Schematic of experimental system: (a) Coupling of trapping and detection laser beams into the optical trap, (b) schematic of imaging setup.
Dimensions of photodiode array in micrometers.
Alignment of signal to center of QPD using secondary laser beam. (a) shows bad alignment with the cross segments of the QPD not visible, (b) shows a case of good alignment with the image of the cross brightest and most symmetric.
Position calibration for Ludl MAC5000 microscope stage. (a) Initial position of stuck bead. (b) New position of bead. (c) Merged image.
Position calibration for AOD beam deflection. (a) Image showing the extreme positions of trapping laser when it was deflected by an AOD. (b) Position of spot centers.
Normalized X position signal vs bead displacement for a trapped bead.
Position fluctuations of 1.1 μm diameter trapped bead for different averaging times.
Position detector cross talk between X and Y axes.
Typical power spectra obtained using the QPD for a trapped (a) 1.1 μm bead, (b) 3 μm, and (c) 16 μm bead. All spectra were fit to hydrodynamically correct power spectra (Eq. (5), black lines) as well as Lorentzians (dotted lines), and yielded corner frequency values of (a) 165 Hz, (b) 56.5 Hz, and (c) 11 Hz. The corresponding values of the fit parameter A which gives the diffusion constant D comes out to be (a) 0.093, (b) 0.036, and (c) 0.055. The fit coefficients for the hydrodynamic fits have been included in each plot. The term y0 indicates an offset term that is added to Eq. (5) – this is like a white noise term that represents the measured amplitude of the uncertainty of positions produced in our detection system. The calculated values of f ν and f m are held constant during the fit.
Residuals of fit data against frequency. The zero line is indicated in both plots. (a) shows an acceptable structure of the residuals with random distribution around zero and no frequency-dependent structure evident, while (b) shows a case of bad fitting with the residuals skewed in the positive side of zero, and also having high amplitude. Peaks at certain frequencies are also seen.
Linear dependence of corner frequency with trapping laser power.
Power spectrum of 1.1 μm beads with 100 kHz sampling rate averaged over 49 independent power spectra calculated from consecutive time series.
Comparison of experimentally measured displacement sensitivity and thermal resolution limit.
Comparison of diffusion constant calculated from fitting the experimental power spectrum and that estimated theoretically from the Einstein equation.
Comparison of measured displacement sensitivity and thermal resolution limit for different averaging times.
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