PassiveCalibrationModel

lumicks.pylake.PassiveCalibrationModel

class PassiveCalibrationModel(bead_diameter, viscosity=None, temperature=20, hydrodynamically_correct=False, distance_to_surface=None, rho_sample=None, rho_bead=1060.0, fast_sensor=False, axial=False)

Model to fit data acquired during passive calibration.

Passive calibration involves fitting a power spectral density using a physical model of Brownian motion of a bead inside an optical trap.

The power spectrum calibration algorithm implemented here is based on a number of publications by the Flyvbjerg group at DTU [1] [2] [3] [4] [5] [6]. Please refer to the theory section and tutorial on force calibration for more information on the calibration methods implemented.

Parameters:

• bead_diameter (float) – Bead diameter [um].

• viscosity (float, optional) – Liquid viscosity [Pa*s]. When omitted, the temperature will be used to look up the viscosity of water at that particular temperature.

• temperature (float, optional) – Liquid temperature [Celsius].

• hydrodynamically_correct (bool, optional) – Enable hydrodynamic correction.

• distance_to_surface (float, optional) – Distance from bead center to the surface [um]. When specifying None, the model will use an approximation which is only suitable for measurements performed deep in bulk.

• rho_sample (float, optional) – Density of the sample [kg/m^3]. Only used when using hydrodynamic corrections.

• rho_bead (float, optional) – Density of the bead [kg/m^3]. Only used when using hydrodynamic corrections.

• fast_sensor (bool) – Fast sensor? Fast sensors do not have the diode effect included in the model.

• axial (bool) – Is this an axial force model?

Raises:

• ValueError – If physical parameters are provided that are outside their sensible range.

• ValueError – If the distance from the bead center to the surface is set smaller than the bead radius.

• ValueError – If the hydrodynamically correct model is enabled, but the distance to the surface is specified below 0.75 times the bead diameter (this model is not valid so close to the surface).

• NotImplementedError – If the hydrodynamically correct model is selected in conjunction with axial force calibration.

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).

Examples

f = lk.File("passive_calibration.h5")
force_slice = f.force1x

# Decalibrate existing data
volts = force_slice / force_slice.calibration[0]["Response (pN/V)"]

power_spectrum = lk.calculate_power_spectrum(
    volts.data,
    sample_rate=78125,
    excluded_ranges=[[4400, 4500]],  # Exclude a noise peak
    num_points_per_block=350,
)

model = lk.PassiveCalibrationModel(
    bead_diameter=4.89,
    temperature=25,
    hydrodynamically_correct=True,  # Should use hydrodynamic model for big beads
)

fit = lk.fit_power_spectrum(power_spectrum, model)
fit.plot()

__call__(f, fc, diffusion_constant, *filter_params) → ndarray

Call self as a function.

calibration_results(fc, diffusion_constant_volts, filter_params, fc_err, diffusion_constant_volts_err, filter_params_err) → dict

Compute calibration parameters from cutoff frequency and diffusion constant.

Parameters:

• fc (float) – Corner frequency, in Hz.

• diffusion_constant_volts (float) – Diffusion constant, in V^2/s

• filter_params (list of float) – Parameters for the filter model.

• fc_err (float) – Corner frequency standard error, in Hz

• diffusion_constant_volts_err (float) – Diffusion constant standard error, in Hz

• filter_params_err (list of float) – Standard errors for the filter model