PHS3000 Optical Tweezers

This documents the monashspa.PHS3000.optical_tweezers library that you will import into code used in the PHS3000 unit when performing experiment 1.3 Optical Tweezers.

monashspa.PHS3000.optical_tweezers.cf_linearised(f, ps, initial_fc, call_show=True)[source]

Finds the corner frequency value for a lorentzian power spectrum

Finds the corner frequency (\(f_c\)) of a power spectrum of the form:

\(y=\frac{a}{(f_c^2+f^2)}\)

by transforming into the logarithmic domain and determining when the spectrum is linearised.

Parameters:

  • f – A 1D numpy array containing the frequency values associated with the power spectrum

  • ps – A 1D numpy array containing the power spectrum data (must be the same length as f)

  • initial_fc – An initial guess for the corner frequency

Keyword Arguments:

call_show – Whether to call matplotlib.pyplot.show() at the end of the function (prior to returning). Defaults to True. Set this to False if you are not using Spyder/IPython and wish your entire script to complete before showing any plots. Note, you will need to explicitly call matplotlib.pyplot.show() if you set this to False.

Returns:

The best estimate for the corner frequency \(f_c\).

monashspa.PHS3000.optical_tweezers.corner_freq(f, ps, initial_fc, call_show=True)[source]

Finds the corner frequency value for a lorentzian power spectrum

Finds the corner frequency (\(f_c\)) of a power spectrum of the form:

\(y=\frac{a}{(f_c^2+f^2)}\) by nonlinear fitting.

Parameters:

  • f – A 1D numpy array containing the frequency values associated with the power spectrum

  • ps – A 1D numpy array containing the power spectrum data (must be the same length as f)

  • initial_fc – An initial guess for the corner frequency

Keyword Arguments:

call_show – Whether to call matplotlib.pyplot.show() at the end of the function (prior to returning). Defaults to True. Set this to False if you are not using Spyder/IPython and wish your entire script to complete before showing any plots. Note, you will need to explicitly call matplotlib.pyplot.show() if you set this to False.

Returns: a 1D numpy array (\(f_c\), \(uf_c\)) which contains

the best estimate for the corner frequency \(f_c\) and the uncertainty in the corner frequency \(uf_c\).

monashspa.PHS3000.optical_tweezers.ps_load(filepath)[source]

Imports the power spectrum data from optical tweezers file

Parameters:

filepath – The path to the .lvm file produced by the optical tweezers acquisition software

Returns:

A tuple (f, psx, psy) where f is a 1D numpy array containing the frequency values associated with the power spectrums in psx and psy (which are also both 1D numpy arrays).

monashspa.PHS3000.optical_tweezers.trap_k_theory(r, w, alpha, eccentricity, I)[source]

Calculates the theoretical spring constant (\(k\)) for an optical tweezers trap for specified parameters

Calculates using the equation:

\(k=\alpha\,I_0\,\omega\,\frac{2\,\pi\,\epsilon^3}{c\,\xi^3}\left(\sqrt{\frac{\pi}{2}}\,\left(\left(\frac{\xi\,a}{\epsilon}\right)^2-1\right)\,\mathrm{exp}\left[-\frac{a^2}{2}\right]\,\mathrm{erf}\left[\frac{\xi\,a}{\sqrt{2}\,\epsilon}\right]+\frac{\xi\,a}{\epsilon}\,\mathrm{exp}\left[-\frac{a^2}{2\,\epsilon^2}\right]\right)\)

from Bechhoefer 2002. Corrects for the difference in definition of beam waist between Bechhoefer and standard laser literature_.

If the input arguments are numpy arrays, then the output will also be an array of the appropriate dimension. Otherwise a single number will be returned.

Parameters:

  • r – Sphere radius (m)

  • w – The \(1/e^2\) radius (beam waist) of the trapping beam (m)

  • alpha – \(n_p^2/n_0^2 - 1\), where \(n_p\) is the refractive index of the microsphere and \(n_0\) is the refractive index of water

  • eccentricity – The eccentiricty of the trapping beam

  • I – Trapping beam intensity (W/m^2)

Returns:

The theoretical spring constant (\(k\))

Return type:

k