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 toTrue
. Set this toFalse
if you are not using Spyder/IPython and wish your entire script to complete before showing any plots. Note, you will need to explicitly callmatplotlib.pyplot.show()
if you set this toFalse
.Returns: The best estimate for the corner frequency \(f_c\).
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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)
wheref
is a 1D numpy array containing the frequency values associated with the power spectrums inpsx
andpsy
(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.
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