  We present a new particle image correlation technique for resolving
nanoparticle flow velocity using confocal laser scanning microscopy (CLSM). The
two primary issues that complicate nanoparticle scanning laser image
correlation (SLIC) based velocimetry are (1) the use of diffusion dominated
nanoparticles as flow tracers, which introduce a random decorrelating error
into the velocity estimate, and (2) the effects of the scanning laser image
acquisition, which introduces a bias error. To date, no study has quantified
these errors or demonstrated a means to deal with them in SLIC velocimetry. In
this work, we build upon the robust phase correlation (RPC) and existing
methods of SLIC to quantify and mitigate these errors. First, we implement an
ensemble RPC instead of using an ensemble standard cross correlation, and
develop an SLIC optimal filter that maximizes the correlation strength in order
to reliably and accurately detect the correlation peak representing the most
probable average displacement of the nanoparticles. Secondly, we developed an
analytical model of the SLIC measurement bias error due to image scanning of
diffusion dominated tracer particles. We show that the bias error depends only
on the ratio of the mean velocity of the tracer particles to that of the laser
scanner and we use this model to correct the induced errors. We validated our
technique using synthetic images and experimentally obtained SLIC images of
nanoparticle flow through a micro-channel. Our technique reduced the error by
up to a factor of ten compared to other SLIC algorithms for the images tested
in this study. Moreover, our optimized RPC filter is reducing the number of
image pairs required for the convergence of the ensemble correlation by two
orders of magnitude compared to the standard cross correlation.
