On 30 Mar 2009, at 18:18, James Holton wrote:
Phil Evans wrote:
The “corrected” sd(Ihl) is calculated in Scala for each observation
as
sd(Ihl)corrected = SdFac * sqrt{sd(I)**2 + SdB*Ihl*LP +
(SdAdd*Ihl)**2}
with the parameters SdFac, SdB & SdAdd determined by trying to make
the RMS normalised deviation Delta(hl) = (Ihl - Ih(avg))/
sd(Ihl)corrected = 1.0 for all intensity ranges (different
parameters for each run). If the sd estimates are correct, then the
distribution of Delta(hl) should have SD = 1.0, and this
“correction” tries to enforce this. This is more or less
equivalent to making the RMS scatter == average SD. However the
uncertainties in how best to estimate the real error do then
influence the reliability of the Mn(I/sd) statistic (see (ii) above)
Uhh... What is "LP"?
I had to look into the latest SCALA manual for that. ;)
Actually I need to correct this expression: I did have an LP (lLorentz-
Polarisation) factor in there for a while, but on further
consideration I decided to take it out again, so the current
expression is
sd(Ihl)corrected = SdFac * sqrt{sd(I)**2 + SdB*Ihl + (SdAdd*Ihl)**2}
Interesting that the manual says that SDB has "no obvious physical
meaning". I think it does!
What I have learned from simulation is that SDADD is basically the
quadrature sum of all the fractional errors in the experiment.
These are things like shutter jitter and beam flicker that change an
intensity by an amount that is proportional to the intensity. I. E.
things that introduce a "% error". One of these is the "ripple
noise" induced by the detector calibration errors. In fact, ripple
noise seems to be the dominant source of fractional error in PX (~3%).
yes I agree
A non-unity value of SDFAC actually implies an error in detector
gain. Took me a while to figure this out, but it turns out that if
you use the right value of GAIN in MOSFLM, then SDFAC will refine to
1.0. The problem is that MOSFLM encourages you to use the wrong
value of GAIN because the calculation of BGRATIO assumes that
adjacent pixels are statistically independent. That is, the point-
spread function (PSF) is not infinitely sharp. The PSF has the
effect of "averaging" the background and giving the pixels the
appearance of being less noisy than they actually are. For example,
consider a flood-field of 10,000 photons/pixel. On an ideal
detector, the rms deviation from average pixel value (rmsd) will be
100 photons, but if you apply a smoothing function to the image (a
PSF), you will get an rmsd of less than 100, giving the illusion
that the GAIN setting is too high. Unfortunately, this illusion
does not extent to sharp features such as spots, which will contain
the "real" amount of noise.
Yes
Now we come to SDB, which would represent noise that is proportional
to the square root of intensity. Photon-counting noise is one of
these! MOSFLM was supposed to estimate this for us, but Woops! We
used the wrong GAIN! What does that do? It makes you have to back-
calculate what the intensity on the detector was in photons, and
then update the error that way. I think this is exactly what you
are doing with SDB.
back calculating to the photon count was the reason I put in the LP
correction, to get back to the raw intensity, but then I realised that
the major effect of the Lorentz factor was to spread the spot over
more images, rather than increasing the counts on each image (for
reflections close to the rotation axis), so I took it out again.
Empirically, I put in SdB because you can't get a good fit with just
SdFac & SdAdd
You may be right
Phil
Let me know if I am guessing wrong about any of this.
-James
