Search the CONFOCAL archive at
http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
Localisation accuracy is a classic issue in the field of single particle
tracking (SPT) and quite a lot has been written about it in literature. The
calculation of the error is, however, not a trivial matter since it depends
on several factors: S/N (number of photons collected), particle speed,
method to determine the particle position (correlation, centre of mass,
geometric centre, Gaussian fit, ...), background noise, camera readout
noise, dark current, pixilation and frame rate.
To get you started on this, check out following references:
Bobroff 1986, Kubitscheck 2000, Thompson 2002, Ober 2004
BOBROFF N
POSITION MEASUREMENT WITH A RESOLUTION AND NOISE-LIMITED INSTRUMENT
REVIEW OF SCIENTIFIC INSTRUMENTS 57 (6): 1152-1157 JUN 1986
Kubitscheck U, Kuckmann O, Kues T, et al.
Imaging and tracking of single GFP molecules in solution
BIOPHYSICAL JOURNAL 78 (4): 2170-2179 APR 2000
Thompson RE, Larson DR, Webb WW
Precise nanometer localization analysis for individual fluorescent probes
BIOPHYSICAL JOURNAL 82 (5): 2775-2783 MAY 2002
Ober RJ, Ram S, Ward ES
Localization accuracy in single-molecule microscopy
BIOPHYSICAL JOURNAL 86 (2): 1185-1200 FEB 2004
In practice, however, people are ESTIMATING the positional accuracy by
imaging immobilized particles with the same illumination and camera
settings. The standard deviation on the measured position is then a measure
for the localisation accuracy (typically in the order of 1-100nm). Note that
this is only the lower limit of the error since in reality the particles
will be moving during frame acquisition which will deteriorate the
localisation accuracy. Also the S/N can differ for different particles (e.g.
depending on labeling degree), so the error obtained this way is only a
rough estimate.
As you correctly suggest, the localisation accuracy poses a lower limit on
the movement that can be measured for a given frame rate. Anything that
moves more slowly than that cannot be measured and should be considered
below the detection limit (i.e. stationary). A workaround for very slow
objects is to measure the displacement between images that are more than one
frame apart, rather than between subsequent images. Then the localisation
error remains the same while the distance that the object has moved
increases.
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.
Finally there is the error of unwanted drift. For example, your stage might
be drifting in xy over time, or, when measuring the movement of particles in
living cells, the cells might be moving too. This can be taken into account
by measuring the movement with respect to a stationary object. In case of a
drifting stage, one could use particles fixed to the cover glass. In case of
living cells it is more complicated since you need a reference object that
is fixed to the cell.
Hope this helps,
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 Eric Olson
> Verzonden: dinsdag 26 juni 2007 23:28
> Aan: [log in to unmask]
> Onderwerp: Particle speed calculation
>
> Search the CONFOCAL archive at
> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
>
> I am curious how people have dealt with the issue of variance
> in positional measurement ( using the measuring tool in ImageJ, for
> example) and its contribution to particle speed measurements.
> The positional variance produces paradoxical "speed" for non
> moving particles - if particle displacement is determined
> between successive images. This effect directly increases
> with sampling frequency.
>
> I have looked at a number of papers on cell migration and not
> found a correction or mention of this effect - which can be
> large for high sampling frequencies.
> One idea would be to define a minimum detectable displacement
> based on the standard deviation of the measurement. Every
> value less than that minimum would be set to zero???
>
> Thanks,
> Eric
>
>
> Eric C. Olson, PhD
> Assistant Professor
> Department of Neuroscience and Physiology
> SUNY Upstate Medical
> 3295 Weiskotten Hall
> 766 Irving St.
> Syracuse, NY 13210
>
> office: 315-464-7776
> lab : 315-464-8157
>
|
