A new post-hoc flat field measurement method for the Solar X-ray and Extreme Ultraviolet Imager onboard the Fengyun-3E satellite

Space weather is important to satellites, spacecraft and astronauts as human exploration expands from our home planet Earth to the Moon, Mars, and beyond. The expansion of technological infrastructure on Earth also highlights the impact of space weather. The primary driver of space weather is the Sun (Schwenn 2006). Its highly dynamic atmosphere produces various activities such as solar flares and coronal mass ejections. In the extreme ultraviolet (EUV) wavelength, almost all of solar activities in the outer layers of the solar atmosphere (i.e., the chromosphere, the transition region, and the corona) can be observed. Solar active regions usually show bright loop systems in EUV images, and with the evolution of the magnetic field in active regions, the loop systems of the active regions also change dynamically. When a flare occurs, the source region can be identified from EUV images, and then the flare process can be tracked and studied (Song et al. 2022). In EUV images, coronal holes are also observed, which are cooler, less dense regions in solar atmosphere. Coronal holes are generally believed to be the source of the solar wind that can cause geomagnetic storms and other space weather disturbances (Pulkkinen 2007). Other solar activities, such as EUV waves (Hou et al. 2022) and filament eruptions can also be well represented on EUV images. Moreover, the variability of solar EUV radiation influences Earth’s atmosphere and further climate on different time-scales. On the short time-scale, major solar flares can affect Earth’s ionosphere, causing disturbances such as blackout of high-frequency radio communication and degradation of low-frequency navigation signals. Solar influence on Earth’s climate is often reflected in the radiation changes of EUV and other wavelengths on the 11-year period of solar cycles (Lockwood 2012).

Therefore, the EUV wavelength is widely used in solar activity research and space weather forecasting. Due to the absorption of Earth’s atmosphere, solar EUV telescopes need to be onboard a satellite or spacecraft. For example, the Transition Region and Coronal Explorer (TRACE, Handy et al. 1999), Extreme ultraviolet Imaging Telescope (EIT, Delaboudinière et al. 1995) for the SOHO Mission, the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI, Howard et al. 2008a) on the twin STEREO spacecraft, the Sun Watcher using Active Pixel System detector and Image Processing (SWAP, Halain et al. 2013) telescope on the PROBA2 technological mission, the Atmospheric Imaging Assembly (AIA, Lemen et al. 2012; Boerner et al. 2012) of the Solar Dynamics Observatory (SDO, Pesnell et al. 2012), and the Solar X-ray and Extreme Ultraviolet Imager (X-EUVI, Chen et al. 2022a, b) onboard the Fengyun-3E (FY-3E, Zhang et al. 2022) satellite. FY-3E is the latest one of China’s second generation polar-orbiting meteorological satellites. Launched on July 5, 2021, FY-3E is now operated in a Sun-synchronous orbit (i.e., dawn/dusk orbit) at $\sim$836 km altitude with an inclination of 98.75\degr. The X-EUVI has multiple X-ray and EUV channels that can be used for space weather forecasting and scientific research. In the EUV wavelength, it provides full-disk 195 Å images of the Sun with a moderate spatial resolution ($\sim$2.\arcsec5 per pixel) and a high time resolution up to a few seconds. In addition, the solar images of X-EUVI can be combined with the images of the Advanced Space-based Solar Observatory (ASO-S, Gan et al. 2019) and the Chinese H${\alpha}$ Solar Explorer mission (CHASE, Li et al. 2022) for multi-band comprehensive observations to study solar activities.

