Theoretical calculation of trapping forces in oil-immersed microscope objectives

One of the main problems in using oil immersed objectives for optical trapping is due to the reflective index mismatch. While in water immersed lens or in "classical" ones the index mismatch is, at most, because of the propagation from a low-index to a high-index medium so no big aberrations appear, in the oil-immersed ones the aberrations cannot be neglected. Due to the propagation of a focalized beam from a high refraction index medium to a low one, spherical aberrations appear. But the numerical aperture an oil immersed objective can reach is usually above 1.2, so theoretically, the Q-factor can reach higher values. In this paper we confront two different methods of force calculations. The first one is based on Ashkin's (Biophys. J. - Feb. 1992) formulas and uses a ray-tracing approach. Using this approach we can observe the asymmetry of the forces along the optical axis and the high Q-factors values on the orthogonal plane. The second approach is a more rigorous one and is based on wave optics. We analyze the Gaussian beam propagation using the scalar version of the diffraction theory and the formulas of the scattering and gradient forces developed by W.H.Wright &al. (Applied Optics - March 1994). This approach, although more precise in defining the focus shape, is not necessarily more precise in determining the force value. This essentially because of the approximations used in the force formulas. While in the ray-tracing approach, the error can be minimized by changing the sampling period of the beam, in the wave-optics approach this cannot be done. In the same time, in the latter approach, the beam shape can be described better so the accuracy of the simulation improved. To our belief the possibility of using both simulations must be taken into account while in the "resonance" regime and, function of the needs one has, decide which one is to be considered reliable.