  The use of atomic force microscopy on nanomechanical measurements requires
accurate calibration of the cantilever's spring constant ($k_c$) and the
optical lever sensitivity ($OLS$). The thermal method, based on the
cantilever's thermal fluctuations in fluid, allows estimating $k_c$ in a fast,
non-invasive mode. However, differences in the cantilever geometry and mounting
angle require the knowledge of three correction factors to get a good
estimation of $k_c$: the contribution of the oscillation mode to the total
amplitude, the shape difference between the free and the end-loaded
configurations, and the tilt of the cantilever respect to the measured surface.
While the correction factors for traditional rectangular and V-shaped
cantilevers geometries have been reported, they must be determined for
cantilevers with non-traditional geometries and large tips. Here, we develop a
method based on finite element analysis to estimate the correction factors of
cantilevers with arbitrary geometry and tip dimensions. The method relies on
the numerical computation of the effective cantilever mass. The use of the
correction factor for rectangular geometries on our model cantilever (PFQNM-LC)
will lead to values underestimated by 16%. In contrast, experiments using
pre-calibrated cantilevers revealed a maximum uncertainty below 5% in the
estimation of the $OLS$, verifying our approach.
