Reduction of Far Field Positions to BAT Coordinates
BAT Cal Memo 2003-05-28
28 May 2003
C. Markwardt
Reduction of Far Field Positions to BAT Coordinates
Summary
The BAT far field imaging test involves measuring the positions of a
rad source using both the BAT imaging system and a theodolite system,
at a distance of about 20 meters from the BAT detector plane. The
first step in analyzing the data is to reduce the data into the
BAT_X/Y/Z coordinate system, which I perform in this memo.
Coarse grid position variance (rms):
e(BAT_X) = 0.025 cm e(BAT_Y) = 0.013 cm e(BAT_Z) = 0.012 cm
Introduction
The BAT far field imaging test is an extension of the Coarse Grid
imaging test (see BAT Cal Memo
2003-03-10), where a radioactive source was placed approximately 3
meters from the detector plane. In the far field test, the
radioactive source was placed at roughly 20 meters from the BAT
detector plane.
The far field test was done by suspending (in most cases) a Ba-133
source from the Building 7 crane, at various positions above the BAT
array, which was removed from the tent for the test. Co-57 and Cd-109
were also used.
This memo produces the positions of the rad source for each test,
expressed in BAT coordinates.
Techniques
The technique used here is basically the same as described for the
Coarse Grid test.
The theodolite system was used to measure the positions of the rad
source for each run. The theodolite was also used to measure the
positions of various "control" points. There were two kinds of
control points. The first were scale bar measurements, consisting of
two fiducial points at the end of a fixed length bar. The bar was
moved to several different positions and measured; this provides
enough information to the theodolite software to generate an
(arbitrary) coordinate system.
The second set of measurements were of the mask fiducial locations.
See BAT Cal Memo 2003-03-10 for the locations of these positions.
I found that using the scale bar measurements alone were not
sufficient to generate a valid coordinate system. There were
noticeable problems in the physical coordinate scale, specifically
that the spacing between mask fiducials was not correct.
Ultimately, I opted to insert into the theodolite software, all pairs
of mask fiducial spacings. This is equivalent to specifying the exact
positions of the fiducials, except for a translation and rotation, and
this constrained the coordinate system to have a proper scale. [
Scale bar measurements 1,3,4 and 5 were also included in the
coordinate "bundling" operation. Scale bar measurement 2 had
excessive variance and was excluded. ]
Once this was achieved, then the procedure was the same as for the
Coarse grid, namely finding a best-fit rotation and translation which
brings the (arbitrary) theodolite coordinates into the BAT-centric
coordinate system.
I determined the measurement error iteratively, first by making a fit,
then examining the residual variance in each dimension, and then
assigning appropriate error bars. The results are:
Far Field Test
e(BAT_X) = 0.025 cm e(BAT_Y) = 0.013 cm e(BAT_Z) = 0.012 cm
e(THE_X) = 0.010 in e(THE_Y) = 0.005 in e(THE_Z) = 0.005 in
The second triplet gives the assigned errors in the theodolite
coordinate system, and the first gives an equivalent error in the BAT
coordinate system. Surprisingly, the error budget is competitive with
the coarse grid test. I believe this is because the theodolite
viewing angles of the BAT instrument were better (i.e. more
orthogonal).
The best fit transformation parameters are (in inches and degrees):
Line 1 X Transl. Y Translate Z translate Z Euler Ang Y Euler Ang X Euler Ang
Line 2 Error of " Error in " Error in " Error in " Error in " Error in "
Far Field Test
-2859.1435 -445.90788 465.50082 139.97430 -52.822134 126.10537
0.040687239 0.10905707 0.23050174 0.0014845567 0.0022728765 0.0029411910
With a chi-square of 52 and 48 degrees of freedom. The uncertainties
in the Z translation are ~0.6 cm, which corresponds to about 1
arcminute at 20 meters. Thus, the maximum errors are just within my
desired tolerances of about 1 arcmin.
