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 earlierPointer in this tutorial. As it is, I don't think it is optimized in terms of speed of execution...
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, but I find it handy to perform this quick check.
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.
• "Statistical and Sampling Issues When Using Multiple Particle Tracking"
T. Savin and P.S. Doyle, Phys. Rev. E, 76:021501, 2007.
doiPointer or pdfPointer
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.
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.
doiPointer or pdfPointer
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.
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.
doiPointer or pdfPointer
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.