  Active particle tracking microrheometers have the potential to perform
accurate broad-band measurements of viscoelasticity within microscopic systems.
Generally, their largest possible precision is limited by Brownian motion and
low frequency changes to the system. The signal to noise ratio is usually
improved by increasing the size of the driven motion compared to the Brownian
as well as averaging over repeated measurements. New theory is presented here
which gives the complex shear modulus when the motion of a spherical particle
is driven by non-linear forces. In some scenarios error can be further reduced
by applying a variable transformation which linearises the equation of motion.
This allows normalisation which eliminates low frequency drift in the
particle's equilibrium position. Using this method will easily increase the
signal strength enough to significantly reduce the measurement time for the
same error. Thus the method is more conducive to measuring viscoelasticity in
slowly changing microscopic systems, such as a living cell.
