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Date:         Wed, 2 Sep 1992 12:40:45 -0700
From:         "Patrick Brooks" <AZPAB@ASUACVAX.BITNET>
Subject:      Fiber Distribution Problem

To STAT-L folks:

I am not sure if I should title this "The Distribution for Hell"
or equivalently, "Somebodies Thesis"  :-) but here goes:
   -----------------------------

Do any of you have experience with characterizing distribution of
diameters using Electron Microscopy?  I am looking for
literature, people, software that would help us.  I will outline
the problem in more detail below.  I think this is a problem
encountered in other physical sciences and hopefully you all will
have some ideas.

1. A cross section of paper made of fibers (the fibers are
roughly .2 to 10 microns in size) is exposed to Electron
Microscopy.  Particles of filler are also included.  The
assumption is that any thing over 10 microns in size is filler
and ignored.

2. Two magnifications are used, 2000x and 4000x.  Photographs are
taken of the same region of sample.  However, due to the
magnification differences,  the particles "seen" are different.
There are 4 4000x photographs to 1 2000x photograph.  But when
you change magnification your "center" obviously changes.  There
is no way of making the 4000x region quadrant or known region of
the 2000x magnification.

3. A computer program has the ability to calculate the "minimum
diameter" for a closed edge that is completely in the view.
Incomplete edges of fibers, that are on the edge of the view, are
discarded.

3.1 PROBLEM TWIST: fibers are in different orientations.  Thus
the "minimum diameter" for each particle does not account for the
angle of a fiber presented to the view.  Fibers that are strait
on will look like circles.  Fibers at an angle will look like
eclipses.

4. Bins are formed for "minimum diameter" intervals.  There are
more bins at 4000x than at 2000x.  For a particular
magnification, the computer counts the number of "minimum
diameter" that fall into a bin.

4.1 WARM FUZZY: At 4000x accuracy/fuzzes is best between 0.2 and
about 3 microns.  With the warmest fuzzes being in the middle
;-).  At 2000x, fuzzy is from about 1 micron to about 10.

4.2 PROBLEM:  How can the data from the two magnifications be
combined to describe the distribution of fiber diameter?
4.3 PROBLEM:  How do you exclude by, by assumption, or include by
theory :-), the orientation and fuzzes?

5. BIG PROBLEM: Given some type of empirical distribution can be
found:
5.1 What is a good way to estimate central tendency, scale, and
shape?
5.2 How can repeated measures from the same sample be combined?
5.3 Can comparisons from different samples be made?

Thanks in advance

Pat B.

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Patrick Brooks                     | Of making many books there is no
Bitnet:   AZPAB@ASUACVAX           | end, and much study is a weariness
Internet: AZPAB@ACVAX.INRE.ASU.EDU | of the flesh.
                                   |   -Qoheleth
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