Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture

Back-focal-plane interferometry is a method capable of determining the three-dimensional position of a particle with high precision (< 3 nm) at high sampling rates (1 MHz). We investigated theoretically the performance of such a system for dielectric spheres with diameters D = 0.53-3 microm and for metallic spheres with D < or = 300 nm. Good sensitivity and linearity were achieved for a detection angular aperture sin(alpha) of no more than 0.5. A value of sin(alpha) > 0.7 should be used only for dielectric spheres with diameters approximately equal to the laser wavelength. Harmonic optical traps can be calibrated by measurement of the thermal motion of the sphere. We performed Brownian dynamics simulations and subsequent thermal noise analyses to prove that the wrong sin(alpha) incorrectly suggests an increased and nonharmonic axial trapping potential.