  We demonstrate a method of micromotion minimization of a trapped ion in a
linear Paul trap based on the precision measurement of the ion trapping
position displacement due to a stray electric field in the radial plane by ion
fluorescence imaging. The amount of displacement in the radial plane is
proportional to the strength of a stray electric field. Therefore, we evaluated
the micromotion compensation condition by measuring the ion displacements from
the ion equilibrium position using two different radial trap frequencies with
various combinations of the compensation voltage. The residual electric field
uncertainty of this technique reached a few volts per meter. This compensation
technique does not depend on the orientation of the incident cooling laser or
the detuning and imaging direction. Therefore, this method is suitable for a
planar ion trap, a stylus ion trap, which limits the propagation angle of
lasers, or miniaturized ion trap systems for sensing and metrological
applications.
