Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies – A general framework published in Biomedical Optics Express

Different sampling methods for the trajectory of a particle. (Adapted from the manuscript.)
Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies — A general framework
Laura Pérez-García, Martin Selin, Antonio Ciarlo, Alessandro Magazzù, Giuseppe Pesce, Antonio Sasso, Giovanni Volpe, Isaac Pérez Castillo, Alejandro V. Arzola
Biomedical Optics Express, 14, 6442-6469 (2023)
doi: 10.1364/BOE.495468
arXiv: 2305.07245

Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector’s finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.

Roadmap for Optical Tweezers published in Journal of Physics: Photonics

Illustration of an optical tweezers holding a particle. (Image by A. Magazzù.)
Roadmap for optical tweezers
Giovanni Volpe, Onofrio M Maragò, Halina Rubinsztein-Dunlop, Giuseppe Pesce, Alexander B Stilgoe, Giorgio Volpe, Georgiy Tkachenko, Viet Giang Truong, Síle Nic Chormaic, Fatemeh Kalantarifard, Parviz Elahi, Mikael Käll, Agnese Callegari, Manuel I Marqués, Antonio A R Neves, Wendel L Moreira, Adriana Fontes, Carlos L Cesar, Rosalba Saija, Abir Saidi, Paul Beck, Jörg S Eismann, Peter Banzer, Thales F D Fernandes, Francesco Pedaci, Warwick P Bowen, Rahul Vaippully, Muruga Lokesh, Basudev Roy, Gregor Thalhammer-Thurner, Monika Ritsch-Marte, Laura Pérez García, Alejandro V Arzola, Isaac Pérez Castillo, Aykut Argun, Till M Muenker, Bart E Vos, Timo Betz, Ilaria Cristiani, Paolo Minzioni, Peter J Reece, Fan Wang, David McGloin, Justus C Ndukaife, Romain Quidant, Reece P Roberts, Cyril Laplane, Thomas Volz, Reuven Gordon, Dag Hanstorp, Javier Tello Marmolejo, Graham D Bruce, Kishan Dholakia, Tongcang Li, Oto Brzobohatý, Stephen H Simpson, Pavel Zemánek, Felix Ritort, Yael Roichman, Valeriia Bobkova, Raphael Wittkowski, Cornelia Denz, G V Pavan Kumar, Antonino Foti, Maria Grazia Donato, Pietro G Gucciardi, Lucia Gardini, Giulio Bianchi, Anatolii V Kashchuk, Marco Capitanio, Lynn Paterson, Philip H Jones, Kirstine Berg-Sørensen, Younes F Barooji, Lene B Oddershede, Pegah Pouladian, Daryl Preece, Caroline Beck Adiels, Anna Chiara De Luca, Alessandro Magazzù, David Bronte Ciriza, Maria Antonia Iatì, Grover A Swartzlander Jr
Journal of Physics: Photonics 2(2), 022501 (2023)
arXiv: 2206.13789
doi: 110.1088/2515-7647/acb57b

Optical tweezers are tools made of light that enable contactless pushing, trapping, and manipulation of objects, ranging from atoms to space light sails. Since the pioneering work by Arthur Ashkin in the 1970s, optical tweezers have evolved into sophisticated instruments and have been employed in a broad range of applications in the life sciences, physics, and engineering. These include accurate force and torque measurement at the femtonewton level, microrheology of complex fluids, single micro- and nano-particle spectroscopy, single-cell analysis, and statistical-physics experiments. This roadmap provides insights into current investigations involving optical forces and optical tweezers from their theoretical foundations to designs and setups. It also offers perspectives for applications to a wide range of research fields, from biophysics to space exploration.

Faster and more accurate geometrical-optics optical force calculation using neural networks published in ACS Photonics

Focused rays scattered by an ellipsoidal particles (left). Optical torque along y calculated in the x-y plane using ray scattering with a grid of 1600 rays (up, right) and using a trained neural network (down, right). (Image by the Authors of the manuscript.)
Faster and more accurate geometrical-optics optical force calculation using neural networks
David Bronte Ciriza, Alessandro Magazzù, Agnese Callegari, Gunther Barbosa, Antonio A. R. Neves, Maria A. Iatì, Giovanni Volpe, Onofrio M. Maragò
ACS Photonics 10, 234–241 (2023)
doi: 10.1021/acsphotonics.2c01565
arXiv: 2209.04032

Optical forces are often calculated by discretizing the trapping light beam into a set of rays and using geometrical optics to compute the exchange of momentum. However, the number of rays sets a trade-off between calculation speed and accuracy. Here, we show that using neural networks permits one to overcome this limitation, obtaining not only faster but also more accurate simulations. We demonstrate this using an optically trapped spherical particle for which we obtain an analytical solution to use as ground truth. Then, we take advantage of the acceleration provided by neural networks to study the dynamics of an ellipsoidal particle in a double trap, which would be computationally impossible otherwise.