The coverage of the far field points is shown in Figure 1:
Figure 1. Far field image test coverage map. The coordinates are
tangent-plane image coordinates, i.e. BAT_X/BAT_Z and BAT_Y/BAT_Z.
Revisions
02 Jun 2003 - Added coverage map
Appendix 1. Far Field Target Positions
Name BAT_X BAT_Y BAT_Z e(BAT_X _Y _Z)
FARFIELD::CO57_04APR03_0_0_A 38.0829 147.2606 1928.2105 0.0251 0.0133 0.0127
FARFIELD::CO57_04APR03_0_0_B 38.1365 147.2355 1928.2414 0.0251 0.0133 0.0127
FARFIELD::CO57_04APR03_0_0_C 38.0375 147.2812 1928.1962 0.0251 0.0133 0.0127
FARFIELD::CO57_04APR03_0_0_D 38.0347 147.2513 1928.1969 0.0251 0.0133 0.0127
FARFIELD::BA133_04APR03_0_0_A 38.1569 147.3057 1928.3660 0.0251 0.0133 0.0127
FARFIELD::BA133_04APR03_0_0_B 38.1833 147.3503 1928.3602 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_5_0_A -32.9833 -376.5298 2021.0283 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_N25_0_A 29.4325 582.8553 1977.1840 0.0251 0.0133 0.0127
FARFIELD::CO57_05APR03_N25_0_A 29.5523 582.2803 1977.1279 0.0251 0.0133 0.0127
FARFIELD::CO57_05APR03_0_SOUTH_A 687.1414 145.5025 1927.7231 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_SOUTH_A 692.3122 145.5241 1927.6852 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_SOUTH_B 692.2799 145.5233 1927.6745 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_SOUTH_C 692.3452 145.5274 1927.7491 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_NORTH_A -533.4477 148.5630 1929.0381 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_NORTH_B -533.4473 148.5980 1929.0215 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_WAYSOUTH_A 1402.7955 -77.3545 1924.9962 0.0251 0.0133 0.0127
FARFIELD::BA133_05APR03_0_WAYSOUTH_B 1402.9234 -77.3637 1925.0715 0.0251 0.0133 0.0127
FARFIELD::CO57_05APR03_0_WAYSOUTH_A 1402.7115 -77.1543 1925.0145 0.0251 0.0133 0.0127
FARFIELD::CD109_05APR03_0_0_A 23.7332 -73.9115 1926.6634 0.0251 0.0133 0.0127
Appendix 2. IDL Procedures used in fitting:
XFORM3D - general 3-D transformation (download)
XFORMTHEO - full theodolite to BAT_X/Y/Z transformation (download)
QTCOMPOSE - see Markwardt IDL Page
QTVROT - see Markwardt IDL Page
Scripts used to reduce the actual data:
Far Field Test
;; Read reference positions (mask fiducials)
spawn, 'cat ff1345m_mask.txt | grep -v "//"', ref_str
ref_str = ref_str(where(strtrim(ref_str,2) NE ''))
refnamelen = 18
;; Read cal source positions (science runs)
spawn, 'cat ff1345m_cal.txt | grep -v "//"', dat_str
dat_str = dat_str(where(strtrim(dat_str,2) NE ''))
datnamelen = 36
;; Initial transformation parameters
p0 = [-2863d, -451d, 453d, 140d, -52d, 127d]
pos_err = [0.010d, 0.005d, 0.005d]
xformtheo, ref_str, dat_str, p0=p0, ptransform=ptransformff, $
dptransform=dptransformff, pos_err=pos_err, $
refpoints=refpointsff, datpoints=datpointsff, $
refnamelen=refnamelen, datnamelen=datnamelen, $
xyz_value=xyz, xyz_nom=xyz_nom, xyz_resid=xyz_resid, $
xyz_fit=xyz_fit, xyz_err=xyz_err, $
pcovar=pcovar, pstatus=pstatus
end
Data Files
ff1345_mask.txt - Mask targets only
ff1345_cal.txt - Science Cal targets only