## Abstract

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 *λ* = 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 1.1×10^{-8}N/m and 1.3×10^{-7}N/m, respectively, for a silica particle (diameter = 2.58*μ*m), and 3.1×10^{-8} N/m and 2.3×10^{-7} N/m, respectively, for a Chinese hamster ovary cell (diameter ~ 10 *μ*m to 15 *μ*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.

© 2005 Optical Society of America

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