1. Introduction
Infrared remote sensing imaging systems are strategically important in the military domain, such as in the space-based infrared system (SBIRS) and infrared search and tracking (IRST) [
1]. Accurate infrared radiometric calibration technology provides the basis for accurate inversion of target radiation intensity, which is crucial for target classification and identification in military contexts. Although the sensor is radiometrically calibrated before a flight, the detector–response relationship changes after orbit due to environmental changes, time drift, and so on [
2]. Therefore, high-precision radiometric calibration in orbit is essential. At present, most on-orbit infrared reference sources are blackbodies, which can realize high-precision absolute and relative radiometric calibration. However, as on-orbit space cameras evolve toward larger apertures, wider fields of view, and deeper cryogenic technologies, the practicality of blackbodies is constrained by the limited resources in orbit. This is particularly true for calibration of the full optical path and low-end detector responses. Consequently, scholars have suggested employing stars as an all-optical absolute radiometric calibration reference source. Stars offer advantages such as low radiation values, long-term stability, and traceability [
3]. The midcourse space experiment (MSX) currently uses an internal blackbody combined with five standard stars (
Lyr,
Cma,
Tau,
Gem, and
Boo) and reference spheres as the on-orbit reference source, with a calibration accuracy of roughly 2–5% [
4,
5,
6]. Similarly, the infrared array camera (IRAC) is an infrared camera system on the Spitzer Space Telescope which uses bright A-type stars as a reference source for calibrations, with a calibration accuracy of 3% [
7]. The James Webb Space Telescope (JWST) leverages five spectroscopically modeled stars (including white dwarfs and A and G stars) at the 1% level with a design calibration accuracy of about 5% [
8]. However, due to the differences in observational wavelengths used in non-astronomical fields, such as remote sensing and space-based target detection, compared with those used in astronomy, there remains uncertainty in understanding the true flux density of stars. Therefore, acquiring high-precision stellar flux data in nonstandard wavelengths is crucial for the on-orbit calibration of space cameras.
Stellar radiative fluxes are mainly affected by stellar spectral model parameters, such as the effective temperature, emissivity, and angular diameter, and can therefore be estimated from the stellar spectral parameters [
9,
10,
11]. Kurucz proposed a stellar spectral model that fits the stellar spectral distribution using parameters such as the temperature, surface gravity field, and metal abundance, with fitting errors in the range of 3–5% [
12]. For improved radiation flux accuracy, Rieke used interpolation for A-type and solar-type stars in combination with the Kurucz model to obtain special information in the range of 1–25
m, with an accuracy of approximately 2% [
13,
14]. Rebassa-Mansergas et al. used the Sloan Digital Sky Survey (SDSS) with spectral template fitting to estimate the spectral parameters, such as the stellar temperature and surface gravity [
15]. Nonetheless, such methods require a large amount of observational data, or they will limit the number of calibrated stars by targeting only certain types of stars.
Recently, it has been proposed to leverage the vast amount of stellar information in catalogs for flux estimation [
16,
17]. This type of method focuses on estimating stellar spectral parameters from catalog information to construct stellar spectra. Zhang et al. used the stochastic particle swarm optimization (SPSO) method to estimate the stellar temperature and the observation angle [
17]. However, due to the different compositions of stellar atmospheres, stellar spectra have different emissivity values at different wavelengths, resulting in spectra that are not identical to a blackbody, which can lead to certain estimation errors [
18,
19]. Therefore, Zhang used stochastic particle swarm optimization to estimate the stellar emissivity for stellar radiation flux estimation, and the accuracy of this method, based on the MSX catalog, was approximately 5% [
20]. Despite this, the extrapolation accuracy of such methods still cannot meet the required accuracy of our on-orbit space camera calibrations. In response, we further carried out a study on the estimation of stellar infrared radiation fluxes based on stellar catalog information. Harnessing a wealth of observations from existing catalogs, we expanded the infrared standard stellar network, enabling the targeted selection of extensive stellar data for precise on-orbit radiometric calibrations.
The observation of stars in orbit is constrained by the detector’s field of view, which only allows for the monitoring of celestial bodies within specific regions. The scarcity of calibration stars fails to satisfy the demand for frequent calibrations, necessitating the development of a method that can obtain a large number of calibration stars to support rapid correction cycles and real-time performance evaluation. Incorporating more calibration stars helps to mitigate the randomness associated with observations that depend on a limited number of stars. The star catalogs encompass diverse star types and luminosities. Fully utilizing the information in catalogs for extrapolation can provide more possibilities for the selection of calibration stars. Consequently, this study primarily investigates methods for estimating stellar radiance flux, which are notably more efficient and cost-effective. It leverages the rich data available in star catalogs to advance the calibration of instruments in spaceborne platforms.
In order to further enhance the accuracy of estimating stellar radiation flux based on the catalogs, we introduce a novel method that integrates a dual-band thermometry approach with an improved grey wolf optimization (I-GWO) algorithm. The challenge of estimating stellar spectral parameters from catalog information lies in the disparity between the number of unknowns and the available equations, primarily due to emissivity variability across different wavelengths. This discrepancy often leads to reduced estimation accuracy and instability. In order to mitigate this issue, we consider starting by reducing the unknown quantities through the use of the catalog information to estimate the effective stellar temperature using the dual-band thermometry method. The subsequent estimation of the remaining spectral parameters is then performed using additional band information. The choice of the optimization algorithm is also important in influencing the accuracy of the parameter estimation. Thus, we used the I-GWO algorithm to estimate the specific spectral band emissivity as well as the stellar observation angles. Furthermore, to enhance computational efficiency, we introduced isophotal radiative flux reduction, which simplifies the computational complexity. Consequently, the proposed method can effectively and efficiently estimate the radiative flux of stars in specific spectral bands, providing support for in-orbit radiometric calibration.
