bib

docs/theory/force_calibration/active.rst

@@ -18,12 +18,18 @@ This viscosity in turn depends strongly on the local temperature around the bead
 physical parameters (e.g. the power of the trapping laser, the buffer medium, the bead size and material)
 and is typically poorly known.
 
-During active calibration, the trap or nanostage is oscillated sinusoidally. These oscillations result
-in a driving peak in the force spectrum. Using power spectral analysis, the force can then be calibrated
-without prior knowledge of the drag coefficient.
-
-When the power spectrum is computed from an integer number of oscillations, the driving peak is visible
-at a single data point at :math:`f_\mathrm{drive}`.
+During active calibration, the nanostage is oscillated sinusoidally.
+The fluid then co-moves with the stage, forcing the bead out of the center of the trap sinusoidally.
+This oscillatory motion can be measured and results in a peak in the power spectrum spectrum (the driving peak).
+Using power spectral analysis on the force detector readout, we can estimate the amplitude of this peak in volts.
+Based on a model of the bead position in the trap we can calculate how much the bead should move.
+This model uses the known amplitude of the stage motion (in microns) and the corner frequency parameter of the thermal fit to calculate an expected amplitude in microns.
+Considering that we now have the amplitude both in microns and volts, this means we can determine the positional calibration without prior knowledge of the drag coefficient.
+
+Mathematical background
+^^^^^^^^^^^^^^^^^^^^^^^
+
+When the power spectrum is computed from an integer number of oscillations, the driving peak is visible at a single data point at :math:`f_\mathrm{drive}`.
 
 .. image:: figures/driving_input.png
   :nbattach: