force_calibration: coupling model for active calibration

[JoepVanlier]

Why this PR?
When performing active calibration, we get a smaller velocity around the beads than expected when dealing with a dual trap configuration. This can lead to biases when not taken into account in the model that predicts the oscillation amplitude of the beads:

$R_{d, corrected} = c R_d$
$R_{f, corrected} = \frac{R_f}{c}$
$\kappa_{corrected} = \frac{\kappa}{c^2}$

Various models exist to calculate the correction factor c. In the context of optical tweezers, I have seen Oseen (acting force being a point function) and Rotne Prager used [1]. For us, this seems to correct well for large distances, but seems to fail at short distances*. [2] seems to fare better for both regimes, but only covers oscillations parallel to the bead axes. A fraction with a reciprocal polynomial for oscillations perpendicular to the bead axes can be found in [3].

Based on these two models, we can compute a combined model (see the documentation for more information on this). If we use this to correct data over the entire trap range, we see that this corrects the calibration factors pretty nicely. See graphs below.

Docs here: whats new, theory, tutorial and example.

Note: I have marked this functionality as alpha, since testing has been somewhat limited so far. That said, for conditions where they are valid, the results obtained with these models is much more reasonable than without.

Calibrations are obtained by putting trap 2 in a static location and moving trap 1 in the x-direction. We are showing results for trap 2 here, since there is an unexplained additional dependence of the sensitivity on the x position for trap 1. Note that we have used the Stimson model for horizontal oscillations and the Wakiya approximation model as presented by Goldmann model for Y oscillation here.

Active calibration with two 4.38 um beads (X). Here we moved a second bead around in the trap range of motion and calibrating the bead that was at a fixed position.

Active calibration with two 4.38 um beads (Y). Here we moved a second bead around in the trap range of motion and calibrating the bead that was at a fixed position.

[1] https://core.ac.uk/download/pdf/270293467.pdf
[2] Stimson, M., & Jeffery, G. B. (1926). The motion of two spheres in a viscous fluid. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 111(757), 110-116 (2007).
[3] Goldman, A. J., Cox, R. G., & Brenner, H. (1966). The slow motion of two identical arbitrarily oriented spheres through a viscous fluid. Chemical Engineering Science, 21(12), 1151-1170.

• Note that [2] contains a typographical error in equation 37, where it should read 4/3 and not 2/3
• Note that the value reported in [2] for alpha=0.5 should be 0.6596.