  Colloidal probes are often used in force microscopy when the geometry of the
tip-sample interaction should be well controlled. Their calibration requires
the understanding of their mechanical response, which is very sensitive to the
details of the force sensor consisting of a cantilever and the attached
colloid. We present analytical models to describe the dynamics of the
cantilever and its load positioned anywhere along its length. The thermal noise
calibration of such probes is then studied from a practical point of view,
leading to correction coefficients that can be applied in standard force
microscope calibration routines. Experimental measurements of resonance
frequencies and thermal noise profiles of raw and loaded cantilevers
demonstrate the validity of the approach.
