Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: the Effects of Noise and Limited Spatial Resolution

TL;DR

This paper examines how noise and limited resolution affect methods that resolve the azimuthal ambiguity in solar magnetic field data using the divergence-free property, proposing improvements to enhance accuracy.

Contribution

It introduces a two-step approach to improve the global minimisation method for resolving azimuthal ambiguity under noisy and limited resolution conditions.

Findings

Current divergence-based methods are sensitive to noise and resolution limits.

The proposed two-step approach improves ambiguity resolution in synthetic tests.

Smoothing algorithms help mitigate noise effects in magnetic field data.

Abstract

We investigate how the azimuthal ambiguity in solar vector magnetogram data can be resolved by using the divergence-free property of magnetic fields. In a previous article, by Crouch, Barnes, and Leka (Solar Phys. 260, 271, 2009), error-free synthetic data were used to test several methods that each make a different assumption about how the divergence-free property can be used to resolve the ambiguity. In this paper this testing is continued with an examination of the effects of Poisson photon noise and limited instrumental spatial resolution. We find that all currently available methods based on the divergence-free property can produce undesirable results when photon noise or unresolved structure are present in the data. We perform a series of experiments aimed at improving the performance of the global minimisation method, which is the most promising of the methods. We present a two-step approach that produces reasonable results in tests using synthetic data. The first step of this approach involves the global minimisation of a combination of the absolute value of the approximation for the divergence and a smoothness constraint, which is designed to minimise the difference between the magnetic field in neighbouring pixels. In the second step, pixels with measurements known to be strongly affected by photon noise are revisited with a smoothing algorithm that also seeks to minimise the difference between the magnetic field in neighbouring pixels.