BAT Imaging Performance
BAT Cal Memo 2003-06-03
03 Jun 2003
C. Markwardt & BAT Team
(extensively revised 09 Dec 2003)
BAT Imaging Performance
Summary
I report an in-depth analysis of the coarse and fine grid imaging
performance tests. The image plate scale is uniform, with deviations
only at the <1 arcmin scale. The BAT point spread function is also
quite uniform, with a FWHM of 20.7' +/- 1.6 and 21.9 +/- 0.3 arcmin
for the near and far field tests respectively, which are both
consistent with the theoretical expectation of 22.0 arcmin. Any
energy-dependent change to the focal length, for reasonable incident
continuum spectra, is expected to produce less than 1 arcmin shift in
the image centroid (at 45 deg off-axis; no shift on-axis).
Only small offsets and focal length changes were detected, which were
consistent with small translations (~1 mm) of the mask from our
understanding of its design position. After these corrections are
accounted for, the RMS position residuals are <0.92 arcmin in BAT_X
and <0.67 arcmin in BAT_Y. Remaining systematic offsets are less than
1 arcmin, and within the expected tolerances from the mechanical
misalignments and the errors inherent to the theodolite measuring
system used.
Introduction
The BAT imaging performance tests were composed of the "coarse grid"
(near field) and far field tests. Both tests involve placing a
radioactive source at various positions in the BAT field of view. The
source is imaged using the BAT imaging system, and also measured using
a theodolite system. The goal of the performance test is to compare
the positions derived from both systems, and determine the extent to
which they agree. Any disagreement can be folded back into the BAT
team knowledge of the instrument geometry so that future imaging tests
can be corrected. [ Specifically the BAT aperture file can be
corrected. ]
BAT Cal Memo 2003-03-10 and Memo 2003-05-28 outline the determination of the
source positions using the theodolite system. The next section
outlines how the BAT imaging positions were found.
BAT Near Field Imaging System Positions
The coarse grid raw data were combined into a detector plane image
(DPI) file, without regard to energy (i.e. full energy band image).
The detector images were deconvolved to form "sky" images using the
batfftimage tool,
batfftimage file.dpi file.img NONE detmask=file.mask2 maskoffx=0 \
maskoffy=-0.143 maskoffz=+0.2 bat_z=bat_z corrections=NONE
The maskoffx/y/z parameters are set so that the current offsets
embedded in the aperture file are nullified, which places the mask at
its "design" position. Corrections are turned off (of which
batfftimage only supports an autocollimation).
The bat_z position is set two different ways:
(a) a grid of bat_z positions was used, and the image centroid was
found in each one;
(b) the theodolite bat_z position was used, including an offset for
the size of rad source packaging.
In the first method, I was hoping to be able to solve for the bat_z
height of the rad source without using the theodolite system at all.
This actually worked pretty well, when the source was in the BAT fully
coded field of view, but was systematically off, sometimes drastically
so, when outside of the fully coded field of view. Ultimately, I used
the theodolite-derived height, and then solved for a source Z offset.
Once the image was computed, I used an IDL script called fitbatpeak.pro to locate the peak and find
its centroid. [ I also verified that the BAT pipeline tool
batcelldetect task produces very close results. ]
The resulting positions are presented in Appendix 1.
Imaging Corrections
Next, I examined the (imaged-theodolite) position vs. the theodolite
position. If the BAT geometry model were perfectly correct, this plot
should be a flat and zero. Figure 1 shows the actual results. A
transverse shift in the mask position, in either the BAT_X or BAT_Y
directions, will cause an additive offset in the image. A discrepancy
in the effective focal length (i.e. the detector to mask separation)
will lead to a magnification of the BAT images compared to the
theodolite positions. The residuals shown in Figure 1 show both
effects: a constant offset and a linear trend.
Figure 1. (Imaged-Theodolite) positions vs. the theodolite position.
Deviations from zero are apparently linear.
The residuals were fit with a simple model,
(image)_X = M_X*(theo)_X + B_X (eqn 1)
(image)_Y = M_Y*(theo)_Y + B_Y,
where M_X/Y are the linear magnification terms, and B_X/Y are the
additive offsets. The best fit coefficients are:
M B chi-square (30 dof)
------------------------------------------------------
X 1.00115 +/- 0.00009 0.0014 +/- 0.0001 22
Y 1.00098 +/- 0.00007 -0.0008 +/- 0.0001 83
Table 1. Linear fit with no cross terms
One thing I found was that the first seven measurements showed
significant non-statistical trends (see Figure 1, circular points).
