= Sinusoidal-stage optical trap calibration
{title2=$\beta=u_0/[A_s\sqrt{(2\pi f_c)^2+\Omega^2}]$}
For an overdamped <harmonic optical trap>, impose a known sinusoidal local fluid <velocity> of amplitude $u_0$ and <angular frequency> $\Omega$. The coherent bead response has amplitude $A_x=u_0/\sqrt{(k/\zeta)^2+\Omega^2}$. Measuring the thermal corner <frequency> $f_c=k/(2\pi\zeta)$ and detector-voltage amplitude $A_s=A_x/\beta$ therefore determines the position sensitivity in the displayed formula without a drag coefficient as input. Use a thermal record with the drive line removed to obtain stiffness from the <equipartition theorem>. Fluid-following, detector response and hydrodynamic corrections must remain valid. Combined thermal and stage measurements have experimentally calibrated an optical trap without drag as an input.<Calibration of optical tweezers with positional detection in the back-focal-plane by Simon F. Tolić-Nørrelykke and others>[2006 preprint abstract: calibration without drag as an input]{ref}
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