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The accurate measurement of microscopic force fields is crucial in manybranches of science and technology, from biophotonics and mechanobiology tomicroscopy and optomechanics. These forces are often probed by analysing theirinfluence on the motion of Brownian particles. Here, we introduce a powerfulalgorithm for microscopic Force Reconstruction via Maximum-likelihood-estimator(MLE) Analysis (FORMA) to retrieve the force field acting on a Brownianparticle from the analysis of its displacements. FORMA yields accuratesimultaneous estimations of both the conservative and non-conservativecomponents of the force field with important advantages over establishedtechniques, being parameter-free, requiring ten-fold less data and executingorders-of-magnitude faster. We first demonstrate FORMA performance usingoptical tweezers. We then show how, outperforming any other availabletechnique, FORMA can identify and characterise stable and unstable equilibriumpoints in generic extended force fields. Thanks to its high performance, thisnew algorithm can accelerate the development of microscopic and nanoscopicforce transducers capable of operating with high reliability, speed, accuracyand precision for applications in physics, biology and engineering.

High-Performance Reconstruction of Microscopic Force Fields from Brownian Trajectories