  The accurate measurement of microscopic force fields is crucial in many
branches of science and technology, from biophotonics and mechanobiology to
microscopy and optomechanics. These forces are often probed by analysing their
influence on the motion of Brownian particles. Here, we introduce a powerful
algorithm for microscopic Force Reconstruction via Maximum-likelihood-estimator
(MLE) Analysis (FORMA) to retrieve the force field acting on a Brownian
particle from the analysis of its displacements. FORMA yields accurate
simultaneous estimations of both the conservative and non-conservative
components of the force field with important advantages over established
techniques, being parameter-free, requiring ten-fold less data and executing
orders-of-magnitude faster. We first demonstrate FORMA performance using
optical tweezers. We then show how, outperforming any other available
technique, FORMA can identify and characterise stable and unstable equilibrium
points in generic extended force fields. Thanks to its high performance, this
new algorithm can accelerate the development of microscopic and nanoscopic
force transducers capable of operating with high reliability, speed, accuracy
and precision for applications in physics, biology and engineering.
