B-X2 · A force scale from a moving bead
How does a bead’s thermal motion reveal the stiffness of an optical trap? A stiffer trap confines the bead to smaller thermal excursions and makes its displacement relax faster. At a known temperature, the displacement variance gives stiffness; the relaxation rate gives a second estimate when the fluid drag is known.
Record a bead’s position signal in a liquid, calculate its displacement spectrum and compare two stiffness estimates. Slow sampling and long exposure show where the calibration becomes unreliable.
Recorded measurements
Record a sample to view its measurement and analysis here.
Detector record
The known detector conversion is applied to the stored voltages. The 3D replay runs at one-eighth speed.
Settings are stored with each measurement. The latest eight acquisitions remain available here.
Record a measurement, then test what it supports.
Both axes are logarithmic. This spectrum is estimated from the same stored displacement samples.
One harmonic transverse coordinate at a fixed known temperature. Stable axial trapping is assumed. Far-wall spherical Stokes drag, thermal white noise and known detector distance calibration are used. Exposure is numerically averaged along the physical trajectory. The PSD and both estimates use stored detector samples. There is no molecular force trace or optical-force field calculation. Cell and bead sizes are schematic. Motion is enlarged separately at the reported scale, without clipping or a wall boundary.
Jun et al. (2014) · calibration comparison
Sarshar et al. (2014) · displacement and spectral methods
Pérez-García et al. · finite detector exposure
Physics tutorial
BackgroundA dielectric bead trapped in water still receives random kicks from the fluid. Near the trap center, its restoring force acts like a spring.
Why it mattersThe amplitude and speed of the bead’s motion provide two ways to estimate stiffness. They depend on different calibration assumptions.
Start with the essentials
This relation assumes equilibrium and a harmonic coordinate. The measured variance can be reduced by exposure averaging.
The bead is spherical and far from walls in a Newtonian fluid. The frequency is in cycles per second.
The continuous equilibrium reference integrates to the displacement variance. The plotted spectrum is a Welch estimate of the stored voltage samples after distance conversion.
Typical misconceptionIf the spectrum is smooth, the stiffness must be accurate.
Better mental modelThe displacement calibration, fluid drag and detector bandwidth remain necessary. The simple decay estimator is withheld when the exposure or sampling cannot resolve its assumptions.
Use Resolve the corner, acquire a sample and analyze it.
What to observe: The variance and short-lag decay estimate stiffness from the same position samples. Finite duration gives random differences.Acquire Slow sampling and Long exposure, then inspect the time series and spectrum.
What to observe: Slow sampling hides the relaxation. Exposure averaging narrows the observed position distribution and biases variance stiffness upward.Acquire Wrong assumed drag and compare the two estimates.
What to observe: Changing the viscosity assumed in analysis changes the decay-based stiffness. The variance estimate uses the known temperature instead.