As a test, I fitted a separate constant (B), but the same linear slope
(M), and found an even better fit. Now, the circular points of Figure
1 are shifted onto the major trend (Figure 2).
Figure 2. Same as Figure 1, but with independent additive offset for
first seven points.
Since there is spatial overlap in both X and Y with these first seven
points, I consider the discrepancy to be a problem in the measurement
of those points -- presumably a bumped theodolite -- and not a problem
with BAT imaging. The linear slope coefficients determined in either
case are consistent, and so I will use the values in Table 1.
The residuals after subtracting the best fit model are shown in Figure
3. The r.m.s. residuals in X are 0.72 arcmin, and in Y are 0.76
arcmin.
Figure 3. Residuals from best fit linear model, for X and Y.
In two dimensions, the residuals appear to be more or less
uncorrelated, as shown in Figure 4.
Figure 4. Residuals from best fit model, shown as 2D vectors.
I should note that I made rather strict cuts on the residuals in order
to exclude outliers. The linear fit can be quite sensitive to
outliers, so I took the approach of performing a gross fit, excluding
gross outliers, then refining the fit, etc. Eventually the filter was
within 1.7 arcmin of zero. The histograms of Figure 5 show that even
without these cuts, the residuals are highly clustered around 0, with
1 sigma widths of 0.92 arcmin in X and 0.67 arcmin in Y.
Figure 5. Histogram of residuals in X and Y, with no filtering.
I also attempted to fit more complicated models, such as adding a
cross term (X position dependent on Y), and quadratic dependence.
These did not appear to improve the fit significantly, and so they
were not persued further.
Far Field Analysis
The same analysis approach was used for the far field data. Positions
are shown in Appendix 1. A linear trend in the residuals was also
apparent, so I used the same model.
Figure 6. (Imaged-Theodolite) positions vs. the theodolite position
for the far field test. Again, linear deviations are apparent.
The resulting best fit model is:
M B chi-square (30 dof)
------------------------------------------------------
X 1.00057 +/- 0.00004 0.0010 +/- 0.0001 30
Y 1.00046 +/- 0.00007 -0.0008 +/- 0.0001 30
Table 2. Far Field - linear fit with no cross terms
The residuals are flat after subtracting this fit
Figure 7. Far field residuals from best fit linear model, for X and Y.
Computation of Mask Corrections
The slopes and offsets quoted in Tables 1 and 2 above can be used to
estimate the basic mask correction parameters, the translational
offsets from the nominal "design" position (see BAT Cal Memo 2003-02-14 for details on
the designed Z layout). In addition, the Z offset of the radioactive
source was considered a nuisance parameter, since its location with
the package was unknown.
Solving for these terms requires us to know how physical offsets in
the mask and source position would translate into the already-fitted
slope and offset parameters listed above.
Simple ray-tracing shows that
M = 1 + z/(z-h) * (dh/h - dz/z - t/(2*h)) (eqn 2)
B_X = - z/(z-h) * (dx/h)
B_Y = - z/(z-h) * (dy/h)
where t is the mask thickness. The various terms are:
dh/h - effect of error in mask height (focal length)
dz/z - effect of error in source height (nuisance)
t/(2*h) - autocollimation effect; effective focal length refers to
midplane of mask tiles
z/(z-h) - near-field correction factor, which tends to unity in the
far-field limit.
The M slope is considered to have the same model for both X and Y,
while the B_X/Y terms are fitted indpendently in each direction. The
dz/z term is ignored in the far-field limit, where it is irrelevant.
The near and far field data are required to be fitted simultaneously
in order to account for the z-dependence of the source height.
