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. = 532 nm, 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(-8)N/m and 1.3x10(-7)N/m, respectively, for a silica particle ( diameter = 2.58 mu m), and 3.1x10(-8) N/m and 2.3x10(-7) N/m, respectively, for a Chinese hamster ovary cell ( diameter similar to 10 mu m to 15 mu m). The set of force constants (K-x, K-y, and K-z) completely defines the optical force field E( x, y, z) = [K-x x(2) + K-y y(2) + K-z z(2)]/ 2 ( in the parabolic potential approximation) on the trapped particle. Practical advantages and limitations of using a pair of orthogonal tracking beams are discussed. (C) 2005 Optical Society of America.