Optical tweezers absolute calibration

TL;DR

This paper advances the absolute calibration of optical tweezers by incorporating primary aberrations into the theoretical model, validated through experiments, enabling more accurate force measurements across various conditions.

Contribution

It overcomes the previous theoretical overestimation of stiffness by including aberrations, validated experimentally, improving the accuracy of optical tweezers calibration.

Findings

Inclusion of aberrations improves calibration accuracy.

Experimental validation shows agreement within error bars.

Calibration applicable across a broad range of parameters.

Abstract

Optical tweezers are highly versatile laser traps for neutral microparticles, with fundamental applications in physics and in single molecule cell biology. Force measurements are performed by converting the stiffness response to displacement of trapped transparent microspheres, employed as force transducers. Usually, calibration is indirect, by comparison with fluid drag forces. This can lead to discrepancies by sizable factors. Progress achieved in a program aiming at absolute calibration, conducted over the past fifteen years, is briefly reviewed. Here we overcome its last major obstacle, a theoretical overestimation of the peak stiffness, within the most employed range for applications, and we perform experimental validation. The discrepancy is traced to the effect of primary aberrations of the optical system, which are now included in the theory. All required experimental parameters are readily accessible. Astigmatism, the dominant effect, is measured by analyzing reflected images of the focused laser spot, adapting frequently employed video microscopy techniques. Combined with interface spherical aberration, it reveals a previously unknown window of instability for trapping. Comparison with experimental data leads to an overall agreement within error bars, with no fitting, for a broad range of microsphere radii, from the Rayleigh regime to the ray optics one, for different polarizations and trapping heights, including all commonly employed parameter domains. Besides signalling full first-principles theoretical understanding of optical tweezers operation, the results may lead to improved instrument design and control over experiments, as well as to an extended domain of applicability, allowing reliable force measurements, in principle, from femtonewtons to nanonewtons.