Particle tracking using IDL -- John C. Crocker and
Eric R. Weeks
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A note about the "radius"
The radius is calculated in a funny way.
The moment of inertia for an object is defined as
I = sum(mass_i *
r_i^2) = (total mass)*(Rg)^2
The last term defines
the radius of gyration Rg. The sum is over i, each
pixel with a given "mass" (its brightness) at a given position
r_i, measured from the center of mass of the particle.
Rewriting, we get that
(Rg)^2 = sum(mass_i*r_i^2) / (total
mass).
However, the calculation that feature
does is actually
(Rg)^2 = sum(mass_i*(r_i^2 + 1/6)) / (total mass)
The factor of 1/6 is a mistake, as far as I can tell (Eric).
John Crocker wrote in an email to me about the factor of 1/6
that "it's unimportant, and not clearly done correctly." Note
also that what is returned is the square of the radius, but
throughout the tutorial we always call this "radius". The bottom
line is that it is related to the size of the particle, but
should not be interpreted as the real radius of gyration. Note
also that the same problem occurs in the
3D
code (feature3d.pro).
We don't want to change the code since we've been using it this
way for many years, although if you want to change
the code, look for the line in feature.pro that says:
mask3= (rsq * mask) + (1./6.)
and remove the "+ (1./6.)" part. Then, take the square root of
the radius column, or insert a sqrt command near the end of
feature.pro where the radius is calculated.
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