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.
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