Preamble

Vol. 66 No. 5

September 2025

Acta Astronomica Sinica

In-flight Radiometric Calibrations of WST and SDI

LI Gen¹,² LI Ying¹,²† LI Qiao¹,² LI Hui¹,²
(1 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023)
(2 School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026)

Abstract

The Lyman-alpha Solar Telescope (LST) is one of the payloads onboard the Advanced Space-based Solar Observatory (ASO-S, also known as "Kuafu-1") satellite, comprising three scientific instruments: the White-light Solar Telescope (WST), the Solar Disk Imager (SDI), and the Solar Corona Imager (SCI). Both WST and SDI have a field of view of 1.2 solar radii (with the full field equivalent to 38.4 arcminutes) and operate in the (360±2) nm (near white-light) and (121.6±4.5) nm (ultraviolet Lyman-alpha) wavebands, respectively. Imaging data from WST and SDI enable exploration of solar eruption processes in the lower solar atmosphere (photosphere, chromosphere, and transition region), including studies of flare triggering mechanisms, physical properties of white-light flares, morphological evolution and kinematics of erupting filaments/prominences, and derivation of solar atmospheric physical parameters. To obtain physical parameters of different solar features observed by WST and SDI—such as flare energy, prominence temperature, and density—it is necessary to convert their observed digital numbers (DN) into physical units (e.g., erg·cm⁻²·s⁻¹·sr⁻¹) through a process known as radiometric calibration. Radiometric calibration is an essential step in the scientific data production pipeline for WST and SDI. Currently, both instruments use the Sun as their reference source for in-flight calibration: WST employs solar spectral data released by the American Society for Testing and Materials (ASTM) in 2020, while SDI utilizes observations from the Extreme Ultraviolet Sensors (EUVS) onboard the Geostationary Operational Environmental Satellite R (GOES-R). This paper presents the in-flight radiometric calibration coefficients and their uncertainties for WST and SDI during normal operations from August 2023 to February 2024. An empirical formula is derived by fitting the daily mean values of the WST calibration coefficients. Using radiometrically calibrated data, researchers can calculate the energy radiated by solar flares in both white-light and Lyman-alpha bands and determine prominence densities, thereby facilitating the achievement of WST and SDI scientific objectives.

Keywords Sun: flares, Sun: prominences, techniques: radiometric calibration, instrumentation: WST, instrumentation: SDI

1 Introduction

The Sun, our nearest star, provides energy for Earth while its atmospheric activities—such as solar flares and coronal mass ejections—serve as primary sources of space weather disturbances that can have catastrophic impacts on terrestrial life \cite{1,2}. The energy driving solar eruptive events originates primarily from the solar magnetic field \cite{3,4}. Consequently, studies of solar magnetic fields, flares, and coronal mass ejections not only deepen our understanding of the energy sources, triggering mechanisms, and dissipation processes of solar eruptive activities but also provide crucial theoretical support for space weather forecasting \cite{5}.

China's first comprehensive solar exploration satellite—the Advanced Space-based Solar Observatory (ASO-S, Chinese name "Kuafu-1")—was successfully launched on October 9, 2022 \cite{6,7,8,9}. The primary scientific objectives of ASO-S are to investigate the origin and evolution of solar magnetic fields, flares, and coronal mass ejections (collectively termed "one magnetic field and two eruptions") and to understand the causal relationships among them \cite{8,9}.

The Lyman-alpha Solar Telescope (LST) is one of three payloads onboard ASO-S, consisting of three scientific instruments: the White-light Solar Telescope (WST), the Solar Disk Imager (SDI), and the Solar Corona Imager (SCI) \cite{10,11,12}. WST and SDI share a field of view of 1.2 solar radii (38.4 arcminutes), operating in the (360±2) nm (near white-light) and (121.6±4.5) nm (ultraviolet Lyman-alpha) wavebands, respectively. SCI has a field of view of 35.2′–80.0′ with two observation bands: (122.6±3) nm (ultraviolet Lyman-alpha) and (700±32) nm (white-light). LST is designed to continuously image the solar disk and inner corona up to 2.5 solar radii simultaneously in both the ultraviolet Lyman-alpha and white-light bands, with the goal of tracking solar eruptive phenomena from the disk center to the inner corona, exploring relationships between eruptive prominences, flares, and coronal mass ejections, studying the dynamic processes and evolution of solar eruptions, diagnosing the solar wind, and deriving physical parameters of the solar atmosphere \cite{10}.

