The filter-type magnetograph is one of the main devices for measuring the solar vector magnetic field. SMAT in Huairou, a solar magnetograph, is initially used for conventional observation in China. It obtains polarization information at a fixed temperature and wavelength point, and then acquires the solar vector magnetic field through the calibration process. Due to the changeable factors such as temperature variation and mechanical errors (e.g., tooth gap), the wavelength points observed by the filter would be altered, which weakens or removes the polarization signal. It would finally affect the accuracy of solar vector magnetic field measurement. The current method of wavelength point calibration takes more time, less data and lower temporal resolution by scanning the spectral line profile and locating wavelength points. In addition, the frequent mechanical rotation lowers the lifetime of filter, which further impedes the acquisition of stable and high-quality data. Last but not least, the current method could not form a real-time and closed-loop system to distinguish and control the wavelength points. In view of this, based on the analysis of the data characteristic of SMAT, we summarize a new data pre-processing way, employ the supervised learning of machine learning and then propose a neural-network-based observation scheme of wavelength point calibration. This scheme has established the relationship between a single frame image and the corresponding wavelength point, which shortens the time of locating the position of wavelength point by a single frame image.

The present study uses the spectral line scan data from SMAT, which are 31 monochromatic images obtained by moving the filter from the blue to the red side of the spectral line, subject to the observation conditions. We first analyze the data characteristics. It is found that the Doppler velocity generated by the rotation of the Sun from west to east causes the image to exhibit a large scale uneven distribution of grayscale (brighter on one side and darker on the other). Therefore, when the filter gradually takes images from the blue side to the red side of the spectrum at different wavelength points, the image gradually changes from bright left and dark right to dark left and bright right with the shooting position (Fig. 2). Then, the data are pre-processed: selecting the data that can be fitted with a smooth spectral profile, and performing P-angle correction, edge dimming removal, and normalization on these data. Next, the information outside the solar circle is removed by polar coordinate transformation, and the image size is also decreased. Then, principal component analysis (PCA) is used to reduce the dimensionality of the data, so as to eliminate the interference of small signals and avoid problems caused by high-dimensional features. Based on this, a regression multilayer perceptron (MLP) network based on back propagation (BP) algorithm is proposed. As for the neural network, we took 70% of the data as the training set and 30% as the test set, and carried out the method validation experiment, grouping test experiment, and experiment to overcome system change, respectively. Finally, we propose the general flow of the observing wavelength point calibration algorithm and select data of different time periods to compare the traditional method and the present method in time consumption, and the results show that the method can greatly save the calibration time.

The results of the method validation experiment show that the mean square errors (MSEs) of the training set and the test set are 0.0003 and 0.0005 (Fig. 10), indicating that 99.73% of the data have the error of less than 0.0009 nm and 0.0015 nm, respectively. In the grouping test experiment, to ensure that the data of the experimental set were observed under a relatively stable system, all data were divided into five experimental sets according to the maintenance records. The MSEs of the training set and the test set are 0.0002 and 0.0027 [Figs. 11(a) and 11(b)], and the test set that is close to the training set in time has a small error in the prediction results [Fig. 11(c)], which illustrates the effectiveness of the method. The gradual increase in error in the test set far from the training set in time is consistent with the actual change of the system from stable to unstable. The experimental results of the other groups are also consistent with this situation (Fig. 12). To overcome the systematic variation in reality, we narrowed the band range and the standard deviation of the errors in the training and test sets were 0.0001 and 0.0006, respectively, indicating that 99.73% of the data had the error of less than 0.0003 nm and 0.0018 nm (Fig. 13). This result indicates that using data with a smaller band range for training the network can effectively overcome the effect of system instability. In terms of time consumption, the time required for calibration by the traditional method is 15-20 min, while that of the proposed method is less than 7 s, showing a 100 times improvement of the proposed method in calibration speed (Table 2).

In this paper, we investigate the calibration of the observing wavelength points of a birefringent narrow band filter-type magnetograph. Firstly, an effective pre-processing scheme of data is proposed based on the reasonable analysis of image data. And then, the BP-based MLP regression network calibration scheme is put forward. Afterwards, this scheme is tested by feasibility verification, grouping test experiment and the experiment to overcome system change. In addition, the scheme is compared with traditional methods in efficiency. At last, the experimental results show that this scheme is more than 100 times faster with reliable and effective data than the traditional method, so it can be regarded as a more efficient method for the calibration of observing wavelength points. Meanwhile, the regression network can be used to judge the operating condition of the instrument, namely, calibrating the same set of data with the network can give the information whether the magnetometer is stably operated or not by the residuals and variation trend of the predicted value and tag value. This method can effectively reduce the shortening of working life of the filter due to the frequent motor rotation during calibration. It can also increase the efficiency and stability of the observation on terrestrial and space solar magnetic field measurements. In the future application, this scheme could support the automatic real-time regulation of the filter position by introducing a real-time closed-loop feedback mechanism in the filter band adjustment, which could ensure the stable and high-quality output of observation data.