Our contributions can be summarized in four main areas. (1) We introduce a dual-band thermometry method to accurately estimate stellar temperatures, providing a solid foundation for any subsequent estimations of stellar radiative flux. (2) Utilizing a stellar spectral model that incorporates emissivity, we propose using the I-GWO algorithm to estimate spectral parameters such as the band emissivity and star observation solid angle. (3) Substitution of full spectral band integration with isophotal radiative flux is carried out to enhance computational efficiency. (4) We estimate the radiative flux of stars at specific camera wavelengths and validate the accuracy of this method through in-orbit experiments, supporting its applicability to in-orbit calibration.
4. Discussion
This study introduced a novel method for estimating stellar radiative flux based on infrared star catalogs, demonstrating (through experimental validation) significant improvements in estimation accuracy, stability, and computational efficiency over existing star catalog-based techniques. Specifically, when compared with other star catalog-based estimation methods, our approach achieved a 75.4% improvement in estimation accuracy and a 91.3% enhancement in estimation stability, and the computation time was reduced to merely 3% of that required by alternative methods. These advancements were primarily attributed to the introduction of dual-band thermometry and enhancements to the grey wolf optimization algorithm. Concurrently, the application of our method to estimating the radiative flux of three well-known calibration stars (Sirius, Vega, and Arcturus) yielded a radiative flux error less than 5%, thus also providing evidence of our method’s efficacy. Furthermore, error analysis revealed that the calibration accuracy of the star radiative fluxes, as established by the proposed method, was within 6.1%. Additionally, the results from the on-orbit experiments demonstrate that the star calibration error remained below 5%.
The dual-band thermometry effectively reduced the number of parameters which needed to be estimated, thereby increasing the overall accuracy of the estimates. Additionally, by analyzing the characteristics of the optimization objective function and incorporating parameters that varied periodically, we refined the grey wolf optimization algorithm by using a periodic variation parameter to more precisely locate optimal solutions, avoiding local minimums and further enhancing the accuracy and stability of parameter estimation. Moreover, by adopting the concept of an isophotal wavelength in place of traditional integration methods, we significantly increased the computational efficiency without sacrificing accuracy.
Despite the progress achieved, there remains room for improvement in the accuracy of radiative flux estimates across specific spectral bands. As indicated by the extrapolation results in
Table 6, the error in some bands was still nearly 5%, mainly due to the assumption of uniform emissivity within certain spectral regions, as well as systematic errors from the star catalogs. On one hand, using higher-precision star catalogs for estimates could be beneficial. On the other hand, higher-resolution stellar emissivity as a function of the wavelength needs to be established to improve estimation accuracy further. For example, the stellar emissivity at a higher wavelength resolution can be estimated by selecting the spectral data provided by the JWST as input data [
39,
40,
41].
For on-orbit radiometric calibration, despite individual stars having data biases, using the radiative data of a large sample of stars and performing statistical averaging can significantly enhance the overall calibration accuracy.
In summary, the method proposed in this study for estimating the stellar infrared radiation flux using infrared star catalogs demonstrated superior performance in terms of accuracy, stability, and computational efficiency, providing an effective tool for stellar calibration research. However, further investigation into the variability of stellar emissivity across different spectral bands will be a focal point of future work.
5. Conclusions
We investigated the spectral characteristics of stars and a camera observation model and then proposed a method to estimate the infrared radiation flux of stars based on existing infrared star catalog data. The proposed method introduces dual-band thermometry with I-GWO algorithms for estimating the stellar parameters which, when combined with observational models, can achieve the estimation of stellar radiative fluxes in any infrared spectral band. The temperature estimation experiments, which were conducted using MSX catalog observational data, demonstrated that the proposed method achieved an accuracy better than 10% for 83.5% of the stellar temperature estimates within the 4000–7000 K range, with an average error of 5.82%. In addition, the proposed method significantly enhanced the accuracy of radiative flux estimates based on stellar catalog methods. When compared with previous catalog-based methods, our approach achieved a 75.4% improvement in estimation accuracy, with the algorithm’s stability improving by 91.3%. The validation of our method’s effectiveness was confirmed through comparative analyses with well-known calibration star data, which revealed that our estimation errors remained below 5%. Additionally, the incorporation of isophotal radiation significantly increased the computational efficiency by 96.9%. Through employing the approach outlined in this study, a multitude of benchmark sources with precision exceeding 1% can be provided for stellar calibration, offering a broader array of options for the in-orbit calibration of space cameras. The proposed method offers new possibilities for star calibration. The experimental results indicate that using this method for on-orbit star calibration can achieve a star calibration error within 5%. Furthermore, this method is capable of not only estimating the emissivity of stars within catalog bands but also calculating the effective temperatures of stars, presenting a novel pathway for the exploration of infrared stellar characteristics. Therefore, this approach holds value in remote sensing applications and scientific research.