Raw data from solar telescopes are recorded as digital numbers (DN) and must undergo calibration procedures (such as dark-field and flat-field corrections) before scientific analysis. To derive physical parameters of the solar atmosphere—such as density and energy—further radiometric calibration is required. Radiometric calibration comprises two types: ground-based (also called laboratory) calibration and in-flight calibration. For in-flight calibration, astronomers typically identify celestial objects within the instrument's field of view that have known irradiance and can be observed stably over long periods. These reference sources include stars, the Sun, and solar system objects (such as planets and comets). Many space-based solar telescopes have employed stars as calibration references, including the Ultraviolet Coronagraph Spectrometer (UVCS) \cite{13} and Large Angle Spectroscopic Coronagraph (LASCO) \cite{14} onboard the Solar and Heliospheric Observatory (SOHO), and the Metis coronagraph onboard Solar Orbiter (SO) \cite{15}. When using stars for in-flight radiometric calibration, the selection criteria typically include: (1) bright stars (apparent magnitude < 8); (2) appropriate spectral types; (3) stable brightness with long-term observability; and (4) visibility to the telescope. For example, SO/Metis in-flight calibration primarily used B-type stars. During calibration observations in June 2020 and March 2021, Metis observed dozens of stars suitable for radiometric calibration, ultimately determining in-flight calibration coefficients and their uncertainties, which were found to be consistent with ground-based measurements. The Sun serves as an alternative reference source because its brightness remains stable in specific wavebands (such as white-light or near white-light), and numerous solar spectral data are available for radiometric calibration \cite{16}.

This paper focuses on the in-flight radiometric calibration of LST/WST and LST/SDI, both using the Sun as a reference source with the aid of solar reference or observational data. The paper is organized as follows: Section 2 describes the specific in-flight radiometric calibration methods for WST and SDI; Section 3 details the calibration processes and presents the resulting in-flight calibration coefficients, uncertainties, empirical formulas, and instrument degradation; Section 4 summarizes and discusses the results.

2 In-flight Radiometric Calibration Methods

Ideally, WST and SDI could use suitable stars as standard reference sources. Unfortunately, during actual calibration observations, neither instrument captured any stars. Given that solar irradiance in WST's 360 nm band is extremely stable with available reference spectral data, and that solar observations in a band similar to SDI's Lyman-alpha band exist internationally (already radiometrically calibrated), both WST and SDI currently use the Sun itself as the reference source for in-flight radiometric calibration, assisted by reference spectral data and solar observations, respectively.

2.1 WST In-flight Radiometric Calibration Method

We use the solar reference spectrum data released by the American Society for Testing and Materials (ASTM) in 2020 (ASTM G173-03) to calibrate WST in-flight. Table 1 [TABLE:1] provides the extraterrestrial solar spectral irradiance from 358 nm to 362 nm at 0.5 nm intervals. Integrating this band yields a total solar irradiance of 3.7349 W·m⁻² (1 W·m⁻² = 10³ erg·cm⁻²·s⁻¹) in the WST (360±2) nm band. This value is then substituted into the equation to obtain the WST in-flight radiometric calibration coefficient (in units of erg·cm⁻²·DN⁻¹), where represents the full-disk integrated count rate observed by WST (in DN·s⁻¹).

