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Back-focal plane interferometry is typically used to determine displacements of a trapped bead which lead to
trapping force measurements in optical tweezers. In most cases, intensity shifts of the back-scattered interference
pattern due to displacements of the bead are measured by a position sensitive detector placed in the microscope
back-focal plane. However, in intensity-based measurements, the axial displacement resolution is typically worse
than the lateral resolution since for axial displacements, the inherent resolution of the position detector cannot
be used. In this paper, we demonstrate that measurement of the phase of the back-scattered light yields high
axial displacement resolution, and can also be used for lateral displacement measurement. In our experiments,
we separate out the back-scattered light from the trapped bead and reflected light from the top surface of
the sample chamber by a confocal arrangement consisting of a spatial filter used in combination with two
apertures. We proceed to beat the two separated components in a Mach-Zehnder interferometer where we
employ balanced detection to improve our fringe contrast, and thus the sensitivity of the phase measurement.
For lateral displacement sensing, we match experimental results to within 10% with a theoretical simulation
determining the shift of the overall phase contour of the back-scattered light due to a given lateral displacement
by using plane wave decomposition in conjunction with Mie scattering theory. Our technique is also able to track
the Brownian motion of trapped beads from the phase jitter so that, similar to intensity-based measurements,
we can use it to determine the spring constant of the trap, and thus the trapping force. The sensitivity of our
technique is limited by path drifts of the external interferometer which we have currently stabilized by locking
it to a frequency stabilized diode laser to obtain displacement measurement resolution ~200 pm.
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