From: Arthur Rowe IMAP <arthur.rowe@nottingham.ac.uk>
  To  : tom.laue@unh.edu
  Date: Tue, 07 Aug 2001 12:27:29 +0000

Re: wiggles in dc/dt plots

Hi Tom (and all other RASMB folks) -

Yes, as Neil Errington has contributed, we see these 'wiggles' just as
others do. Your view that:
"3- The Fourier analysis of the fringe patter can result in oscillations in
> the reduced data."
. . . . . . . . . .. . strikes a considerable chord with me - and I guess
you know what I am going to say !  However, perhaps you will forgive me for
saying it just one more time.

The BCI software for the XL-I interprets the interference pattern by fitting
the (sinusoidal varying) data set of intensities in the 'vertical' direction
at given r to a simple wave function, which yields an estimate for the phase
angle - and hence for the fringe increment at that r. The 'wavelength' (i.e.
fringe spacing) being a fixed parameter. All nice and simple - it derives
from the old DeRosier algorithm of the 1960's, although whether it uses the
particular strategies of DeRosier for coping with the envelope function I do
not know.

The problem with this approach - and this has been a commonplace in the
fringe analysis world since the 70/80's - is that from simple theory one
knows that it must introduce into the estimated phase angle an error which
which is cyclical in nature - that is, the precision in the retrieved phase
angle will vary with the absolute value of the phase angle. Hence people
have long ago moved on to using 'phase stepping' or similar methods, in
which the error in the retrieved parameter is *not* dependent on the
argument. This issue is discussed, and a simple, stable algorithm which
avoids such problems - and works well with AUC interference patterns - has
been published (1,2). OK - there are fancier routines than ours for doing it
these days, but the basic point which I am making is one which has been
presented to fringe analysis professionals both at meetings and by peer
group review, and neither there nor anywhere else has the basic point been
disputed.

However - I think you will agree, Tom, that it's not been taken on board so
far as AUC interference is concerned. My impression is that people think
that 'this is an effect which is real, but does  not matter at the level of
fringe definition (a few times 10^-3 fringes at best) found in AUC work, for
which the simple phase extraction algorithm is adequate'. Well maybe, but:

(i) the XL-I camera gives you a pretty sparse data set, which is always bad
news for any fitting algorithm

(ii) g(s*) procedures, depending upon the *derivative* of the data, put a
much heavier strain on the data quality. Potentially even a small cyclical
noise component would be amplified greatly by derivitisation. Local data
sets (thanks, Neil !) show that the 'wiggles' require a cyclical component
which can be some 2+ orders of magnitude *below* the fringe resolution
quoted above to explain them.

So, could the BCI fringe-fitting algorithm be the cause (or at least a
cause) of the 'wiggles' ? Consistent with this hypothesis we note that the
local 'wavelength' of the 'wiggles' is positively correlated with the
steepness of the fringe gradient. Less consistently, the effect in a given
rotor can vary from cell to cell. So I make a suggestion, rather than a
final diagnosis  . . .

Arthur
--
*******************************************************
Arthur J Rowe
Professor of Biomolecular Technology
NCMH Business Centre
University of Nottingham
School of Biosciences
Sutton Bonington
Leicestershire LE12 5RD   UK

Tel:        +44 (0)115 951 6156
             +44 (0)116 271 4502
Fax:        +44 (0)115 951 6157
email:      arthur.rowe@nottingham.ac.uk
             arthur.rowe@connectfree.co.uk (home)
Web:        www.nottingham.ac.uk/ncmh/business
*******************************************************


> From: "Tom Laue" <tom.laue@unh.edu>
> Reply-To: <tom.laue@unh.edu>
> Date: Mon, 6 Aug 2001 09:38:13 -0400
> To: "Neil Errington" <neil.errington@nottingham.ac.uk>,
> <Gunther.Kern@astrazeneca.com>, <rasmb@alpha.bbri.org>
> Subject: RE: wiggles in dc/dt plots
> 
> Hi Folks,
> The wiggles referred to can come from a couple of sources.
> 1- Jitter in timing the laser pulse: there was a firmware problem in setting
> up the timing of the laser pulse. The software loop to do this required ~1.5
> milliseconds, which is longer than the period of rotation at high rotor
> speeds, and caused problems in data collected at rotor speeds above ~55,000
> rpm. There was a firmware fix released about 18 months ago that fixed this
> problem. Be sure you have the most recent version of the EPROMs in the XLI.
> 2- There is an outstanding issue with the heaters and baseplate flexing that
> David Yphantis and Jeff Lary have documented. This problem is likely due to
> the mounting of this lens to the baseplate... a problem stemming from my
> design. The problem was reported to BCI four years ago, and I have been told
> that BCI has a possible fix. To my knowledge the fix hasn't seen the light
> of day. A related problem is caused by thermal gradients across this lens,
> resulting in a 'twisting' of the fringe image. The fix from BCI should help
> this problem, too. The magnitude of these fluctuations is about 0.01-0.1
> fringe, far worse than the intrinsic capabilities of the design (~0.0006
> fringe).
> 3- The Fourier analysis of the fringe patter can result in oscillations in
> the reduced data. The cause is a mismatch in the frequency of analysis and
> the spatial frequency of the fringes, and it leads to a periodic oscillation
> in concentration calculation. Typically, the magnitude of this oscillation
> is 0.003 fringe or so, though it can be worse if the image is not good (i.e.
> there is dust on the camera). This problem can be minimized by calibration
> of the pixels per fringe (available under the detail settings for the
> interference optics). An even better fix is to replace the camera with one
> containing more pixels in the vertical direction, though this adds a
> one-time cost of about $12,000. David Yphantis has shown that with a larger
> array, and elimination of the temperature fluctuations will result in at
> least a ~100-fold  improved precision. Are you interested in having the
> improvements available?
> Best wishes,
> Tom
> 
> University of New Hampshire
> Rudman 379
> 46 College Rd.
> Durham, NH 03824-3544
> Phone: 603-862-2459
> Fax: 603-862-0013
> 
> 
>