Interference model for back-focal-plane displacement detection in optical tweezers.

The lateral position of an optically trapped object in a microscope can be monitored with a quadrant photodiode to within nanometers or better by measurement of intensity shifts in the back focal plane of the lens that is collimating the outgoing laser light. This detection is largely independent of the position of the trap in the field of view. We provide a model for the essential mechanism of this type of detection, giving a simple, closed-form analytic solution with simplifying assumptions. We identify intensity shifts as first-order far-field interference between the outgoing laser beam and scattered light from the trapped particle, where the latter is phase advanced owing to the Gouy phase anomaly. This interference also reflects momentum transfer to the particle, giving the spring constant of the trap. Our response formula is compared with the results of experiments.

[1]  A. Ashkin,et al.  Optical trapping and manipulation of neutral particles using lasers. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[2]  J. P. Barton,et al.  Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam , 1989 .

[3]  K. Svoboda,et al.  Biological applications of optical forces. , 1994, Annual review of biophysics and biomolecular structure.

[4]  Watt W. Webb,et al.  Measurement of small forces using an optical trap , 1994 .

[5]  S. Chu,et al.  Observation of a single-beam gradient force optical trap for dielectric particles. , 1986, Optics letters.

[6]  J. P. Barton,et al.  Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam , 1989 .

[7]  G Gouesbet,et al.  Prediction of reverse radiation pressure by generalized Lorenz-Mie theory. , 1996, Applied optics.

[8]  Toshimitsu Asakura,et al.  Radiation forces on a dielectric sphere in the Rayleigh scattering regime , 1996 .

[9]  W. Webb,et al.  Scanning-force microscope based on an optical trap. , 1993, Optics letters.

[10]  C. Bustamante,et al.  Overstretching B-DNA: The Elastic Response of Individual Double-Stranded and Single-Stranded DNA Molecules , 1996, Science.

[11]  Robert C. Gauthier,et al.  Optical levitation of spheres: analytical development and numerical computations of the force equations , 1995 .

[12]  Gérard Gouesbet,et al.  Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams , 1994 .

[13]  T. Wilson.  Enhanced differential phase contrast imaging in scanning microscopy using a quadrant detector , 1988 .

[14]  S. Block,et al.  Construction of multiple-beam optical traps with nanometer-resolution position sensing , 1996 .

[15]  Christoph F. Schmidt,et al.  Direct observation of kinesin stepping by optical trapping interferometry , 1993, Nature.

[16]  W. Denk,et al.  Optical measurement of picometer displacements of transparent microscopic objects. , 1990, Applied optics.