Towards absolute calibration of optical tweezers.

Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of Mie-Debye-spherical aberration (MDSA) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass-water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius, and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points, and "hopping" effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.

Characterization of objective transmittance for optical tweezers.

We have measured the overall transmittance of a laser beam through an oil immersion objective as a function of the transverse size of the laser beam, using the dual-objective method. Our results show that the objective transmittance is not uniform and that its dependence on the radial beam's position can be modeled by a Gaussian function. This property affects the intensity distribution pattern in the sample region and should be taken into account in theoretical descriptions of optical tweezers. Moreover, one must consider this position dependence to determine the local laser power delivered at the sample region by the dual-objective method, especially when the beam overfills the objective's back entrance. If the transmittance is assumed to be uniform, the local power is overestimated.