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Hi Bo,

While I still cannot seem to find the one reference I have in mind,
6*sigma^2 would be correct (cfr Suh et al 2005 at the end of the article)
for analysis in 3-D (assuming equal error in all 3 dimensions).

Suh et al, Adv. Drug. Deliv. Rev. 57, 63-78 (2005)

If I find the other article I will let you know.

Best regards,

Kevin

Kevin Braeckmans, Ph.D.
Lab. General Biochemistry & Physical Pharmacy
Ghent University
Harelbekestraat 72
9000 Ghent
Belgium
Tel: +32 (0)9 264.80.78
Fax: +32 (0)9 264.81.89
E-mail: [log in to unmask]
 

> -----Oorspronkelijk bericht-----
> Van: Confocal Microscopy List 
> [mailto:[log in to unmask]] Namens Bo ZHANG
> Verzonden: woensdag 27 juni 2007 11:17
> Aan: [log in to unmask]
> Onderwerp: Re: Particle speed calculation
> 
> Search the CONFOCAL archive at
> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
> 
> > To answer Bo Zhang's question, the localisation error introduces a 
> > constant offset on the MSD (mean square displacement) 
> measurement. For 
> > example, for a moving object one typically plots the MSD vs 
> increasing 
> > time lag, which, for free diffusion, should give a straight 
> line with 
> > intercept zero. If there is a limited localisation accuracy, the 
> > intercept will be a non-zero positive value. This is quite logical 
> > since the position error is independent of time lag and 
> will introduce 
> > a constant offset for all points of the MSD vs time lag 
> curve. There 
> > is also a more rigorous mathematical proof of this in 
> literature, but I don't have the reference here with me at 
> this moment.
> 
> Thanks Kevin! Do you have the exact intercept in mind ? I 
> just wrote out the squared displacement with measurement 
> error vectors, and by taking the expectation, and I got an 
> intercept of  6 * sigma^2 in 3-D situation, where sigma^2 is 
> the variance of the measurement in each axis. I hope this is 
> the right number.
> 
> --
> Bo ZHANG
> Ph.D. Student
> Quantitative Image Analysis Group
> Institut Pasteur
> 25-28, Rue du Docteur Roux
> 75724 Paris Cedex 15, France
> Tel : +33 (0)1 40 61 39 74
> Fax: +33 (0)1 40 61 33 30
> http://www.freewebs.com/bozhang/
>