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Status report 85

		ROSAT Status Report #85
		    Feb 16th 1994


Off-axis Point Spread Function (PSF) for the ROSAT HRI
The  on-axis HRI  PSF  can be   described with two  gaussians plus  an
exponential (due to the HRI halo):

PSF = A1*exp(-0.5*(r/s1)**2) + A2*exp(-0.5*(r/s2)**2) + A3*exp(-r/s3)


s1 = 2.18   A1 = 0.96
s2 = 4.04   A2 = 0.18
s3 = 31.7   A3 = 0.00090

where r,  s1, s2,  and s3 are  in arc seconds.  The on-axis   PSF  was
determined from a long observation of HZ43 which produced  100,000 net
counts.  Analysis  of  a sample  of  point  sources   observed on-axis
(mostly  stars),  shows that  the  HRI PSF varies  from observation to
observation (due to residual  errors in  the aspect solution). Fitting
the above function form of the PSF to this sample shows that s1 varies
from 2.0 to  3.0 arc seconds, and  s2  varies  from  3.2   to  4.6 arc
seconds.  When  possible, the   user should use the image   of a known
point source within 5' of their target as a template for the HRI PSF.

We  recently derived  a parametric representation   of the azimuthally
averaged off-axis HRI  PSF which  is a  simple extension of  the above
expression.   To  determine the  off-axis    PSF we  generated surface
brightness profiles for 8 observations of HZ43, spanning a range of 2'
to 16' off-axis.  The peak surface brightness  was used as the origin,
since this generates a monotonically decreasing profile.  The set of 8
HZ43 surface  brightness profiles were first fit  to  the on-axis PSF,
treating the normalization and  width  of  the  two gaussians  as free
parameters (the photon  statistics in these  data were insufficient to
fit the exponential term).  We found that  the best  fit values of the
smaller gaussian were  essentially independent of  the angle off-axis.
We then refit  the set of  8 profiles  treating only the  width of the
broader gaussian as a free  parameter.  The best fit  values of s2 are
well  parameterized by a cubic polynomial   in the off-axis angle, and
are given by

     s2 = 3.3 + 0.019*theta -0.016*theta**2 + 0.0044*theta**3

where theta is the  angle off-axis in arc  minutes.  Substituting this
expression  into  the on-axis  HRI  PSF  gives the   general  off-axis
representation.  Note, however, that  we do  not force this expression
to  reproduce   the on-axis value  given  above.   The  fact that this
expression gives  s2 = 3.3 for theta=0,  compared to the on-axis value
of   4.0 given above, reflects the   variation in aspect  quality from
observation to observation given above.

Users should   note   that point  sources   observed  off-axis exhibit
significant amounts of nonazimuthal symmetry.  The above expression is
useful for determining  scattering corrections and  for  use in detect
algorithms, but should not be used for image deconvolution.  There are
a large number  of sequences in the  PROS calibration directory xrcal$
containing several objects observed at different angles off-axis.  The
actual   HRI data should    be   used for  any  two-dimensional  image

The information given above is  also  available within IRAF/PROS (type
"help prfroshri" - note a typo in the help file:  "A4" should be "s3")
and in the report "The ROSAT  High  Resolution Imager  (HRI)"  by L.P.
David, et  al.  (1993),  which  is available from  the  anonymous site
legacy.gsfc.nasa.gov and was distributed with the Solicitation for AO5
Observing Proposals.