Data was taken from AO9 (center of the dish) on day3 (24may18) starting around 11:15 . A 4 GHz bandwidth scan was done. The scan included the dish, ground screen, hills behind ground screen, below the dish (through the panel holes), and a few shots of the platform.

An uncalibrated data set was left for AO to play with. 11 .las files were provided:

Scan pattern

The scanner coordinate system was:

centered at ao9 (the center of the dish).

It was about .5 meters above the bottom of the dish

xyz coordinates

y was about 31 degrees west of north
x was about 31 degrees north of east
+z was vertical up

r,theta,phi(el)

r was distance in meters from the scanner
theta(az) was about the +z axis. CCW was positive
phi(el) was measured from z=0. positive was up

The first set of plots shows the scan pattern (.ps) (.pdf)

Page 1: entire scan

The range, azimuth, and elevation come from the scanner values.

the azimuth 0 was about 31 degrees west of north.

top: range vs time for the 2900 second scan

The data was smoothed to .333 seconds
The sample rate was 36108 smp/sec

To get this i used an az rate of 1deg/sec and then fit for az vs sample.

each step in range is a different elevation scan
the green vertical line is the edge of the dish (using max elevation= 17.53 degrees)
The dips in range are from the hf dipole antennas in the dish blocking the scanner view.

middle: azimuth angle vs time

There were 9 azimuth scans (the last 2 are off the dish).
The blue line is the area blown up on the 2nd page

bottom: the elevation angle vs time

The black line uses the raw scanner values
the red line offsets the scanner z value by .5 meters. This is close to the offset of the scanner base from the dish.
The averaging has smoothed the 4 degree nodding of the elevation.

Page 2: 360 deg azimuth strip with elevation around 9 degrees

there are 12e6 points in a strip. I plotted every 1000th point to keep the file size reasonable.
Top: range vs azimuth angle

the vertical smearing is from the 4 degree elevation nodding.
The range dropouts are where the scanner hits the 5 and 8 MHz hf dipoles. They stick up from the bottom of the dish.

2nd frame: azimuth vs sample

The red line is a linear fit to the azimuth vs sample
Page 3 is a blowup around the blue dashed line

3rd frame: azimuth - linear fit vs azimuth

You can see the deviation of the azimuth pattern from a linear swing.
There are sections that line up with where we hit the hf dipoles. Not sure why they should have offsets or different slopes?

bottom frame: elevation angle vs azimuth

You see the 4deg elevation nodding.

Page 3: .5 second blowup, full resolution (see blue line on page 2)

top: range vs time

the 63 to 98 meter nodding comes from the elevation moving 4 degrees by the scanner mirror.

middle: azimuth vs time

the azimuth is increasing.
On top of that, there is a sawtooth that increases and decreases with the elevation nodding.

It's not obvious why increasing the elevation (and range) should change the azimuth rate.. It may be from the laser offset from the center of azimuth rotation.

bottom: elevation vs time

there is a 4 degree up down motion (done by a mirror in the scanner).
It takes about 30 milliseconds to move the 4 degrees.

Scan Pattern summary:

9 azimuth scans of 360 degrees. The last two were off the dish
data points output at 36108 points/second
the azimuth rotation was 1 deg/second
the elevation was nodded by 4 degrees at 30ms/4deg
the elevation step between az strips was about 3.5 degrees.
Questions:

why does the azimuth fit show jumps after each hf dipole dropout?

processing: x101/blackmore/ao9_4g/plot_scanpat.pro

Filtering out points not on the dish

A number of recorded points did not come from reflections off the dish. They include:

The last 2 azimuth strips were the ground screen and above.
the hf dipoles block areas of the dish
the laser would occasionally see through the holes in the panels.

limiting in x,y,z and elevation:

A first attempt at limiting the points was to limit the x,y,z , and elevation of the data points:

