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.

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)

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.

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.