2.2 SDI In-flight Radiometric Calibration Method

We use data from the Extreme Ultraviolet Sensors (EUVS) onboard the Geostationary Operational Environmental Satellite R (GOES-R) for SDI in-flight radiometric calibration. GOES-R/EUVS operates in the ultraviolet Lyman-alpha band (118–127 nm), which closely matches SDI's working band (117.1–126.1 nm). Notably, the Lyman-alpha line (121.6 nm) dominates the contribution in both bands, while other lines or continuum contributions are minimal \cite{17}. Level 2 EUVS data are readily available daily from the GOES-R website. Figure 1 [FIGURE:1] shows the full-disk integrated flux in the Lyman-alpha band observed by EUVS in January 2023, with panel (a) presenting the complete observations and panel (b) showing the results after removing geocoronal absorption effects. The SDI in-flight radiometric calibration coefficient (in erg·cm⁻²·DN⁻¹) is obtained through the relation , where is the full-disk integrated count rate observed by SDI (in DN·s⁻¹). It should be noted that GOES-R/EUVS enters Earth's atmosphere at fixed times daily, and because ultraviolet photons are easily absorbed by Earth's atmosphere, EUVS flux measurements are significantly lower than normal during these periods (as shown in the small box in the upper right corner of Figure 1(a)). Therefore, these data must be removed (as in Figure 1(b)) before being used for SDI in-flight radiometric calibration.

3 In-flight Radiometric Calibration

Both WST and SDI in-flight radiometric calibrations use Level 1 data, where images have been corrected for dark-field and flat-field effects. Before formal radiometric calibration, the Level 1 data require preprocessing, such as removing outliers, followed by radiometric calibration using reference irradiance values for the Sun at 360 nm or in the Lyman-alpha band. The radiometrically calibrated WST and SDI data are defined as Level 2 data and can subsequently be used for calculating various physical parameters.

3.1 WST In-flight Radiometric Calibration

Figure 2 [FIGURE:2] displays a WST Level 1 image with intensity units in DN. Since WST in-flight radiometric calibration uses full-disk integrated counts, we need to fit the solar disk (shown as a white circle). Given the large number of daily images from WST, fitting the solar disk for each image would be computationally expensive. Verification shows that background pixels outside the solar disk contribute only about 0.1% of the total image brightness. Therefore, we instead use the sum of all pixel values in the entire image for WST in-flight radiometric calibration, which dramatically improves computational efficiency while having negligible impact on the calibration results. Additionally, due to image anomalies (such as bad blocks), WST data contain some outliers that can be identified and removed by calculating the variance across all data. It should be noted that WST has two attenuators with different transmittances, resulting in different radiometric calibration coefficients. Since WST primarily uses attenuator 1 for in-flight observations, this paper focuses on radiometric calibration of data obtained with attenuator 1.

Due to unstable data during the in-orbit commissioning phase (November 2022 to April 2023) and satellite eclipse periods (May to July 2023), we only use data from the normal observation period (after August 2023) for radiometric calibration. Specifically, the WST in-flight radiometric calibration dataset covers August 2023 to February 2024. Figure 3 [FIGURE:3] presents the WST in-flight radiometric calibration results. Panel (a) shows the full-disk integrated counts (with outliers removed) and exposure time as functions of time, while panel (b) displays their ratio—the full-disk integrated count rate over time. From August 2023 to late December 2023, the full-disk integrated counts (and count rate) from WST show an increasing trend, followed by a gradual decrease through February 2024. This variation is actually related to changes in the Sun-Earth distance, which can be corrected by multiplying by a scaling factor equal to the square of the ratio of the current Sun-Earth distance to the mean Sun-Earth distance. The corrected full-disk count rate is shown as the cyan curve in Figure 3(b), revealing that after correction, the count rate decreases over time, reflecting gradual degradation of WST instrument performance. Figure 3(c) shows the WST in-flight radiometric calibration coefficient over time after accounting for Sun-Earth distance variations. The calibration coefficient exhibits an overall increasing trend, which also indicates instrument performance degradation.

