[Ifeffit] continuous scan data

[Bruce Ravel]

Carlo said:

 >> However, mesuring for one second per point on, say, a 0.25 eV grid
 >> is similar in a counting statistics sense to two measurements of
 >> one second per point on a 0.5 eV grid.  That counting statistics
 >> improvement is not lost in the interpolation of chi(E) to chi(k).
 >>

 CS> I think that this last sentence is the answer that I was looking
 CS> for.  I wanted to know if the counting statistics improvement is
 CS> propagated in the transformation to k-space.  This is good since
 CS> it means that we do not have to write our own rebinning or
 CS> smoothing routines before handing the data off to athena and
 CS> ifeffit.

Hmm.... upon further reflection, I think that what I said is not
right.  Or, more specifically, it depends upon how the interpolation
is done and what the densities are of the starting and ending grids.

Suppose you are interpolating ONTO a 1eV grid FROM a 0.5 eV grid using
three-point interpolation.  Then every point you measure gets used to
determine points on the new grid.  However, if you do the same
interpolation ONTO a 1 eV grid FROM a 0.25 eV interpolation, then 1/2
of the points never get used to determine the new grid.  For any
polynomial interpolation, this argument will hold for any starting
grid that is sufficiently dense compared to the ending grid.

I had to reread what Numerical Recipes has to say about cubic spline
interpolation (i.e. Ifeffit's splint() function), but it too has this
problem of relative densities.  Because second derivatives of the
starting grid are computed, the splint makes better use of the denser
grid.  However, the splint may fail to use some of the information
provided in the chi(E) to chi(k) conversion -- particularly far above
the edge where the k-grid is very sparse compared to the E-grid.

As Matt said yesterday, Ifeffit uses a quadratic, i.e. three-point,
interpolation to make chi(k) from chi(E) (Source divers: See
src/lib/spline.f at line 364) onto a 0.05invAng grid (a hardwired
value set in consts.h).

Sorry I misled you yesterday.  But since the E-grid does not map
linearly onto the k-grid, you will need to think hard about how you
do any rebinning.  Whatever you come up with, you should let us know.
It may be something worth putting into either Athena or Ifeffit.

B

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