Parametric study of the forces on microspheres held by optical tweezers

Abstract

Optical-trapping forces exerted on polystyrene microspheres are predicted and measured as a function of sphere size, laser spot size, and laser beam polarization. Axial and transverse forces are in good and excellent agreement, respectively, with a ray-optics model when the sphere diameter is ≥ 10 µm. Results are compared with results from an electromagnetic model when the sphere size is ≤ 1 µm. Axial trapping performance is found to be optimum when the numerical aperture of the objective lens is as large as possible, and when the trapped sphere is located just below the chamber cover slip. Forces in the transverse direction are not as sensitive to parametric variations as are the axial forces. These results are important as a first-order approximation to the forces that can be applied either directly to biological objects or by means of microsphere handles attached to the biological specimen.

Implementing both short- and long-working-distance optical trappings into a commercial microscope

“…10,11,15,24,29,30 Conversely to the hydrodynamic coupling, the spherical aberration increases when h / a increases, causing the decrease of F Ќ for h / a Ͼ 5 ͑see Fig. 4; note that in this region F Ќ ͑0͒ Х F Ќ ͒.…”

“…4͒ is only apparent, being caused by the hydrodynamic coupling of the particle with the wall. In theory, this artifact can be eliminated by applying a correction factor to the measured escape force, 10,11,25 .…”

“…In comparison to the two-beam concept, the single-beam trap has the twofold advantage of simplicity and size independence; i.e., particles with sizes ranging from less than 1 m up to about 20 m can be trapped with the same setup, without any adjustment except that of the beam power. 10,11 Simplicity stems from the fact that the trap just needs a single collimated beam, directed through a microscope objective with a very large aperture. The laser beam must be expanded to be wide enough to cover the exit pupil of the objective.…”

“…The test procedures are similar to those used in recent works about RP forces and the influence of spherical aberration in optical tweezers. 10,11,15 Long-WD threedimensional trapping in two-beam mode is demonstrated, and transverse trapping efficiencies are measured as a function of the interfoci distance ͑⌬͒, for various particle sizes. In both modes, we test the linearity of the measured trapping force versus the laser power.…”

“…1͑b͒ and 1͑c͔͒ traps. As optical tweezers have been the matter of a considerable literature, we do not dwell on the physical principles of singlebeam trapping, and rather refer the reader to articles quoted in the reference list, 9,11,12,15,16 and to other references therein. We simply remind that the focal zone of a very large aperture laser beam acts as a three-dimensional ͑3D͒ potential well for particles whose index of refraction is larger than that of the surrounding medium.…”