[Ifeffit] A basic question about data collection

[scalvin at slc.edu]

Hi all,

A basic question about EXAFS data collection strategies occurred to me
today, so I thought I'd see what you all think.

I was taught to collect data points spaced equally in k-space. The
argument given to me was that collecting data points spaced equally in
energy over-sampled at high-k, relative to low-k, since of course E ~ k^2.

But before analyzing my data (applying a FT or whatever), we generally
k-weight it.

So let's say we're in a situation where random noise is significant, and
suppose k-weight 1 gives a spectrum that is fairly uniform in amplitude
over the k-range we are planning to analyze. (I know there have been
various rationales put forth for using various k-weights, but that's not
the subject of this post...) If the noise is itself independent of k, then
that will mean our signal-to-noise ratio decreases with increasing k
(constant noise; signal decreases as 1/k). So it would seem reasonable to
me to correct for that by taking more data at high k than at low k. A
start in that direction would be to collect data spaced equally in energy,
although because Poisson noise falls off as the square root of the number
of counts, that's not enough to give a constant signal-to-noise ratio even
for a k-weight of 1, and certainly not enough for k-weights of 2 or 3. But
at least it's closer than data that's evenly spaced in k.

I'm sure this is something those of you who work with dilute samples have
thought a lot about...I eagerly await your collective wisdom.

--Scott Calvin
Sarah Lawrence College