The solution, including both the near and far field data, is,
dh = 0.105 +/- 0.008 [cm] Shift in mask height in +BAT_Z direction
dx = -0.109 +/- 0.003 [cm] Shift in mask in +BAT_X direction
dy = 0.078 +/- 0.002 [cm] Shift in mask in +BAT_Y direction
dz = -0.149 +/- 0.030 [cm] Shift in BAT_Z position of coarse grid src
These parameters are included in the present BAT aperture files (as of
Dec 2003), as offsets from the "design" position. Generally speaking,
there are offsets of about one millimeter in each direction. While
the design tolerances of the BAT mechanical structure are tighter than
that, I consider it reasonable that (a) I did not fully account for
all the material in the bat layout (BAT
Cal Memo 2003-02-14) or (b) the instrument and/or electronics were
not built exactly to design. In either case, the offsets now permit
us to perform imaging to within 1 arcminute over almost the entire BAT
field of view.
A note regarding the best fit to eqn 2. The largest contributor is in
the X-offset term of the near field data, by about 1 arcminute, or
(although it is formally 5 "sigma"). Thus, while the statistical
uncertainties are of order 1 arcmin (1 sigma; see Fig. 5), there may
be a systematic offset, also of order 1 arcmin. This systematic
offset is well within tolerances, and certainly is not much larger
than the statistical uncertainties.
Error Budget
Here is an estimated error budget for the angular performance of the
BAT, based on limitations of the current measurements.
Source Offset Magn. Modeled (eqn 2)?
Theodololite Meas. Sys. ~0.5' - No
Mech. Alignment 0.3' - No
Autocollimation - 1' Yes
Mask-DAP Focal Length - <1' Yes
Height of Source - <0.5' Yes
The magnification column shows the expected offset at 45' off-axis.
The theodolite measurement system errors are based on the internal
consistency checks done by repeated shots of the same targets. (See
BAT Cal Memos related to reduction of theodolite coordinates). The
mechanical alignment error comes from measured rotational errors in
the BAT Mask-DAP determined by the mechanical group. The
autocollimation, focal length and source height terms are included in
equation 2, and therefore are not considered to be errors. Thus, the
expected systematic errors, based on the first two rows, are of order
0.6'.
Energy Dependence of Focal Length
Equation 2 above lists the focal length as a constant, h. In reality,
the absorption depth of the mask tiles and the detectors is a function
of energy. I estimated the absorption depths by using the NIST mass
absorption coefficients for CZT and lead. A CZT density of 5.9 g
cm^{-3} was assumed; these were divided by mass into their atomic
constituent partial densities, and this was then used in the
absorption equation. In the case where the absorption length exceeded
half of the tile/detector thickness, I assumed that the mean
absorption depth was the mid-plane. Figure 9 shows the effective
focal length for monoenergetic photons.
Figure 9. BAT focal length change with energy, for monoenergic
photons. The sense is always a focal length increase.
The focal length increases fairly dramatically up to 100 keV, where it
flattens at around 0.5 mm, due to both the mask and detectors becoming
optically thin. The absorption edges of lead and CZT cause a dip in
the function (i.e. reduction in focal length) between about 25 and 50
keV, but the focal length never shortens beyond the nominal value.
How does this affect the imaging performance? To see this effect, I
took a narrow-line source (2 keV width), folded it through the Monte
Carlo response matrix that we developed in 2001 (modulated version),
and estimated the mean angular displacement based on the mean focal
length change. For such a narrow line, one can almost directly read
the change from Figure 9. I show in Figure 10 this effect explicitly
for a source at 45 degrees off-axis. (of course, since it is a focal
length change, the effect is proportional to tan(theta)).
Figure 10. BAT centroid shift due to 2 keV gaussian incident spectrum,
for a source 45 deg from the instrument axis.
Clearly there can be shifts of up to 2 arcmin, which can be
significant, but still small compared to the PSF width (see below).
On the other hand, this is an extremely unrealistic spectrum. Most
astrophysical spectra are expected to be continua. To more accurately
model this, I sampled a grid of power law spectra, with photon indices
that ranged from 0 to 3, which covers the range expected. The results
are shown in Figure 11.
Figure 10. BAT centroid shift due to a range of incident power law
continuum spectra (or a source 45 deg from the instrument axis).
Clearly for all realistic spectra, up to a flat photon spectrum with a
photon index of 0, the systematic shifts are all less than 0.8 arcmin,
and much less for steeper spectra. This reduction in the amplitude is
a consequence of the reduced BAT sensitivity above 100 keV, where the
focal length effect is strongest. For bright, extremely hard, gamma
ray bursts, it may necessary to correct for the energy dependent focal
length effect, but even for very hard spectra, the correction is
smaller than 1 arcmin, and thus unlikely to be significant.
