fit_power_spectrum

lumicks.pylake.fit_power_spectrum

fit_power_spectrum(power_spectrum, model, analytical_fit_range=(10.0, 10000.0), ftol=1e-07, max_function_evals=10000, bias_correction=True) → lumicks.pylake.force_calibration.power_spectrum_calibration.CalibrationResults

Fit a power spectrum.

Performs force calibration. The power spectrum calibration algorithms implemented here are based on 1 2 3 4 5 6.

Parameters

  • power_spectrum (PowerSpectrum) – A power spectrum used for calibration

  • model (CalibrationModel) – The model to be used for power spectrum calibration.

  • analytical_fit_range (tuple (f_min, f_max), optional) – Tuple of two floats, indicating the frequency range to use for the analytical simple Lorentzian fit, used to obtain initial parameter guesses [Hz]

  • ftol (float) – Termination tolerance for the model fit.

  • max_function_evals (int) – Maximum number of function evaluations during the fit.

  • bias_correction (bool) – Apply bias correction to the estimate of the diffusion coefficient according to [5]. This bias correction is calculated as N/(N+1) where N represents the number of points used in the computation of each data point in the power spectral density.

Returns

Parameters obtained from the calibration procedure.

Return type

CalibrationResults

Raises

  • RuntimeError – If there are fewer than 4 data points to fit in the power spectrum.

  • TypeError – If the supplied power spectrum is not of the type PowerSpectrum.

  • RuntimeError – If there is insufficient data to perform the analytical fit used as initial condition.

References

1

Berg-Sørensen, K. & Flyvbjerg, H. Power spectrum analysis for optical tweezers. Rev. Sci. Instrum. 75, 594 (2004).

2

Tolić-Nørrelykke, I. M., Berg-Sørensen, K. & Flyvbjerg, H. MatLab program for precision calibration of optical tweezers. Comput. Phys. Commun. 159, 225–240 (2004).

3

Hansen, P. M., Tolic-Nørrelykke, I. M., Flyvbjerg, H. & Berg-Sørensen, K. tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers. Comput. Phys. Commun. 175, 572–573 (2006).

4

Berg-Sørensen, K., Peterman, E. J. G., Weber, T., Schmidt, C. F. & Flyvbjerg, H. Power spectrum analysis for optical tweezers. II: Laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth. Rev. Sci. Instrum. 77, 063106 (2006).

5

Tolić-Nørrelykke, S. F, and Flyvbjerg, H, “Power spectrum analysis with least-squares fitting: amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers.” Review of Scientific Instruments 81.7 (2010)

6

Tolić-Nørrelykke S. F, Schäffer E, Howard J, Pavone F. S, Jülicher F and Flyvbjerg, H. Calibration of optical tweezers with positional detection in the back focal plane, Review of scientific instruments 77, 103101 (2006).