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Abstract
The image information of distant objects shows a diffuse speckle pattern due to diffraction limit, non-uniform scattering, etc., which is difficult to achieve object discrimination. In this study, we have developed a staring spectral video imaging system mounted on a ground-based telescope observation platform to detect the high orbit space objects and gain their spectral images for six groups of GEO targets. The speckle remains basically the same characteristic as the projection structure of the object due to “the balloon inflation phenomenon of near parallel light during long-distance atmospheric transmission” under the premise of considering the bi-directional reflection distribution function (BRDF), Rayleigh scattering theory, and the memory effect. Based on this phenomenon, a mathematical model of remote target scattering spectrum imaging is established where the speckle can be treated as both a global speckle and speckle combination of texture blocks caused by various components of the target. The radial basis function (RBF) neural network is separately used to invert the global speckle and the speckle combination of the texture blocks on account of the typical target material database. The results show that the target materials are of relatively fewer kinds in the global inversion with only including gallium arsenide panel (GaAs) and carbon fiber (CF), for which the highest goodness of curve fitting is only 77.97. An improved algorithm makes their goodness of fit reach 90.29 and 93.33, respectively, in view of one conjecture that the target surface contains unknown materials. The spectral inversion result of the texture blocks shows that the types of materials in each target texture block increase significantly, and that the area ratio of different materials inverted in the block is different from each other. It is further confirmed that the speckle image contains the overall projection structure of distant target and the spectral image projection of each component is relatively fixed, which is the result of the comprehensive action of various mechanisms of ultra-long-haul atmospheric transmission and optical system focusing imaging after BRDF spectral scattering. The spectral image fine inversion is expected to restore the clear structure of the target. This discovery provides important support for the remote imaging and identification of distant and ultra-diffractive targets.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical detection of distant weak and small targets, such as ground-based detection of space targets, has always been a research hotspot in the field of remote detection and recognition. However, it is still difficult to meet the requirements of overcoming atmospheric attenuation, scattering, and environmental interference [1–3]. Scattering spectral detection of space objects at long distance is possible according to the spectral fingerprint characteristics of different materials [4]. Currently, scattering spectral imaging technology, with the ability to provide higher dimensional information, brings new technical means for this kind of research [5].
A lot of efforts have been made on the optical detection of on-orbit space targets, space debris and other distant weak targets [6–8]. The ground-based astronomical telescope is used as a platform to obtain the target spectral data under normal conditions. Moreover, the material composition of the target surface is analyzed by establishing the spectral scattering characteristics which are mainly based on the plenoptic function and the bi-directional reflection distribution function (BRDF) scattering theory [9–11]. The spectral studies about orbital space targets have made some progress in the physical properties of the materials [12–15]. As for the spectral imaging technology, the space target model detection is carried out indoors. The material characteristics of each part are analyzed based on the material identification method of space objects by Tucker decomposition [16]. But it is so difficult to acquire the spectral images for the material distribution of the target to be analyzed and the real-time projection structure to be obtained. The crux is that only a few pixels of blurred images are obtained because the optical detection aperture is limited and the information is strongly diffused due to the strong scattering influence of the atmospheric medium in the long-distance measurement. The image texture of the target is enlarged, blended, blurred, and basically made unrecognizable. Fortunately, there are some breakthroughs in the study of optical transmission in complex scattering media, where the memory effect and the conventional spatial displacement invariance are unified [17,18]. The optical transmission matrix in the ultra-thick anisotropic scattering media is also correlated [19], which is beneficial to dissect the atmospheric medium interference in space debris detection. To analyze the mixing structure, the material information of the target can be effectively constructed by spectral de-aliasing and the analysis and inversion of the BRDF of the target material [20–23]. These research results are obtained under different local conditions which are not suitable to orbital space object imaging detection directly. For the scattering analysis of complex structure target, the distortion of information beam and broad-band spectral feature should be considered and amended after the ultra-thick scattering media transmission, which needs to be done based on a new kind of model and inversion method.
This paper selects a ground-based hyperspectral detection method and a mathematical model for spectral scattering imaging of distant objects to achieve their identification by overcoming diffraction limitation and non-uniform scattering. The characteristics of scattered light in the atmospheric medium transmission of the mosaic structure target are analyzed according to the optical channel theory. The spectral-aliasing of the mosaic projection structure and the least squares method are adopted in this research. The material information of objects is inverted and analyzed by obtaining the spectral characteristics of image elements in different regions of the spectral image. These studies lay on a foundation for the projection structure recovery and identification of distant space objects.
2. Space objects scattering spectral transmission model
2.1 Ground-based detection model for scattering spectral images of space targets
The process of using ground-based telescope measuring space targets involves two important factors besides the telescope equipment itself. The first is the radiation distribution of the target scattered sunlight into space, and the second is the atmospheric transmission of the light field information received in the telescope field of view. The former mainly considers the scattering process of the object in the spatial geometry angle, which can be characterized by the BRDFs of materials of different structures that make up the target. The latter mainly experiences physical processes in the atmosphere including the absorption and scattering of aerosol, water, and atmospheric molecules, where, though turbulence, Rayleigh, and Mie scattering play important roles, most of the previous researchers only considered the energy transmittance through physical approximation. Both factors must be considered as a whole in order to obtain the target structure characteristics represented by the detected beam information. In this study, a complex beam propagation model with more dimensional information is studied to realize the structural cognition of space objects in order to find a key solution to identify distant space objects.
