Sagnac interferometer-enhanced particle tracking in optical tweezers

A set-up is proposed to enhance tracking of very small particles, by using optical tweezers embedded within a Sagnac interferometer. The achievable signal-to-noise ratio is shown to be enhanced over that for standard back-focal-plane interferometry. The enhancement factor increases asymptotically as the interferometer visibility approaches 100%, but is capped at a maximum given by four times the ratio of the trapping field intensity to the detector saturation threshold. For an achievable visibility of 95%, the signal-to-noise ratio can be enhanced by a factor of up to 158 and the minimum trackable particle size is 2.3 times smaller than without the interferometer. This technique is particularly useful for optical tweezers which require counter-propagating trap beams.