Uncertainty is a crucial metric for evaluating WST in-flight radiometric calibration errors. Figure 4 [FIGURE:4] illustrates the temporal evolution of WST in-flight radiometric calibration uncertainty. First, the daily variation (shown as error bars in Figure 4) is obtained from the standard deviation of daily mean calibration coefficients, yielding an overall uncertainty of 0.12% (denoted as ) for the entire period. Second, since the calibration uses dark-field and flat-field corrected data, the precision of these corrections must be considered. WST flat-field calibration employs the Kuhn-Lin-Loranz (KLL) method \cite{18,19} with an uncertainty of 0.42% ( ); WST dark-field is simulated and its uncertainty cannot yet be determined. Finally, the total WST in-flight radiometric calibration uncertainty is given by:

where is the number of uncertainty components and represents each uncertainty value. Using this formula, the total WST uncertainty during August 2023 to February 2024 is at least 0.44%. Additionally, if we use the monthly average variation rate of WST in-flight radiometric calibration coefficients (pink points in Figure 4) as the instrument performance degradation rate, WST performance degraded by approximately 1.02% during this period.

Fitting the daily mean values of WST in-flight radiometric calibration coefficients from August 2023 to February 2024 yields an empirical formula that greatly facilitates WST scientific data production. Given that the calibration coefficients increase approximately linearly with time, we employ a linear function for fitting. Figure 5 [FIGURE:5] shows the fitting result (green line), yielding the empirical formula , where is time (in seconds, with the starting point at 12:00:00 UTC on January 1, 2000) and is the in-flight radiometric calibration coefficient. Radiometric calibration of WST images can be performed using either the daily mean calibration coefficients or this empirical formula. Figure 6 [FIGURE:6] shows the radiometrically calibrated result, where image DN values have been converted to irradiance.

3.2 SDI In-flight Radiometric Calibration

Figure 7 [FIGURE:7] shows a Level 1 SDI image with intensity units in DN. In the ultraviolet Lyman-alpha band, cosmic rays and occasional bad pixels or blocks in SDI images cause some outliers in the full-disk integrated counts, which are removed before radiometric calibration.

The SDI in-flight radiometric calibration dataset covers the same period as WST, from August 2023 to February 2024. Figure 8 [FIGURE:8] presents the SDI in-flight radiometric calibration results. Panel (a) shows the full-disk integrated counts (with outliers removed) and exposure time over time, while panel (b) displays their ratio—the full-disk integrated count rate (blue curve). During this period, SDI full-disk integrated counts (and count rate) show an overall decreasing trend with superimposed periodic variations of approximately 25 days. These periodic changes are consistent with variations in the Lyman-alpha flux observed by GOES-R/EUVS (purple curve in Figure 8(b)). The SDI in-flight radiometric calibration coefficients derived using EUVS Lyman-alpha flux are shown in Figure 8(c). The coefficients exhibit an overall increasing trend (primarily due to instrument degradation) with a superimposed ~25-day periodic variation. Possible causes for this periodicity include: (1) transition region radiation (represented by Lyman-alpha) varies with solar rotation and activity with a ~25-day period \cite{20}; (2) incomplete matching between SDI and EUVS bandpasses and instrument response functions; and (3) differences in orbital characteristics between SDI and EUVS. The latter two factors cannot fully remove the periodic variation.

Figure 9 [FIGURE:9] shows the temporal evolution of SDI in-flight radiometric calibration uncertainty, calculated similarly to WST. First, the standard deviation of daily mean calibration coefficients (daily variation, shown as error bars in Figure 9) yields an overall standard deviation of 0.59% ( ) for August 2023 to February 2024. Second, SDI flat-field and dark-field calibration errors must be considered, with SDI flat-field calibration uncertainty at 2.32% \cite{18,19} ( ). Since SDI dark-field is not a true dark measurement, its uncertainty is difficult to assess. Finally, the GOES-R/EUVS radiometric calibration uncertainty of 10% \cite{16} ( ) must be included. Using Equation (1), the SDI in-flight radiometric calibration uncertainty during this period is at least 10.28%.

