  It is known that line optical tweezers (LOT) can measure potential of mean
force (PMF) between colloidal particles in the bulk. However, PMF obtained with
LOT is empirically modified before showing the result of the final form in
order to correct the potential rise at long distances. In the present letter,
we derive theoretical correction methods for acquisition of PMF by using
statistical mechanics. Using the new methods, PMF can be obtained without the
empirical fitting equation. Through the new methods, external potential acting
on the trapped two colloidal particles induced by LOT can also be obtained. As
an additional study, we explain two methods for obtaining PMF between colloidal
particles on a substrate surface, in which a normal single optical tweezers
with a fixed focal point is used, and for obtaining PMF between colloidal
particles trapped by dual-beam optical tweezers in the bulk. These methods can
also obtain the external potential acting on the trapped two colloidal
particles.
