  The accurate characterization of the spatial potential generated by a planar
electrode in a surface-type Paul trap is of great interest. To achieve this, we
employ a simple yet highly precise parametric expression to describe the
spatial field of a rectangular-shaped electrode. Based on this, an optimization
method is introduced to precisely characterize the axial electric field
intensity created by the powered electrode and the stray field. In contrast to
existing methods, various types of experimental data, such as the equilibrium
position of ions in a linear string, equilibrium positions of single trapped
ions and trap frequencies, are utilized for potential estimation in order to
mitigate systematic errors. This approach offers significant flexibility in
voltage settings for data collection, making it particularly well-suited for
surface electrode traps where ion probe trapping height may vary with casual
voltage settings. In our demonstration, we successfully minimized the
discrepancy between experimental observations and model predictions to an
impressive extent. The relative errors of secular frequencies were suppressed
within $\pm$ 0.5$\%$, and the positional error of ions was limited to less than
1.2 $\mu$m, all surpassing those achieved by existing methodologies.
