An overview of existing algorithms for resolving the 180^° ambiguity in vector magnetic fields: Quantitative tests with synthetic data

We report here on the present state-of-the-art in algorithms used for resolving the 180° ambiguity in solar vector magnetic field measurements. With present observations and techniques, some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.