Flash Talk by A. Magazzù at 729. WE Heraeus Seminar on Fluctuation Induced Forces, Online, 15 February 2022

Schematic of the experimental setup used in the experiment. (Image by A. Magazzù.)
Controlling the dynamics of colloidal particles by critical Casimir forces
Alessandro Magazzù
729. WE-Heraeus Stiftung Seminar on Fluctuation-induced Forces
15 February 2022, 14:50 CET

Critical Casimir forces can play an important role for applications in nano-science and nano-technology, owing to their piconewton strength, nanometric action range, fine tunability as a function of temperature, and exquisite dependence on the surface properties of the involved objects. Here, we investigate the effects of critical Casimir forces on the free dynamics of a pair of colloidal particles dispersed in the bulk of a near-critical binary liquid solvent, using blinking optical tweezers. In particular, we measure the time evolution of the distance between the two colloids to determine their relative diffusion and drift velocity.

Raman Tweezers for Tire and Road Wear Micro- and Nanoparticles Analysis published in Environmental Science: Nano

Optical beam focused into the liquid: the tire particles are pushed away from the laser focus.

Raman Tweezers for Tire and Road Wear Micro- and Nanoparticles Analysis
Pietro Giuseppe Gucciardi, Gillibert Raymond, Alessandro Magazzù, Agnese Callegari, David Bronte Ciriza, Foti Antonino, Maria Grazia Donato, Onofrio M. Maragò, Giovanni Volpe, Marc Lamy de La Chapelle & Fabienne Lagarde
Environmental Science: Nano 9, 145 – 161 (2022)
ChemRxiv: https://doi.org/10.33774/chemrxiv-2021-h59n1
doi: https://doi.org/10.1039/D1EN00553G

Tire and Road Wear Particles (TRWP) are non-exhaust particulate matter generated by road transport means during the mechanical abrasion of tires, brakes and roads. TRWP accumulate on the roadsides and are transported into the aquatic ecosystem during stormwater runoffs. Due to their size (sub-millimetric) and rubber content (elastomers), TRWP are considered microplastics (MPs). While the amount of the MPs polluting the water ecosystem with sizes from ~ 5 μm to more than 100 μm is known, the fraction of smaller particles is unknown due to the technological gap in the detection and analysis of < 5 μm MPs. Here we show that Raman Tweezers, a combination of optical tweezers and Raman spectroscopy, can be used to trap and chemically analyze individual TWRPs in a liquid environment, down to the sub-micrometric scale. Using tire particles mechanically grinded from aged car tires in water solutions, we show that it is possible to optically trap individual sub-micron particles, in a so-called 2D trapping configuration, and acquire their Raman spectrum in few tens of seconds. The analysis is then extended to samples collected from a brake test platform, where we highlight the presence of sub-micrometric agglomerates of rubber and brake debris, thanks to the presence of additional spectral features other than carbon. Our results show the potential of Raman Tweezers in environmental pollution analysis and highlight the formation of nanosized TRWP during wear.

Featured in:
University of Gothenburg > News and Events: New technology enables the detection of microplastics from road wear
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Nonsologreen > Green: Le Raman-tweezers per la guerra alle nanoplastiche che inquinano fiumi e mari

Presentation by L. Pérez García at OSA-OMA-2021

FORMA allows to identify and characterize all the equilibrium points in a force field generated by a speckle pattern.
FORMA and BEFORE: Expanding Applications of Optical Tweezers. Laura Pérez Garcia, Martin Selin, Alejandro V. Arzola, Giovanni Volpe, Alessandro Magazzù, Isaac Pérez Castillo.
Submitted to OSA-OMA 2021,  ATh1D.5
Date: 15 April
Time: 15:45 (CEST)

Abstract: 
FORMA (force reconstruction via maximum-likelihood-estimator analysis) addresses the need to measure the force fields acting on microscopic particles. Compared to alternative established methods, FORMA is faster, simpler, more accurate, and more precise. Furthermore, FORMA can also measure non-conservative and out-of-equilibrium force fields. Here, after a brief introduction to FORMA, I will present its use, advantages, and limitations. I will conclude with the most recent work where we exploit Bayesian inference to expand FORMA’s scope of application.

Presentation by D. Bronte Ciriza at OSA-OMA-2021

Optical forces calculated on a sphere with the geometrical optics (left column) and the machine learning (center column) approaches. The difference between both approaches is shown in the column on the right, illustrating the removal of artefacts with the machine learning method.