Uniformity of Point Source Imaging
I tested the uniformity of the BAT imaging by examining the imaged
peak width (gaussian sigma parameter). Each peak was fitted to a 2D
gaussian (symmetric) function, where the width of the peak was allowed
to vary. If there were significant distortions in the image with
off-axis angle, they would show up as trends in the gaussian sigma
value. Figure 8 shows that the peak widths are extremely stable, with
a mean value of 8.9 arcmin and an RMS value of 0.7 arcmin, with no
obvious trends over the field of view.
[ The gaussian function is fitted in tangent plane coordinates; the
widths plotted in Figure 8 are simply atan(tan_width). In reality,
off-axis PSF widths will scale as 1/(1 + tan^2(theta)) where theta is
the off-axis angle. ]
Figure 8. Coarse Grid Uniformity. The figure shows the fitted
gaussian sigma width of image peak, as a function of the BAT spatial
field of view. No trends are visible.
The measured gaussian sigma corresponds to a FWHM of 20.9 +/- 1.6
arcmin, where the error bar is based on the RMS. The expected value
based on coded mask theory is sqrt(wd^2 + wm^2) / h, or 22 arcmin,
where wd is the detector width (4.2 mm), wm is the mask tile width (5
mm) and h is the focal length (100 cm). Clearly, the measured value
is consistent with the theoretical expectations. The far field tests
show a PSF width of 21.9 +/- 0.3 arcmin (FWHM), also in reasonable
agreement with expectations.
Appendix 1. Raw Position Data
Coarse Grid Raw Positions
Filename refers to the file name of the calibration file containing
the detector plane image. Point refers to the theodolite point name.
"Theodolite Position" refers to the position of the radioactive source
as measured by the theodolite system. The Z offset from the packaging
has been included.
"Img Peak at THEO_Z" refers to the determination of the postion of the
image peak, at the measured theodolite Z position (plus an offset due
to the rad source package).
"Image Interpolation" refers to the determination of the position of
the radioactive source by image interpolation alone, without use of
the theodolite information at all. I do NOT recommend using
this set of positions, but it is interesting to see how well the coded
mask can determine all three dimensions of the position.
Filename Point Theodolite Position Img Peak at THEO_Z Image Interpolation
BAT_X BAT_Y BAT_Z BAT_X BAT_Y BAT_Z BAT_X BAT_Y BAT_Z
(cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm)
cg_x_ba133_030304_1.dpi CG1::CG01 40.74 16.56 304.66 40.91 16.28 304.66 40.91 16.28 304.65
cg_x_ba133_030304_2.dpi CG1::CG02 40.66 16.80 304.66 40.91 16.28 304.66 40.91 16.28 304.66
cg_x_ba133_030304_3.dpi CG1::CG02 40.66 16.80 304.66 40.88 16.52 304.66 105.39 42.59 785.53
cg_x_ba133_030304_4.dpi CG1::CG03 -54.77 8.01 304.35 -54.62 7.72 304.35 -54.59 7.72 304.22
cg_x_ba133_030304_5.dpi CG1::CG04 -143.12 10.09 304.74 -143.05 9.82 304.74 -143.00 9.81 304.65
cg_x_ba133_030304_7.dpi CG1::CG05 87.20 204.93 305.87 87.44 204.85 305.87 87.38 204.64 305.61
cg06_x_ba133_030304_8.dpi CG1::CG06 -29.44 207.51 305.53 -29.26 207.43 305.53 -29.24 207.17 305.19
cg07_x_ba133_030304_9.dpi CG1::CG07 -159.51 237.48 305.05 -159.57 237.42 305.05 -159.29 236.95 304.52
cg08_x_ba133_030304_10.dpi CG1::CG08 -238.78 9.52 304.49 -238.71 9.24 304.49 -238.70 9.24 304.49
cg09_x_ba133_030304_11.dpi CG1::CG09 -230.92 91.99 304.60 -230.76 91.82 304.60 -230.75 91.82 304.60
cg10_x_ba133_030304_12.dpi CG1::CG10 -222.07 170.15 305.07 -221.96 170.02 305.07 -221.86 169.93 304.93
