Three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers with a pair of orthogonal tracking beams and the determination of the associated optical force constants.

We report the first experimental results on quantitative mapping of three-dimensional optical force field on a silica micro-particle and on a Chinese hamster ovary cell trapped in optical tweezers by using a pair of orthogonal laser beams in conjunction with two quadrant photo-diodes to track the particle's (or the cell's) trajectory, analyze its Brownian motion, and calculate the optical force constants in a three-dimensional parabolic potential model. For optical tweezers with a 60x objective lens (NA = 0.85), a trapping beam wavelength lambda = 532nm, and a trapping optical power of 75mW, the optical force constants along the axial and the transverse directions (of the trapping beam) were measured to be approximately 1.1x10-8N/m and 1.3x10-7N/m, respectively, for a silica particle (diameter = 2.58microm), and 3.1x10-8 N/m and 2.3x10-7 N/m, respectively, for a Chinese hamster ovary cell (diameter ~ 10 microm to 15microm). The set of force constants (Kx, Ky, and Kz ) completely defines the optical force field E(x, y, z) = [Kx x2 + Ky y2 + Kz z2]/2 (in the parabolic potential approximation) on the trapped particle. Practical advantages and limitations of using a pair of orthogonal tracking beams are discussed.