Optical force field reconstruction using Brownian trajectories

Optical force field reconstruction using Brownian trajectories
Laura Pérez García, Jaime Donlucas Pérez, Giorgio Volpe, Alejandro V. Arzola & Giovanni Volpe

Click here to see the slides.
Twitter Link: here.

Optical tweezers have evolved into sophisticated tools for the measurement and application of nanoscopic forces; its use ranges from mechanobiology to cooling and trapping atoms.
Despite their ever-growing interest, the methods employed to measure optical forces have not changed much in the last 30 years. The key methods measure the potential function, the autocorrelation function (ACF), or the power spectral density (PSD) of an optically trapped particle’s motion. Unfortunately, all these techniques have some drawbacks: they require large amounts of data acquired for long times (potential) or at high frequency (ACF and PSD); they cannot identify non-conservative force-field components; they can only measure the properties of stable equilibrium positions, and they require setting several parameters carefully and expertly [1]. These shortcomings have limited the possibility of measuring nanoscopic forces in many potential applications, such as experiments with non-conservative force fields and out-of-equilibrium conditions.

We have recently introduced a simple, robust, and fast algorithm that permits to reconstruct microscopic force fields from Brownian trajectories, Force Reconstruction via Maximum-likelihood-estimator Analysis — FORMA. FORMA 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. Its key advantages are that FORMA does not require setting analysis parameters, it executes orders-of-magnitude faster than other more standard methods, and it requires ten times fewer data to achieve the same precision and accuracy. Finally, FORMA also permits the characterization of non-conservative force fields and non-stable equilibrium positions in extended force fields [2].


[1] Jones et al. Optical tweezers: Principles and applications. Cambridge, 2015.
[2] L. Pérez García, et al. Nat. Commun. 9, 5166 (2018).

Poster Session
Time: June 22nd 2020
Place: Twitter

POM Conference
Time: June 25th 2020
Place: Online

Poster Slides

Laura Pérez García – POM Poster – Page 1
Laura Pérez García – POM Poster – Page 2
Laura Pérez García – POM Poster – Page 3
Laura Pérez García – POM Poster – Page 4

Soft Matter Lab presentations at the Photonics Online Meet-up, 22 June 2020

Six members of the Soft Matter Lab (Aykut Argun, Falko Schmidt, Laura Pérez-Garcia, Saga Helgadottir, Alessandro Magazzù, Daniel Midtvedt) were selected for poster presentations at the Photonics Online Meet-up (POM).

POM is an entirely free virtual conference. It aims to bring together a community of early career and established researchers from universities, industry, and government working in optics and photonics.

The meeting, at its second edition, will be held on June 25th 2020, 9-14.30 Central European Time. The virtual poster session will take place on June 22nd, on Twitter and virtual reality.

The poster contributions being presented are:

Aykut Argun
Enhanced force-field calibration via machine learning
Twitter Link: here.

Falko Schmidt
Dynamics of an active nanoparticle in an optical trap
Twitter Link: here.

Laura Pérez-García
Optical force field reconstruction using Brownian trajectories
Twitter Link: here.

Saga Helgadottir
DeepTrack: A comprehensive deep learning framework for digital microscopy
Twitter Link: here.

Alessandro Magazzù
Controlling the dynamics of colloidal particles by critical Casimir forces
Twitter Link: here.

Daniel Midtvedt
Holographic characterisation of subwavelength particles enhanced by deep learning
Twitter Link: here.

Link: Photonics Online Meet-up (POM)

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications on ArXiv

Schematic of a bistable potential generated with a double-beam optical tweezers.

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications
Jan Gieseler, Juan Ruben Gomez-Solano, Alessandro Magazzù, Isaac Pérez Castillo, Laura Pérez García, Marta Gironella-Torrent, Xavier Viader-Godoy, Felix Ritort, Giuseppe Pesce, Alejandro V. Arzola, Karen Volke-Sepulveda & Giovanni Volpe
arXiv: 2004.05246

Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this Tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future application of optical tweezers. This Tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All the examples are complemented by the sample data and software necessary to reproduce them.

Presentation by Laura Pérez at the OSA Biophotonics Congress, Tucson, 16 Apr 2019

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

More information can be found on the link: https://www.osapublishing.org/abstract.cfm?uri=OMA-2019-AT2E.2


FORMA – Enhanced Optical Tweezers Calibration published in Nature Commun.

High-Performance Reconstruction of Microscopic Force Fields from Brownian Trajectories

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)
doi: 10.1038/s41467-018-07437-x
arXiv: 1808.05468

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.

See also freeware software at 10.6084/m9.figshare.7181888

Featured in:
Optimerad optisk pincett, Forskning.se

Laura Pérez-García joins the Soft Matter Lab

Laura Pérez-García starts her PhD at the Physics Department of the University of Gothenburg on 15th November 2018.

Laura has a Master degree in physical sciences from Universidad Nacional Autónoma de México in México City, where she submitted a Master thesis about optical forces in speckle fields.

The aim of her  PhD project is to study the behavior of active matter using Light Sheet Microscopy.

Seminar on non-conservative optical forces in speckle fields by Laura Pérez García from UNAM, Faraday, 26 jun 2018

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[6]. 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.

  1.  J.C. Dainty. Laser speckle and related phenomena. Topics in Applied Physics. Springer-Verlag, 1984.
  2.  J.W. Goodman. Speckle Phenomena in Optics: Theory and Applications. Roberts & Company, 2007.
  3. H.J. Rabal and R.A. Braga. Dynamic Laser Speckle and Applications. Optical Science and Engineering. CRC Press, 2008.
  4. 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.
  5. 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.
  6. 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.

Place: Faraday room, Fysik Origo, Fysik
Time: 26 June, 2018, 15:00