cg11_x_ba133_030304_13.dpi CG1::CG11 -317.37 164.69 303.99 -317.34 164.68 303.99 -317.23 164.62 303.89
cg12_x_ba133_030304_14.dpi CG1::CG12 -309.23 88.93 304.54 -309.20 88.72 304.54 -309.33 88.75 304.66
cg13_x_ba133_030304_15.dpi CG1::CG13 -400.86 86.86 303.98 -400.91 86.66 303.98 -400.99 86.67 304.03
cg15_x_ba133_030304_17.dpi CG1::CG15 -303.79 9.91 304.63 -303.83 9.66 304.63 -303.93 9.66 304.72
cg16_x_ba133_030304_18.dpi CG1::CG16 -201.39 10.28 304.58 -201.21 9.99 304.58 -201.19 9.99 304.56
cg17_x_ba133_030304_19.dpi CG1::CG17 -121.20 3.88 304.97 -120.98 3.61 304.97 -120.95 3.61 304.91
cg18_x_ba133_030304_20.dpi CG1::CG18 -131.57 -73.55 304.50 -131.35 -73.75 304.50 -131.35 -73.75 304.51
cg19_x_ba133_030304_21.dpi CG1::CG19 -208.33 -66.68 303.98 -208.12 -66.88 303.98 -208.06 -66.86 303.89
cg20_x_ba133_030304_22.dpi CG1::CG20 -279.20 -54.23 304.46 -279.08 -54.57 304.46 -279.12 -54.58 304.50
cg21_x_ba133_030304_23.dpi CG1::CG21 -368.85 -56.56 304.28 -368.76 -56.90 304.28 -2041.99 -315.20 1684.22
cg22_x_ba133_030304_24.dpi CG1::CG22 -367.92 -140.93 304.40 -367.79 -141.30 304.40 -1603.07 -615.99 1326.05
cg23_x_ba133_030304_25.dpi CG1::CG23 -288.96 -145.88 303.99 -288.80 -146.24 303.99 -288.59 -146.13 303.80
cg24_x_ba133_030304_26.dpi CG1::CG24 -203.72 -148.97 303.91 -203.52 -149.35 303.91 -203.47 -149.31 303.84
cg25_x_ba133_030304_27.dpi CG1::CG25 -133.13 -153.78 304.51 -132.85 -154.15 304.51 -132.84 -154.13 304.48
cg26_x_ba133_030304_28.dpi CG1::CG26 -146.54 -246.94 303.87 18.52 25.87 303.87 -86.21 -122.03 -1434.43
cg27_x_ba133_030304_29.dpi CG1::CG27 -221.67 -232.61 303.40 -221.46 -232.94 303.40 5776.18 6078.28 -7923.41
cg28_x_ba133_030304_30.dpi CG1::CG28 -289.15 -235.94 303.34 -47.61 55.30 303.34 -203.19 235.80 1293.79
cg29_x_ba133_030304_31.dpi CG1::CG29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
cg30_x_ba133_030304_32.dpi CG1::CG30 -57.35 -247.57 303.87 -57.09 -248.04 303.87 -57.10 -248.09 303.92
cg31_x_ba133_030304_33.dpi CG1::CG31 -56.18 -171.73 304.22 -55.86 -172.03 304.22 -55.84 -171.95 304.09
cg33_x_ba133_030304_35.dpi CG1::CG33 -55.16 -56.78 304.54 -54.93 -56.98 304.54 -54.93 -56.97 304.51
cg34_x_ba133_030304_36.dpi CG1::CG34 -93.31 -29.19 304.43 -92.85 -29.51 304.43 -92.88 -29.52 304.52
cg35_x_ba133_030304_37.dpi CG1::CG35 -78.73 56.31 305.13 -77.08 56.99 305.13 -77.03 56.95 304.93
cg36_x_ba133_030304_38.dpi CG1::CG36 -151.96 50.00 304.86 -151.73 49.83 304.86 -151.72 49.83 304.85
cg37_x_ba133_030304_39.dpi CG1::CG37 -229.33 61.87 304.73 -229.07 61.70 304.73 -229.10 61.71 304.77
cg38_x_ba133_030304_40.dpi CG1::CG38 -202.22 108.18 304.31 -201.99 107.99 304.31 -201.91 107.95 304.19
cg39_x_ba133_030304_41.dpi CG1::CG39 -211.99 -28.37 304.56 -212.07 -28.64 304.56 -212.00 -28.63 304.46
cg_x_ba133_200_21_030306_1.dpi CG2::CG01 385.23 -35.93 414.35 386.40 -36.20 414.35 386.21 -36.18 414.16
cg_x_ba133_200_21_030306_2.dpi CG2::CG02 377.94 -122.93 412.66 378.97 -123.30 412.66 2374.71 -772.62 2585.29
cg_x_ba133_200_21_030306_3.dpi CG2::CG03 171.41 234.42 408.17 171.92 234.24 408.17 172.00 234.36 408.36
cg_x_ba133_200_21_030306_4.dpi CG2::CG04 -68.55 -282.33 397.14 -67.97 -283.15 397.14 -67.94 -283.02 396.98
cg_x_ba133_200_21_030306_5.dpi CG2::CG05 -210.86 -277.55 393.68 -210.74 -278.62 393.68 -210.78 -278.67 393.75
cg_x_ba133_200_21_030306_6.dpi CG2::CG06 165.29 -284.10 391.93 166.15 -284.85 391.93 165.94 -284.46 391.44
Far Field Raw Positions
The descriptions for these columns is the same, except that I do not
include the "Image Interpolation" position.
