From: Tom Laue <tom.laue@unh.edu>
  To  : Arthur Rowe IMAP <arthur.rowe@nottingham.ac.uk>
  Date: Tue, 7 Aug 2001 08:52:14 -0400

RE: wiggles in dc/dt plots

Hi Arthur,
You make a good point- with computers being faster, it is possible to use
more computer-intensive algorithms to extract the fringe displacement with
greater accuracy, and that concept should be re-examined. I am not familiar
with 'phase stepping' methods- do you mean the image analysis routines used
by electron microscopists to extract repetitive features from a noisy
signal? These algorithms are not well-suited to improving the accuracy of
the signal extracted from the interference signal where fixed flaws in the
image move relative to the fringes. However, you may have another scheme in
mind- would you mind sending me the citations?

For the examination of low concentrations, Fourier error is an insignificant
player in the problem described- its contributions to the noise will be
100-fold less than the other two problems listed.  For machines that are
installed properly, the frequency match between the signal and the Fourier
will be OK and won't need adjusting. Until the thermal problem and sparse
array problems are fixed, moshing around with the fringe extraction
algorithm is moot.

The sparse array problem has been discussed in detail by David Yphantis and
Jeff Lary, and can be a major source of noise. Their data show that a flaw
at a one or two adjacent pixels (e.g. a dust flake) will result in a
significant (0.01 fringe) phase-dependent error in the fringe determination.
I suspect that the 'local error' problems you allude to result from this
cause. Only a detailed algorithm that takes into account the position of
each flaw relative to the fringes (i.e. there would have to be ~24 cases for
the algorithm to sort through) would help. Furthermore the algorithm would
need to be updated frequently to take into account any changes in the image.
The best way to minimize this contribution is to have more pixels in the
vertical direction. Suitable cameras and computer interfaces are available-
the $12,000 I mentioned covers the cost of these. Installation, software
development, etc. would add to the cost. David and Jeff, and Walter Stafford
have constructed systems using large array cameras, and we are developing
one as well. I am certain that we would be happy to help anyone duplicate
our systems. Even with these cameras, though, the temperature problem needs
to be fixed before anything else.
Best wishes,
Tom



University of New Hampshire
Rudman 379
46 College Rd.
Durham, NH 03824-3544
Phone: 603-862-2459
Fax: 603-862-0013

-----Original Message-----
From: Arthur Rowe IMAP [arthur.rowe@nottingham.ac.uk]">mailto:arthur.rowe@nottingham.ac.uk]
Sent: Tuesday, August 07, 2001 8:27 AM
To: tom.laue@unh.edu; Neil Errington; Gunther.Kern@astrazeneca.com;
rasmb@alpha.bbri.org
Subject: 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
>
>
>