  We explain and demonstrate a new method of force- and position-calibration
for optical tweezers with back-focal-plane photo detection. The method combines
power spectral measurements of thermal motion and the response to a sinusoidal
motion of a translation stage. It consequently does not use the drag
coefficient of the trapped ob ject as an input. Thus, neither the viscosity,
nor the size of the trapped ob ject, nor its distance to nearby surfaces need
to be known. The method requires only a low level of instrumentation and can be
applied in situ in all spatial dimensions. It is both accurate and precise:
true values are returned, with small error-bars. We tested this experimentally,
near and far from surfaces. Both position- and force-calibration were accurate
to within 3%. To calibrate, we moved the sample with a piezo-electric
translation stage, but the laser beam could be moved instead, e.g. by
acousto-optic deflectors. Near surfaces, this precision requires an improved
formula for the hydrodynamical interaction between an infinite plane and a
micro-sphere in non-constant motion parallel to it. We give such a formula.