Filename Point Theodolite Position Img Peak at THEO_Z
BAT_X BAT_Y BAT_Z BAT_X BAT_Y BAT_Z
(cm) (cm) (cm) (cm) (cm) (cm)
arr_x_co57_200_21_0_0_030404_1.dpi FARFIELD::CO57_04APR03_0_0 38.07 147.26 1928.53 40.20 145.82 1928.53
arr_x_ba133_200_21_0_0_030405_1.dpi FARFIELD::BA133_04APR03_0_0 38.17 147.33 1928.68 40.20 145.80 1928.68
arr_x_ba133_200_21_0_0_030405_2.dpi FARFIELD::BA133_04APR03_0_0 38.17 147.33 1928.68 40.21 145.80 1928.68
arr_x_ba133_200_21_0_0_030405_3.dpi FARFIELD::BA133_04APR03_0_0 38.17 147.33 1928.68 40.22 145.81 1928.68
arr_x_ba133_200_21_0_0_030405_4.dpi FARFIELD::BA133_04APR03_0_0 38.17 147.33 1928.68 -29.43 -360.89 1928.68
arr_x_ba133_200_21_0_0_030405_5.dpi FARFIELD::BA133_04APR03_5_0 0.00 0.00 0.00 0.00 0.00 0.00
arr_x_ba133_200_21_0_0_030405_6.dpi FARFIELD::BA133_05APR03_N25_0 29.43 582.86 1977.50 31.40 581.56 1977.50
arr_x_co57_200_21_n25_0_030405_6.dpi FARFIELD::CO57_05APR03_N25_0 29.55 582.28 1977.44 31.72 581.14 1977.44
arr_x_co57_200_21_n25_0_030405_9.dpi FARFIELD::CO57_05APR03_0_SOUTH 687.14 145.50 1928.04 689.75 144.22 1928.04
arr_x_ba133_200_21_0_south_030405_10.dpi FARFIELD::BA133_05APR03_0_SOUTH 692.31 145.52 1928.02 694.60 144.18 1928.02
arr_x_ba133_200_21_0_north_030405_12.dpi FARFIELD::BA133_05APR03_0_NORTH -533.45 148.58 1929.35 -531.77 147.10 1929.35
arr_x_ba133_200_21_0_south45_030405_13.dpi FARFIELD::BA133_05APR03_0_WAYSOUTH 1402.86 -77.36 1925.35 1405.26 -78.72 1925.35
arr_x_co57_200_21_0_south45_030405_14.dpi FARFIELD::CO57_05APR03_0_WAYSOUTH 1402.71 -77.15 1925.33 1405.72 -78.57 1925.33
arr_x_cd109_200_21_0_0_030405_15.dpi FARFIELD::CD109_05APR03_0_0 23.73 -73.91 1926.98 25.37 -75.49 1926.98
arr_x_cd109_200_21_0_0_030405_16.dpi FARFIELD::CD109_05APR03_0_0 23.73 -73.91 1926.98 25.37 -75.51 1926.98