Fig. 4.

Comparison of trapping performance between the circular rotation/lock-in demodulation scheme [6, 15] (black) and the algorithm developed in this work (red). The setup and time-averaged intensity of the circular rotation scheme are depicted in the inset of (a). The rotation is implemented as 256 point traversal on the circle at a rate of 26 kHz. Feedback voltages are generated after each rotation cycle and last throughout the subsequent cycle. For both algorithms, 300 ms of trapping data is generated for characterizing the position fluctuations (σ) of the object in the trap and a total of 20 trapping traces are simulated for a specific diffusion coefficient. For each algorithm and each D value, the feedback gain (g · μ) was fine tuned to minimize the position variance. Other simulation parameters for the new algorithm are the same as in Fig. 3. (a) Standard deviation of (1-D) position fluctuation as a function of diffusion coefficient. Outliers at high D arose from trapping runs during which the object had escaped, and those runs are eliminated from calculation of the mean. The solid lines are linear fits of the means. (b) Cumulative vector plot of the lock-in outputs during a trapping event of a D = 100 µm²/s object. (c) Radial distance histogram of the lock-in outputs. The cycles with one photon detected produce vectors on the periphery of the circle in (b) and the right peak in (c). (d) Cumulative vector plot of the Kalman filtered posterior estimates (6) during a trapping run of a D = 100 µm²/s object. (e) Histogram of the posterior estimate along one dimension