Procedures of HEND data convolution for mapping of neutron Martian emission Workshop

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Procedures of HEND data convolution for mapping
of neutron Martian emissionWorkshopThe First
year of HEND operations on the NASA Odyssey Mars
OrbiterMoscow, RussiaMay 20-22, 2002
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• The signal detected by HEND consists of
• Flux of neutrons from Mars (this we need to know
  to build maps of Martian neutron flux)
• Flux of secondary neutrons generated in Odyssey
  by isotropic galactic cosmic rays (this we know
  and subtract from detected signal to determine 1)
• Flux of secondary neutrons generated in Odyssey
  by radiation from Mars (this we need to know, but
  at present stage this isnt determined value)

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The flux of secondary neutrons generated in
Odyssey by isotropic galactic cosmic rays is
determined during aerobraking phase of
mission. This value was defined as signal
obtained at big (gt 104 km) distances from Mars.
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The HEND have time resolution is 19.2 sec. During
this interval instrument accumulate counts for
all detectors, and only after end of interval
measured counts are write in spacecraft memory
and transmitted on Earth. This interval is called
frame. Accordingly, the signal from Mars in i
-th frame we define as
where Ni measured counts during i-th frame,
Bi counts of isotropic galactic cosmic
rays in i-th frame, ?Mars angular
radius of Mars as seen from Odyssey Ci
signal from Mars in i-th frame.
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Due to HEND placed on spacecraft with very
complex shape, some constructive elements and
instruments are between HEND and Mars. Here
shown a projection of HENDs field of view,
geometrical visible part of Mars (orange area),
spacecraft
shadow (violet area) and area limited by physical
neutron collimation in soil and atmosphere (blue
area). The Martian neutrons only from blue area
can be detected by HEND.
At present stage this effect not takes in to
account. But in future analyses it must be done.
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• Building the Map
• On the surface of planet we make a mesh with
  selected size of pixels. In each pixel we will
  independently accumulate counts and exposure
  time.
• We select a time interval, detector and set of
  channels to create map.

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• To minimize computing time we assume the
  trajectory projection during i-th time bin is
  well fitted by line.
• Moving through selected time interval we going
  from one frame to another. For each frame we
  determine the fractions ( k1, k2, , kn ) of the
  trajectory projection on Martian surface length
  corresponded this pixel

where li - length of a part of
trajectory projection which lay in i -th pixel,
L total length of trajectory
projection for current frame.
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• According this fractions ki for
  selected frames we accumulate counts and exposure
  time in all pixels on map

where Cj count in j-th frame,
tj duration of j-th frame,
kij fraction of j-th frame
length in i-th pixel, n
number of frames in selected time interval,
Ei total counts accumulated in
i-th pixel, Tiexposure
total exposure time for i-th pixel,
Fi average flux in i-th pixel.
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The map of fluxes is produces by ratio Fi . This
ratio is well determined, if Tiexposure enough
large (for example, Tiexposure gt 60 sec). The
maps for exposure time accumulated during Mapping
stage of the Mission from February 18 to May 16
(320 000 frames).
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Due to orbit of the 2001 Mars Odyssey have
inclination 86 where are two areas around North
and South poles with 250 km radii which
spacecraft dont cross. Therefore, using this
maps building procedure we will never fill polar
pixels of map if theirs size lt 4. So, in
future we need to develop new procedure, based on
reverse scattering of measured counts on
visible from spacecraft Martian surface.
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