.ps) (.pdf).The
first plot is the west half of the dish while the second plot is the east
half. Up is north and down is south. The lines are targets. Deflections
left/right on the line are proportional to the normal errors. To the right
implies the target is too low (the dish is sagging) to the left has the
target too high. A deflection that equals the separation of two lines is
6.25 mm (each tick would be a normal error of 10 mm). The blue lines sit
atop the main cables. The red lines are the target columns between the
main cables. This plot will show the larger errors. Errors less than a
few mm will not be apparent.
In general you can see that the targets over the main cables have much
less scatter than the intercable targets.
Some patches have an oscillation on the intercable targets low,hi,low,hi
as you move along Y. The adjacent cable targets do not show this.
The horizontal lines that point to the right (too low) are where new east,west
cables have been installed. They must be relaxing. The targets over the
main cables do not show this. At this point there should be a strong scalloping
on the dish.
You can see some bad spots at X=100, y=50To100 where both the main cable
and intercable targets are bad. This is where the cables cross the moat.
For reference, td4 is at (166,-96). I looked at this spot of the dish and
it looks like there are diagonal tieback cables that might block an adjustment
trolley from passing thru. Figure 4 showed that some of these points did
not change between survey 1 and survey2.
Fig 8 The
median and rms normal errors along a north/south column of targets (.ps)
After throwing out 3 outliers, I computed the median and rms of the normal
error along each of the north/south columns (see fig 7). The top plot is
the median of the normal error, the bottom plot is the rms of the normal
error along each north south column. There are 161 columns spaced 6.25
feet apart. Every 4th column there the targets are above a main cable.
The red * are above the main cables, the black * are in between the main
cables. The median value shows a sag of up to .6 mm between the support
cables. The rms (bottom plot) shows a larger variation as you move away
from the column over the main cables (up to 2mm rms along the center column
between two main cables). The west half of the dish shows a large variation
of the rms than the east half. It also has a lower rms along the main cables
than the east half. The large rms's around 50-100 feet are from the
bad points at y=-150 to -200 in y.