FORMA: Force Reconstruction via Maximum-likelihood-estimator Analysis
Laura Pérez García, Jaime Donlucas Pérez, Giorgio Volpe, Alejandro V. Areola & Giovanni Volpe
OSA Biophotonics Congress, Tucson (AZ), USA
16 April 2019
Microscopic force characterization is often done by using a microscopic colloidal particle which probes local forces. These particles are often held by a harmonic trapping potential with stiffness k so that a homogeneous force acting on the particle results in a displacement Δx from the equilibrium position and the force can, therefore, be measured as k Δx . To perform such measurement, it is necessary to determine the value of k , which is often done by measuring the Brownian fluctuations of the particle around its stable equilibrium position. This is achieved by measuring the particle position as a function of time, x (t) , and then using some calibration algorithms; the most commonly employed techniques are the potential analysis that relies on the fact that the force is derived from a potential; and the power spectral density (PSD) and the auto-correlation function (ACF) methods that require a regular sampling in time. Besides the previous requirements, all methods depend on the choice of some analysis parameters. This has inhibited the applicability of force measurement methods to characterize force fields with non-conservative components or where the particle freely explores an extended potential landscape. We propose a method for Force Reconstruction via Maximum-likelihood-estimator Analysis (FORMA) that exploits the fact that in the proximity of an equilibrium position the force field can be approximated by a linear form and, therefore, optimally estimated using a linear Maximum-likelihood-estimator (MLE).
Session: Biological Applications 10:30 AM–12:00 AM, Tuesday, April 16, 2019
High-Performance Reconstruction of Microscopic Force Fields from Brownian Trajectories Laura Pérez García, Jaime Donlucas Pérez, Giorgio Volpe, Alejandro V. Arzola & Giovanni Volpe
Nature Communications 9, 5166 (2018)
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 analysis (FORMA) to retrieve the force field acting on a Brownian particle from the analysis of its displacements. FORMA estimates accurately 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 demonstrate FORMA performance using optical tweezers, showing how, outperforming other available techniques, it can identify and characterise stable and unstable equilibrium points in generic force fields. Thanks to its high performance, FORMA can accelerate the development of microscopic and nanoscopic force transducers for physics, biology and engineering.
Non conservative optical forces of speckle fields generated with a SLM
Seminar by Laura Pérez García from the Universidad National Autónoma de México (UNAM).
Speckle patterns arise when a highly coherent light source impinges on a rough surface or when it propagates through an inhomogeneous media. This phenomenon appeared after the invention of the laser in the 70’s and, initially was considered as a feature to avoid in optical setups since it limits the imaging resolution. However, speckle patterns can give information about the process that generates it and also can be incorporated by researchers in astronomy, surface characterization, biology, medicine and chemical processes [1, 2, 3]. In particular, speckle has been used in the last years in the area of optical micromanipulation to study the interaction of colloidal particles in random potentials[4, 5]. It is important the use of speckle patterns since it has a wide range of characteristic lengths, optical vortexes and intrinsic robustness to misalignment.
We’ve studied speckle patterns generated by a spatial light modulator (SLM), emphasizing in the intensity distribution, its spatial properties and the dynamical properties of particles subjected to these fields. Specifically, I studied the dynamical behavior of 1.54μm and 1μm spherical polystyrene particles embedded in deionized water in the presence of a speckle light field. We generated the speckle pattern using a 532 nm-wavelength laser which impinged on an SLM, which projected random values for each pixel, and then redirected to an optical micromanipulation system. It is important to mention that, by varying the optical resolution of the system with a diaphragm, we allowed the interference between all the wavefronts.
We analyzed the particle’s trajectories in the overdamped regime as an approximation for the particle dynamics. We didn’t assume the existence of a scalar potential, so we can study the nonconservative nature of the optical forces. Additionally, the mean squared displacement was calculated and com- pared with free diffusion, we observed different regimes, owing to the spatial features in the speckle patterns used.
J.C. Dainty. Laser speckle and related phenomena. Topics in Applied Physics. Springer-Verlag, 1984.
J.W. Goodman. Speckle Phenomena in Optics: Theory and Applications. Roberts & Company, 2007.
H.J. Rabal and R.A. Braga. Dynamic Laser Speckle and Applications. Optical Science and Engineering. CRC Press, 2008.
Florian Evers, Christoph Zunke, Richard D L Hanes, J ̈org Bewerunge, Imad Ladadwa, Andreas Heuer, Stefan U. Egelhaaf, Giorgio Giovanni Volpe, Giorgio Giovanni Volpe, and Sylvain Gigan. Particle dynamics in two-dimensional random-energy landscapes: Experiments and simulations. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics, 88(2):3936, 2014.
Giorgio Volpe, Giovanni Volpe, and Sylvain Gigan. Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation. Scientific Reports, 4:3936, 2014.
Pinyu Wu, Rongxin Huang, Christian Tischer, Alexandr Jonas, and Ernst Ludwig Florin. Direct measurement of the nonconservative force field generated by optical tweezers. Physical Review Letters, 103(10):4–7, 2009.