With the SDI in-flight radiometric calibration coefficients, Level 1 SDI images can be calibrated to Level 2. Figure 10 [FIGURE:10] shows the radiometrically calibrated result of the solar image from Figure 7, where DN values have been converted to irradiance. Additionally, long-term variation in the calibration coefficients allows estimation of SDI instrument degradation. Similar to WST, we use monthly mean values of SDI in-flight radiometric calibration coefficients (pink points in Figure 9) to estimate the degradation rate. The monthly mean coefficients show a linear increasing trend with a variation rate of approximately 6.71%, indicating that SDI performance degraded by about 6.71% during this period. It should be noted that the degradation rate has stabilized during this timeframe; in fact, SDI performance degraded by more than 30% during the first few months after launch.

4 Summary and Discussion

This paper describes the in-flight radiometric calibration processes and results for ASO-S/LST/WST and ASO-S/LST/SDI. Radiometric calibration is an essential step in the scientific data production pipeline for WST and SDI; only after radiometric calibration can the data be used to calculate various physical quantities such as temperature, density, and energy.

Both WST and SDI use the Sun as their reference source for in-flight radiometric calibration. The calibration dataset covers August 2023 to February 2024. The in-flight radiometric calibration coefficients for both instruments increase slowly with time, indicating gradual instrument performance degradation. SDI calibration coefficients also exhibit fluctuations with a period of approximately 25 days.

During August 2023 to February 2024, the in-flight radiometric calibration uncertainties for WST and SDI are approximately 0.44% and 10.28%, respectively, while the performance degradation rates are 1.02% and 6.71%, respectively. SDI detector degradation is thus more pronounced than that of WST.

The empirical formula for WST in-flight radiometric calibration coefficients is , where is time (in seconds, starting from 12:00:00 UTC on January 1, 2000) and is the in-flight radiometric calibration coefficient. This empirical formula is applicable at least for the period from August 2023 to February 2024.

For WST in-flight radiometric calibration, the currently used reference irradiance is treated as constant (time-independent). In reality, solar irradiance at 360 nm varies with solar activity (e.g., flares, plages) and exhibits an ~11-year cycle over the solar activity cycle, although the variation is relatively small. As Solar Cycle 25 approaches its peak (expected in 2025), this long-term variation can be measured with increasing precision, and future calibrations will incorporate and correct for this effect.

Solar activity, particularly flares, significantly affects solar radiation flux in the Lyman-alpha band. During periods of frequent solar activity, SDI in-flight radiometric calibration errors increase accordingly. It should be noted that GOES-R/EUVS radiometric calibration errors during flares can be as high as 25% \cite{23}, which would significantly increase SDI in-flight radiometric calibration uncertainty (from the current 10.28% to over 25%). This is why we currently use daily mean calibration coefficients rather than instantaneous values for radiometric calibration. During solar activity maximum, dozens of large flares (M-class or above) may occur daily, necessitating further consideration of flare effects on SDI in-flight radiometric calibration uncertainties.

In-flight radiometric calibration must be performed throughout the satellite's entire lifetime. WST and SDI in-flight radiometric calibrations will require continuous monitoring and tracking in the coming years. On one hand, calibration results should be updated periodically (e.g., the WST radiometric calibration coefficient empirical formula); on the other hand, instrument performance degradation must be monitored. When instrument degradation reaches a certain level, self-cleaning procedures or adjustments to regular exposure times may be required.

Currently, both WST and SDI use the Sun as their reference source for in-flight radiometric calibration. While not ideal, this is the most practical operational approach. In future calibration observations, if WST and/or SDI capture sufficiently bright stars, planets, or even comets, we will attempt radiometric calibration using these reference sources and compare the results with the current solar-based approach.

Acknowledgments

We thank the reviewers for their valuable suggestions, which significantly improved the quality of this paper.

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