Due to the large-scale vignetting in the optical system, the small-scale pixel-to-pixel variation of the charge-coupled device (CCD) detector and the unavoidable intermediate-scale contamination or dust from the optical elements and the CCD detector, the recorded data from all of the EUV solar telescopes is non-uniform even if the target is a light source with uniform light emitting area. In addition, the nickel mesh supporting the focal-plane filter can also create grid-like features on the observed image, resulting in increased non-uniformity (Boerner et al. 2012; Seaton et al. 2013). Therefore, flat field processing is generally employed to remove the non-uniformity of the whole system in the production of high-quality scientific data from original observed data. However, up to now, how to acquire precise flat field image is still one of the most challenging problems for full-disk solar observations. The best and easy way to measure the instrumental flat field is to find a highly uniform light source (Howard et al. 2008b; Kentischer et al. 2008; Bai et al. 2017; Wang et al. 2019), which is extremely difficult at the EUV wavelength. An alternative way is to adopt a non-uniform light source such as the Sun itself and the flat field is generated by taking several offset solar images with slightly shifted locations on the detector. The offset can be realized by changing the tip-tilt angles of the second mirror. It can also be taken by changing the pointing of the spacecraft. Both of the methods are used for flat field measurement of the EUV imagers of the Sun, e.g., TRACE and SDO/AIA. Once series of offset images are taken, the shifts in the x and y directions relative to the reference image are determined and then the flat field is generated by the Kuhn-Lin algorithm (Kuhn et al. 1991). Other algorithms were also proposed to derive flat field (Chae 2004; Xu et al. 2016; Gao et al. 2020; Li et al. 2021).

If the offset solar images have acentric rotation on the detector due to the attitude control of a spacecraft, there are both rotation and shift during the image registration process, making it difficult to employ the above-mentioned methods to generate the flat field. In this paper, we propose a new post-hoc method to create flat field from the routine concentric rotated coronal images taken by FY-3E/X-EUVI. Similar method has been used for the generation of flat field and polarized offset from regular observed full-disk photospheric filtergrams and Stokes $\frac{Q}{I},\ \frac{U}{I},\ \frac{V}{I}$ maps, respectively (Potts & Diver 2008; Wachter & Schou 2009; Bai et al. 2018). Here we extend it to regular observational data of the corona. The principle of our method is presented in Section 2. Section 3 shows the results of the method application in observational images, following with a conclusion and discussion section (Section 4).

The recorded image I(x,y) taken by a solar EUV telescope can be expressed as:

where $I_{s}(x,y),\ f(x,y)$ and $I_{d}$ represent the solar-disk coronal radiation maps, flat field and dark field of the whole system, respectively. From Eq. 1, the solar-disk radiation $I_{s}(x,y)$ can be recovered from the original recorded data $I(x,y)$ once the flat field and dark field are obtained. The key step is to measure the flat field and dark field. If we try to divide the solar-disk coronal radiation into two parts, $I_{s}(x,y)$ becomes:

Here $I^{l}_{s}(x,y)$ represents the large-scale component that is to say the quiet coronal radiation with limb brightening pattern caused by the optical thin effect of EUV lines (Withbroe 1970), which rarely changes with time (i.e., with low frequency in time variation). $I^{h}_{s}(x,y)$ represents the time-varying medium and small-scale components, such as the active region loops, the coronal holes, and the coronal bright points (i.e., with high frequency in time variation).

If a series of EUV coronal radiation maps $I_{s}(x,y,t)$ having concentric rotation within several days are used to create a data cube and the median value is taken for each spatial pixel, the time-varying component $[I^{h}_{s}(x,y,t)]_{median}\approx 0$ while the large-scale component remains almost the same. Then Eq. 2 can be written as:

Once the non-uniformity of the $I^{l}_{s}(x,y)$ is known, we can divided it from the $[I_{s}(x,y,t)]_{median}$ image and the final image can be treated as a uniformed light source used for flat field measurement. According to Eq. 1, the flat field is calculated from the median of dark-corrected routine EUV coronal images with :

Now the main task is to calculate the the large-scale components $I^{l}_{s}(x,y)$, which has circular symmetry in general since what we observed is a projection of the spherical coronal radiation. It is more convenient to make a conversion of coordinates from Cartesian lattice to polar coordinates to deal with the circular symmetry.

The r and $\theta$ in Eq. 5 are the radius and azimuth angles, respectively. And $I^{{}^{\prime}}(r,\theta)$ is the median of series of dark-corrected routine coronal images in polar coordinates. If we take the median value for the intensities along all of the azimuth angles with the same radius, the quiet coronal radiation and limb brightening curve can be derived, which is described in the below equation:

We are able to further obtain the large-scale coronal component $I^{l}_{s}(x,y)$ by filling in the values in the azimuth direction for each radius with the values in Eq. 6 and transforming it back to Cartesian coordinates. Finally, the flat field is generated from Eq. 4, and the flat field corrected corona radiation is derived with Eq. 1.

