Generally Applicable Holographic Torque Measurement for Optically Trapped Particles

We present a method to measure the optical torque applied to particles of arbitrary shape such as micrometer-sized micro-organisms or cells held in an optical trap, inferred from the change of angular momentum of light induced by the particle. All torque components can be determined from a single interference pattern recorded by a camera in the back focal plane of a high-NA condenser lens provided that most of the scattered light is collected. We derive explicit expressions mapping the measured complex field in this plane to the torque components. The required phase is retrieved by an iterative algorithm, using the known position of the optical traps as constraints. The torque pertaining to individual particles is accessible, as well as separate spin or orbital parts of the total torque.

Figure 1

(a) Schematic sketch of the electromagnetic field $E(x,y)$ arising from the interference of incident and scattered light, which is used to calculate the optical torque acting on the trapped particle. (b) Experimental setup.

Figure 2

Results for field retrieval for beams with a spiral phase $\exp (il\phi )$. (a) Observed interference pattern for $l=+1$. Inset: characteristic fork shape at the center. (b) Retrieved phase for $l=+1$, (c) for $l=-1$, (d) for $l=-5$, and (e) for $l=-10$.

Figure 3

Total optical torque applied to a pair of silica microspheres (diameter $\sim 3\mu \mathrm{m}$) by two traps moved along a circular path shown in the inset. The torque from the simultaneous measurement (solid lines) is compared to the sequential “force times lever” single trap measurement (dashed lines).

Figure 4

Simultaneously measured spin torque (solid lines) and sequentially measured torques with a single trap (dashed lines) for each microsphere of the dumbbell object.