AO9 is at the center of the dish. the scanner was about .5 meters above the bottom of the dish.
the dish is 305 meters across (at the top) so the max x,y values should be 305/2 =152.5 meters

I limited the x,y values to abs(x) abs(y) < 150 meters

The radius of curvature of the dish is 265.176 meters.
the zenith angle to the edge of the dish is 35.1 degrees.

this gives a maximum z elevation of 48.17 meters

zmax=Radius*(1 - cos(zaMaxtel)

this also constrains the maximum elevation to be 17.63 degrees

maxEl=atan((zmax - ao9ToDish)/xymax)

plotting z vs x, the curvature of the plot bottoms out around -.7 meters.

there were 105e6 points recorded.
after constraining x,y,z, and elevation, there remained 78.3 million points.

Median filtering:

We expect the x,y,z values to change slowly as we scan across the dish. Exceptions to this will occur if:

we hit something above the dish
the laser goes through one of the holes in a panel.

To remove sharp jumps:

A median filter of length 15 was used (15 samples is about .06 degrees in elevation nodding)
the filtered data was subtracted from the sample data
any points above or below a threshold were removed.
This was done for x,y,z, radius, azimuth, and elevation

The plots show an example of the median filtering (.ps) (.pdf)

20,000 points are displayed (starting around 1295 seconds into the dataset)
Page 1: x,y

top: x scanning
2nd: x scan - median(x,15)

the red lines show the clipping level = .1 meters

3rd: y scan
bottom: y - median(y,15).

clip level set at .1 meters

Page 2: z scan

top: z scan
2nd: z - median(z,15).

the red lines show the clipping level = .01 meters

Page 3: radius, azimuth

frame1,2: range and range - median(range,15)

the red lines show the clipping level = .1 meters

frame3,4: azimuth and azimuth - median(azimuth,15)

clipping level set at .02 degrees

Page 4: elevation

frame 1,2 : elevation and elevation - median(elevation ,15)

clipping level set at .02 degrees.

Filtering results

78.3 million points before filtering
76.2 million points after filtering

processing: x101/blackmore/ao9_4g/loaddata.pro, chkdata_distVsEl.pro

Plotting range vs elevation

A histogram was made of the measured elevation values (using .01 degree bin size). The reverse index output of the
histogram provided a list of all of the points in each bin.

The plot shows the histogram of elevation and range vs elevation (.ps) (.pdf)

Page 1: histogram of elevation

The red trace is the raw scanner data.

The elevation goes below 0deg since the .5 meter z offset is not included.

The black trace corrects for the .5 meters z offset of the scanner.
the blue lines show the overlap of the azimuth strips.

Page 2: Plotting range vs elevation

The expected range vs elevation from the center of the dish is:

R0=265.176 meters
expectedRange= R0 * sin(2*elevation)/cos(elevation)

black shows the distance averaged over each elevation bin
red uses the median value from each elevation bin
green is the expected radius.
Top frame: without the .5 meter z offset.

distances at low elevation are most affected by this

bottom frame: with the .5 meter z offset correction

the median values follows the expected value pretty well

Page 3: Expected Range - measured range

the green line is the average difference for each az strip
the red center line is the median difference for each az strip
the lowest and upper az strip probably still have a bunch of outliers

the mean doesn't follow the median.

For an azimuth strip, the difference is a function of the elevation nodding for each strip

for the 4 degree elevation nodding
start of 4 degree nod: measured value too low
end of 4 degree nod : measured value too high.

summary range vs elevation:

the error in the measured range changes as a function of the 4 degree nodding in elevation

At the bottom of the nod, the distance measured is too short
at the top of the nod, the distance measured is to long.

processing: x101/blackmore/ao9_4g/chkdata_distVsEl.pro

fitting the center and radius of sphere.

The primary reflector is supposed to have a radius of 870 feet (265.176 meter). A09 should be at the x,y center of the reflector. The base of A09 is about .5 meters above the bottom of the dish. The scanner was mounted on AO9.