We use the EUV coronal images from FY-3E/X-EUVI 195 Å channel to test the performance of the method. Since FY-3E is a polar-orbiting meteorological satellite, its main pointing is Earth and its observational images of the Sun have significant rotation. The X-EUVI has a two-dimensional turntable to point and track the Sun. It also equipped with an imaging stabilization system to rapidly compensate the jitters from the satellite and the turntable to improve the spatial resolution. The routine coronal images rotate with an orbit period of $\sim$101.5 minutes, which is concentric with the help of the imaging stabilization system. If we create a data cube from the staked concentric rotated images taken within one orbit and take the median values for each spatial pixel, the assumption that the $I^{h}_{s}(x,y)\approx 0$ still works. Then we can employ the method in section 2 to derive the flat field.

The routine EUV 195 Å imaging data from FY-3E/X-EUVI has imaging rotation with a speed of 3.5\degr per minute. If several offset solar images taken by changing the satellite’s pointing are used to derive the flat field, it will be very difficult because there are both rotation and shift during the image registration process. In the paper, we proposed a new post-hoc flat field measurement method taking advantage of the concentric rotation property in the routine data taken with the imaging stabilization system of the X-EUVI. An advantage of the post-hoc method is that it does not need to occupy the observation time for the calibration of flat field, which can facilitates convenient and continuous observations, and this is valuable for space weather operations.

The principle of our method is that the small-scale and time-varying component of the coronal radiation is approximately zero if we make a data cube from plenty of concentric rotation images and take the median value for each pixel along the time axis. The large-scale and invariable component can further be derived assuming that it is symmetrical under all rotations about the center of solar disk. Once the large-scale and invariable coronal radiation is removed, the remaining part is the flat field. For the X-EUVI’s routine EUV 195 Å imaging data, the flat field can be generated with cadences from hundreds minutes (one orbit) to several days. The accuracy of the flat field depends on how much coronal radiation is left with the limited data and the processing method. In the paper, the flat field is derived with the period of one orbit, one, two and three days. From the comparison, it is found that higher flat field accuracy can be achieved by employing more data. Obviously if more data (larger n) are used, it takes more time to generated a flat field. Once the instrumental flat field changes during this period, we merely obtained the averaged flat field. From the comparison of Figures 3(a) and 3(b), our method can monitor the changes in the flat field image due to the contamination on the CCD detector and other reasons, and thus it can support routine calibration. It provides a convenient flat field calibration option for observation instruments that are difficult to maintain manually, such as space-based instruments and automatic observatories located in remote areas. The signal to noise ratio from the original imaging data is not included in the derivation of flat field in section 2, which is discussed in Potts & Diver (2008) and Bai et al. (2018) and is the same for coronal observations.

The flat field from July 22, 2021 shows that the new method is able to measure the instrumental spot-like non-uniformity possibly from the contamination on the detector, which mostly disappear after the in-orbit self-cleaning process seen from that taken on October 29 (see Figures3(a) and 3(b)). The dramatic change in the flat field images before and after the self-cleaning process also demonstrates the effectiveness of the self-cleaning mode of the X-EUVI. Furthermore, the quasi-periodic grid-like non-uniformity possibly from the obscuration of the support mesh on the rear filter can also be obtained from the flat field, which have fluctuation with a small amplitude and a period of about 30 pixels, and it is roughly in line with the parameters of the support mesh. After the flat field correction, the instrumental non-uniformity from the original data is effectively removed. The narrow and bright ring at solar limb in the flat field image (see the blue arrow in Figure 3(d)) possibly caused by limited instrument pointing accuracy and stability, which can lead to sub-pixel drift in the position of the center of solar disk, and sometimes resulting in slight asymmetry in the derived median image with Eq. 4. It may also be caused by the limited accuracy of the derived solar disk center. In future works, we will try to remove the influence of the ring and study the changes of the flat field on different time-scales. To better illustrate the availability of our flat field method, we compare the X-EUVI 195 Å data after dark and flat fieldcorrections with the 193 Å imaging data from SDO/AIA. We found that they are consistent with each other except that AIA has higher spatial resolution. Overall, we provide a candidate method for the flat field measurement of current and future solar EUV telescopes.