Machine learning to enhance the calculation of optical forces in the geometrical optics approximation
David Bronte Ciriza, Alessandro Magazzù, Agnese Callegari, Maria A. Iatì, Giovanni Volpe, Onofrio M. Maragò
Submitted to OSA-OMA-2021, AF2D.2 Contribution
Date: 16 April
Time: 17 CEST

Short Abstract: We show how machine learning can improve the speed and accuracy of the optical force calculations in the geometrical optics approximation.

Extended Abstract:

Light can exert forces by exchanging momentum with particles. Since the pioneering work by Ashkin in the 1970’s, optical forces have played a fundamental role in fields like biology, nanotechnology, or atomic physics. Optical tweezers, which are instruments that, by tightly focusing a laser beam, are capable of confining particles in three dimensions, have become a common tool for manipulation of micro- and nano- particles, as well as a force and torque transducer with sensing capabilities at the femtonewton level. Optical tweezers have also been successfully employed to explore novel phenomena, including protein folding and molecular motors, or the optical forces and Brownian motion of 1D and 2D materials.

Numerical simulations play a fundamental role in the planning of experiments and in the interpretation of the results. In some basic cases for optical tweezers, the optical trap can be approximated by a harmonic potential. However, there are many situations where this approximation is insufficient, for example in the case of a particle escaping an optical trap, or for particles that are moving on an optical landscape but are not trapped. In these cases, a more complex treatment of the light-matter interaction is required for a more accurate calculation of the forces. This calculation is computationally expensive and prohibitively slow for numerical simulations when the forces need to be calculated many times in a sequential way. Recently, machine learning has been demonstrated to be a promising approach to improve the speed of these calculations and therefore, to expand the applicability of numerical simulations for experimental design and analysis.

In this work, we explore the geometrical optics regime, valid when the particles are significantly bigger than the wavelength of the incident light. This is typically the case in experiments with micrometer-size particles. The optical field is described by a collection of N light rays and the momentum exchange between the rays and the particle is calculated employing the tools of geometrical optics. The limitation of considering a discrete N number of light rays introduces artifacts in the force calculation. We show that machine learning can be used to improve not only the speed but also the accuracy of the force calculation. This is first demonstrated by training a neural network for the case of a spherical particle with 3 degrees of freedom accounting for the position of the particle. We show how the neural network improves the prediction of the force with respect to the initial training data that has been generated through the geometrical optics approach.
Starting from these results for 3 degrees of freedom, the work has been expanded to 9 degrees of freedom by including all the relevant parameters for the optical forces calculation considering also different refractive indexes, shapes, sizes, positions and orientations of the particle besides different numerical apertures of the objective that focuses the light.

This work proves machine learning as a compact, accurate, and fast approach for optical forces calculation and presents a tool that can be used to study systems that, due to computation limitations, were out of the scope of the traditional ray optics approach.

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications accepted on Advances in Optics and Photonics

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
Advances in Optics and Photonics, 13(1), 74-241 (2021)
doi: https://doi.org/10.1364/AOP.394888
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.

Optical trapping and critical Casimir forces published in EPJP

Measuring the dynamics of colloids interacting with critical Casimir interaction via blinking optical tweezers: graphical representation of the optical traps.

Optical trapping and critical Casimir forces
Agnese Callegari, Alessandro Magazzù, Andrea Gambassi & Giovanni Volpe
The European Physical Journal Plus (EPJP), 136, 213 (2021)
doi: 10.1140/epjp/s13360-020-01020-4
arXiv: 2008.01537

Critical Casimir forces emerge between objects, such as colloidal particles, whenever their surfaces spatially confine the fluctuations of the order parameter of a critical liquid used as a solvent. These forces act at short but microscopically large distances between these objects, reaching often hundreds of nanometers. Keeping colloids at such distances is a major experimental challenge, which can be addressed by the means of optical tweezers. Here, we review how optical tweezers have been successfully used to quantitatively study critical Casimir forces acting on particles in suspensions. As we will see, the use of optical tweezers to experimentally study critical Casimir forces can play a crucial role in developing nano-technologies, representing an innovative way to realize self-assembled devices at the nano- and microscale.

Alessandro Magazzù and David Bronte Ciriza visit the Soft Matter Lab

Alessandro Magazzù and David Bronte Ciriza are visiting the Soft Matter Lab from 2 to 9 November 2020.
Alessandro is currently Post Doc at the IPCF-CNR Messina, Italy, and David is a PhD student at the same institution, and he is one of the ESRs (Early Stage Researchers) of the ActiveMatter MSCA-ITN-ETN.
They will be working on a neural network approach to the calculation of optical forces and torques on dielectric particles in the geometrical optics approximation.

(Foto by Aykut Argun)