A non-linear least squares fit was done to the filtered data points to find the center and radius of the sphere. The fitting function was:

4 parameters were fit for:

C[0] : x offset for center
C[1] : y offset for center
C[2]: z offset for center
C[3]: radius of sphere

The fitting function was:

0= C[3] - sqrt( (x -c[0])^2 + (y-c[1])^2 + (z - c[2])^2)

Two types of fits were done:

fit for all 4 parameters.

Iterate 3 times, each time throwing out points with error greater than .2 meters from the fit radius.

Fit for the center of the sphere.

Force the radius to be 265.176 meters.
Do the same iteration as above.

Results of the fit

**Results from Fitting for Sphere**
	iteration	Npnts	x offset (meters)		y offset (meters)		z offset (meters)		radius (meters)		data-fit (meters)	(Radius-Zoffset) Scanner Z offset from dish
	iteration	Npnts	value	sigma	value	sigma	value	sigma	value	sigma	sigma	meters
Fit all 4 parameters
	1	76177741	1.2445	.0005	1.3728	.0005	262.8752	.0022	263.2814	.0021	.5668	.406
	2	71291522	1.2472	.0006	1.3739	.0006	261.8788	.0023	262.4015	.0021	.0721	.523
	3	*70592209*	*1.2457*	*.0006*	*1.3723*	*.0006*	*261.8628*	*.0023*	*262.3871*	*.0022*	*.0692*	*.524*
Fit 3 parameters. radius fixed at 265.176m
	1	76177741	1.2403	.0006	1.3733	.0005	264.8558	.0001	265.1760	0.0000	.5763	.320
	2	42050976	1.2608	.0007	1.3976	.0007	264.8239	.0002			.1095	.352
	3	40547882	1.2669	.0007	1.4056	.0007	264.8160	.0002			.1032	.360

There is a large x,y offset from AO9 for the center of the sphere: x= 1.2 and y=1.4 meters

This is present with and without the fit for the radius.
The scanner x,y system is rotated about 31 degrees CW looking down the z axis
The 1.2,1.4 offset ends up pointing 10deg east of north..

This is probably from the southern part of the dish having a longer radius than normal.

The x,y 1 sigma errors are less then 1mm.
When including the radius in the fit

the fit radius is about 3 meters less than the expected value
the z and radius 1 sigma errors are 2mm.
the final fit included about 70 million pnts
The data-fit rms is about 7cm

With the fixed radius fit

the z 1 sigma error is less than 1 mm.
the data-fit rms is 10 cm
The final iteration included about 40million points
looking at the points used, almost all of the points from the last az strip (max elevation) have been excluded.

The scanner offset from the bottom of the dish

fitting all params: .52 meters
with fixed Radius: .36 meters
looking at the offset from the base of ao9 to the bottom of the dish looks greater than .5 meters.

To do:

Generate and fit a spherical data set.
change the radius of part of the sphere to see if we can come up with similar fit parameters.

processing:x101/blackmore/ao94g/chkdatafit.pro

Summary

7 azimuth strips were done covering the dish. Each separated by about 3.5 degrees
subtracting a linear fit to the azimuth values on an azstrip shows jumps in the residuals when passing by an HF dipole.
Excluding points outside of the x,y,z range of the dish reduced the number of points from 105million to 78 million
using a median filter and clipping the residuals at .2 meters reduces the points 78million to 76million.
Plotting the expected range - measured range showed:

the 4 deg elevation nodding gives non linear range results.
the range is too short at the start (min elevation) and too long at the end of the nodding (+4 deg)

fitting for the center and radius of the spherical dish showed:

a 1.2 meter x and 1.4 meter y offset of the center. After correcting for the scanner azimuth offset, this points about 10 degrees east of north. This is probably caused by the southern part of the dish being too low.
When including the radius in the fit, the best radius was about 3meters less than the expected value.

DAY 3 from AO9 4GHz bw

25may19

Intro