  Optical tweezers are highly versatile laser traps for neutral microparticles,
with fundamental applications in physics and in single molecule cell biology.
Force measurements are performed by converting the stiffness response to
displacement of trapped transparent microspheres, employed as force
transducers. Usually, calibration is indirect, by comparison with fluid drag
forces. This can lead to discrepancies by sizable factors. Progress achieved in
a program aiming at absolute calibration, conducted over the past fifteen
years, is briefly reviewed. Here we overcome its last major obstacle, a
theoretical overestimation of the peak stiffness, within the most employed
range for applications, and we perform experimental validation. The discrepancy
is traced to the effect of primary aberrations of the optical system, which are
now included in the theory. All required experimental parameters are readily
accessible. Astigmatism, the dominant effect, is measured by analyzing
reflected images of the focused laser spot, adapting frequently employed video
microscopy techniques. Combined with interface spherical aberration, it reveals
a previously unknown window of instability for trapping. Comparison with
experimental data leads to an overall agreement within error bars, with no
fitting, for a broad range of microsphere radii, from the Rayleigh regime to
the ray optics one, for different polarizations and trapping heights, including
all commonly employed parameter domains. Besides signalling full
first-principles theoretical understanding of optical tweezers operation, the
results may lead to improved instrument design and control over experiments, as
well as to an extended domain of applicability, allowing reliable force
measurements, in principle, from femtonewtons to nanonewtons.
