Resources
Here you will find the IDL programs
used to calculate the quantities I mentioned in this website. I also
included some websites and articles, which may be useful.
IDL procedures
This IDL procedure is used to calculate
the ensemble mean and variance of the individual msd with the proper
weighting as described in this website. It also performs a block-average
of the overlapping displacement, solving an issue raised earlier
in
this tutorial. As it is, I don't think it is optimized in terms of speed
of execution...
in
this tutorial. As it is, I don't think it is optimized in terms of speed
of execution...• nbox.pro
This small IDL procedure calculates
the number of tracked particles in each frame of the movie it is used
to ensure that you have a constant number of beads in the tracking volume.
It is actually included in msd_moments.pro, but I find it handy to perform
this quick check.
Websites
The first website to visit. There
you will learn how to do multiple particle tracking, and will be able
to download the procedures in various programming languages. Maintained
by John C. Crocker and Eric R. Weeks.
A page that explains microrheology
and contains links to some applications of this technique. Written by
Eric R. Weeks.
A typical example of a system which
heterogeneity at the micro-scale can affect its macrorheological characteristics.
Written by Marco Caggioni.
Literature
• "Statistical and Sampling
Issues When Using Multiple Particle Tracking"
T. Savin and P.S. Doyle, Phys. Rev. E, 76:021501, 2007.
T. Savin and P.S. Doyle, Phys. Rev. E, 76:021501, 2007.
In this paper we explain all the
issues and methods presented in this tutorial. It goes into more mathematically
detailed demonstrations, and assesses the problem of overlapping displacement
that is not explained on this webpage. It also proposes ways to quantify
the heterogeneity of a material.
• "Methods of Digital
Video Microscopy for Colloidal Studies"
J.C. Crocker and D.G. Grier, J. Colloid Interface Sci., 179:298, 1996.
J.C. Crocker and D.G. Grier, J. Colloid Interface Sci., 179:298, 1996.
This is the original paper that details
the method of video microscopy particle tracking. This method is, to
date, the only measurement technique that can simultaneously track enough
particles to do the heterogeneity measurements described here.
• "A Rational Approach
to Noise Discrimination in Video Microscopy Particle Tracking"
T. Savin, P.T. Spicer and P.S. Doyle, Appl. Phys. Lett., 93:024102, 2008.
T. Savin, P.T. Spicer and P.S. Doyle, Appl. Phys. Lett., 93:024102, 2008.
In this paper we present a way to
optimize the tracking parameters such that the resulting tracking has
best spatial resolution. We show that the choice of these parameters
affects the tracking depth, and characterize ways of evaluating the tracking
depth. This paper makes the link between the various limitations of particle
tracking that affect the msd at short lag times (artifacts in particle
detection) and large lag times (statistical issues presented in this
website).
• "Error Estimates on
Averages of Correlated Data"
H. Flyvbjerg and H. G. Petersen, J. Chem. Phys., 91:461, 1989.
H. Flyvbjerg and H. G. Petersen, J. Chem. Phys., 91:461, 1989.
This is the original paper that presents
the block-average transformation of correlated data. It is used in the
IDL procedure given above.
• "Static and Dynamic
Errors in Particle Tracking Microrheology"
T. Savin and P.S. Doyle, Biophys. J., 83:623, 205.
T. Savin and P.S. Doyle, Biophys. J., 83:623, 205.
This paper explains the issues of
tracking errors and how they appear on the msd. Although the statistical
limitations discussed on this website usually alter the msd at large
lag time, the issues discussed in this paper influence the results at
short lag time.