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Manuscript Title: MatLab program for precision calibration of optical tweezers.
Authors: I.M. Tolic-Norrelykke, K. Berg-Sorensen, H. Flyvbjerg
Program title: tweezercalib
Catalogue identifier: ADTV
Journal reference: Comput. Phys. Commun. 159(2004)225
Programming language: MatLab.
Computer: Any running MatLab.
Keywords: Power spectrum analysis, Precision calibration of optical tweezers, Biology, Computational methods, Utility, Optics, Statistical physics, Thermodynamics.
Classification: 3, 4.14, 18, 23.

Nature of problem:
To calibrate optical tweezers with precision by fitting theory to experimental power spectrum of position of bead doing Brownian motion in incompressible fluid, possibly near microscope cover slip, while trapped in optical tweezers. Thereby determine spring constant of optical trap and conversion factor for arbitrary-units-to-nanometers for detection system.

Solution method:
Elimination of cross-talk between quadrant photo-diode's output channels for positions (optional). Check that the distribution of recorded positions agrees with Boltzmann distribution of bead in harmonic trap. Data compression and noise reduction by blocking method applied to power spectrum. Full accounting for hydrodynamic effects: frequency-dependent drag force and interaction with nearby cover slip (optional) Full accounting for electronic filters (optional), for "virtual filtering" caused by detection system (optional). Full accounting for aliasing caused by finite sampling rate (optional). Standard non-linear least-squares fitting. Statisical support for fit is given, with several plots suitable for inspection of consistency and quality of data and fit.

Data should be positions of bead doing Brownian motion while held by optical tweezers. For high precision in final results, data should be time series measured over a long time, with sufficiently high experimental sampling rate: The sampling rate should be well above the characteristic frequency of the trap, the so-called corner frequency. Thus, the sampling frequency should typically be larger than 10kHz. The Fast Fourier Transform applied requires the time series to contain 2n data points, and long measurement time is obtained with n > 12-15. Finally, the optics should be set to ensure a harmonic trapping potential in the range of positions visited by the bead. The fitting procedure checks for harmonic potential.

Additional comments:
The program requires the MatLab "Optimization Toolbox" and "Statistics Toolbox".

Running time:
(Tens of) minutes.