**Particle tracking using IDL -- John C. Crocker and
Eric R. Weeks** (this page written primarily by Brenton
Hoffman)

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## BACKGROUND:

The purpose of this program is to take the two point correlation
tensor data generated by
msd2pnt.pro
and turn it into distinct
mean squared displacements. These are analogous to normal mean
square displacement but are generated from correlated particle
motions. In a hypothetical system where tracer particles
are trapped in pores in an other wise homogeneous material,
the distinct mean square displacement could be thought of as
the msd the particle "should have" if the particles were
probing bulk mechanical properties. This code assumes that the
material being probe has a Poisson ratio of 0.5.

## REQUIRED INPUTS:

The code requires a two point correlation tensor from
msd2pnt.pro,
either as a filename or IDL variable and the particle separation
distances to be used as determined by the spatial behavior of
the two point correlation tensor (see
tutorial for msd2pnt.pro).
## OPTIONAL INPUTS:

**TMAX**: Maximum time to be used
**A**: approximate particle size
**LFIT**: Additionally the keyword lfit may be
set to use a linear fit to two point correlation tensor data.
This has the effect of only using the part of the correlation
data that decays as 1/r. The option should be used at the
user's discretion and only after 1/r decay has been confirmed
in the spatial behavior in the two point correlation tensor.
However, it does an excellent job of removing correlated
motions from non-continuum fluctuations (like stage vibrations).

## SAMPLE CALL:

**IDL> md=msdd(m2,2,8,a=0.5,tmax=1,/lfit) **

where m2 is a two point correlation tensor, the minimum and
maximum particle separation distances are 2 and 8 microns
respectively, the assumed particle size is 0.5 microns, a
maximum time of 1 second, and a linear fitting of the data
will be used.

## OUTPUT:

The program returns a data structure which is (6,number of
time points) where the
(0,*) column is the time points, in seconds
(1,*) column is the msdd generated from Drr component, in um^2
(2,*) column is the msdd generated from Dtt component, in um^2
(3:4,*) is the standard error in the msdd from the Drr,Dtt components, in um^2
(5,*) column contains N's appropriate for weighted averages

Note: errors may be greater than expected due to correlation
effects in the data. Also, error estimates and N weighting
are only approximate when using 'lfit'.

This program was written by John, and this webpage was written
by Brenton Hoffman, a student working with John (with some
editing to html-ize it by Eric).

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