A nonlinear solar magnetic field calibration method for the filter-based magnetograph by the residual network

Abstract

The method of solar magnetic field calibration for the filter-based magnetograph is normally the linear calibration method under weak-field approximation that cannot generate the strong magnetic field region well due to the magnetic saturation effect. We try to provide a new method to carry out the nonlinear magnetic calibration with the help of neural networks to obtain more accurate magnetic fields. We employed the data from Hinode/SP to construct a training, validation and test dataset. The narrow-band Stokes I, Q, U, and V maps at one wavelength point were selected from all the 112 wavelength points observed by SP so as to simulate the single-wavelength observations of the filter-based magnetograph. We used the residual network to model the nonlinear relationship between the Stokes maps and the vector magnetic fields. After an extensive performance analysis, it is found that the trained models could infer the longitudinal magnetic flux density, the transverse magnetic flux density, and the azimuth angle from the narrow-band Stokes maps with a precision comparable to the inversion results using 112 wavelength points. Moreover, the maps that were produced are much cleaner than the inversion results. The method can effectively overcome the magnetic saturation effect and infer the strong magnetic region much better than the linear calibration method. The residual errors of test samples to standard data are mostly about 50 G for both the longitudinal and transverse magnetic flux density. The values are about 100 G with our previous method of multilayer perceptron, indicating that the new method is more accurate in magnetic calibration.

Calibration scheme for space-borne full-disk vector magnetograph under the influence of orbiter velocity

“…Many studies have used this type of method in tackling astronomical problems. Guo et al (2021) used this method to the inversion of magnetic field. The design of the residual block in ResNet makes training deep networks possible.…”

“…We anticipate what the output azimuth angle is before correcting the 180 degree ambiguity, that is, the predicted transverse field direction can be the reverse of the actual direction. So, we then use the residual between prediction and target, which was used by Guo et al (2021) when training the network of azimuth angle:…”

“…Asensio Ramos & Díaz Baso (2019) applies convolutional neural network (CNN) to solar magnetic field calibration for the first time. Guo et al (2020Guo et al ( , 2021 used MLP and CNN to perform magnetic field inversion on Hinode/SP data and demonstrated the feasibility of neural network for single-wavelength magnetic field calibration. Higgins et al (2021) used the unet code to invert the HMI/SDO data and used the output of regression-by-classification.…”

Physically Motivated Deep Learning to Superresolve and Cross Calibrate Solar Magnetograms

“…Despite the wealth of archival data, differences in resolution, spectral inversion techniques, instrument noise levels, or other instrument properties prevent us from easily combining data across instruments to study magnetic field structures over multiple solar cycles (Figure 1) (e.g., Díaz Baso & Asensio Ramos 2018). Compared to traditional cross-calibration techniques such as pixel-to-pixel comparison (Liu et al 2012), histogram equalization (Riley et al 2014), or harmonic scaling (Virtanen & Mursula 2019), machine learning (ML) has previously been shown to successfully calibrate magnetograms (Guo et al 2021;Higgins et al 2022).…”

Stokes inversion techniques with neural networks: analysis of uncertainty in parameter estimation

“…Another approach, based on real data, was described in (Guo et al, 2021) or (Liu et al, 2020). The authors of the latter used real data taken from the Near InfraRed Imaging Spectropolarimeter at the Big Bear Solar Observatory.…”