In this paper, it is assumed that the overall transmission beam in a shorter time interval is affected by turbulence in a smaller scale. The Rayleigh scattering is mainly considered in the atmospheric transmission process that is not only limited to the attenuation of energy, but also leads to change in the shape of the light spot scattered by the object in the form of diffused reflection. However, the deformation does not represent the complete mixing of scattered light spots reflected by various parts of the target, and some additional rules should be followed.
It is known from the scattering memory effect, which depicts the distortion in the beam spot on the observation plane as being trivial and an aperture called the random phase mask as being considered as a shift-invariant system under the paraxial condition [24], that for this atmospheric transmission from space to the ground, if the uneven atmosphere is regarded as a combination of many dielectric layers with different refractive indices on the transmission path, we should be able to find out the similarities to this memory effect. That is to say, in the case of ultra-far distance and short time interval, the parallel beam with close phase in a narrow spectral band is equivalent to that being obtained in the limited receiving area. Although the atmospheric Rayleigh scattering changes the clarity of the target fragment structure, the relative central position of the light projection of the original structure of the target will keep unchanged relative to the structure itself after the atmospheric transmission. The detected overall speckle structure is similar to the expansion of a balloon. Each partition structure expands outward from its own center, with their edge parts overlapping slightly. This can be called the balloon inflation phenomenon of long-distance atmospheric transmission of near parallel light. The related ground-based scattering spectral detection model for space targets is shown in Fig. 1.
Fig. 1. Ground-based scattering spectral detection model for space targets. (a) BRDF scattering detection model. (b) The speckle evolution model in homogeneous atmospheric medium. (c) Atmospheric Rayleigh scattering effect.
When the sun shines on the target, the light reflected from the target into the detection field of view, ${E_i}$, carries the target information, and it then transmits through the atmosphere and is scattered by atmospheric particles before reaching the ground-based detector. The detector receives the scattered signal ${E_o}$ at a distance of $R$ from the scattering particles. Let $\theta$ be the scattering angle between the incident light and the signal light received by the detector, $\varphi$ the azimuth angle between the scattering surface and the vibration direction of the incident light, then:
where $\delta (\theta ,\varphi )$ is the scattering function of the particle. Equation (1) is the light energy scattered by the particle in the direction of $(\theta ,\varphi )$ per unit stereo angle when the light Is incident with unit intensity. Integrate $\delta (\theta ,\varphi )$ over the whole space to get the total energy scattered off by an individual particle, i.e., ${\delta _z} = \int_{4\pi } {\delta (\theta ,\varphi )} d\varOmega$, where ${\delta _z}$ is the scattering cross section. It describes the total energy of light scattered by a particle, which is equivalent to the corresponding cross section of the incident light of equal energy. In this paper, only the energy received by the field-of-view angle $\phi$ of the detection system is considered, so the scattering cross section is written as ${\delta _z} = \int_\phi {\delta (\theta ,\varphi )} d\varOmega$.According to the Rayleigh scattering theory, when the incident light is natural light, the symmetric scattering function of the particle is only related to the scattering angle. The scattering function is calculated using the Lorentz formula as below:
From Eq. (3), the intensity of scattered light is inversely proportional to the 4th power of the wavelength and inversely proportional to the square of the number density of molecules in the medium.
To further analyze the light transmission process of space object scattering such as space debris, this paper establishes a spatial geometric angle relationship model relative to the sun, the space object, and the ground-based measurement system. As shown in Fig. 1(a), with the target object as the center, the incident light $SUN(t,\lambda )$ is the natural parallel light, the angle with the target vertical normal direction Y is the angle of incidence ${\alpha _i}$, the angle with the X plane is ${\beta _i}$, and the angle between the target and the detection system direction and the target vertical normal is ${\alpha _j}$. The angle between the detection system direction and X-plane is defined as ${\beta _j}$. It is assumed that the incident light satisfies the spectral properties of the scattering theory for the target. Then, the incident light intensity per unit area on a single projection surface and its scattered light intensity satisfy the following equation:
Since the detected signal is largely influenced by the test system transfer function ${T_S}(\lambda )$, Eq. (5) is further supplemented as:
Then, Eq. (7) represents a curve (Fig. 2) that is independent from the properties of the material itself, thus Eqs. (1)-(6) can be written as,
The above equation represents the material information per unit area on a single projection plane, however, the actual target information is often multi-material and multi-structured objects. $F(\lambda ,t,{\alpha _i},{\beta _i},{\alpha _j},{\beta _j})$ is a key parameter to effectively modulate the signal ${E_o}(\lambda ,t,\delta ,{\alpha _i},{\beta _i},{\alpha _j},{\beta _j})$ received by detector.
From the projection principle, it is known that the image information received by the detector is the two-dimensional projection of the target in the direction of the detector. So, the two-dimensional image should contain information about both the material and structure of the target in the direction of detection.
The target structure corresponds to the location of each region in the image, and the light intensity in the overall image should be the sum of the spectral intensity of the corresponding area of the material on each projection surface, i.e.,
In Eq. (11), the subscript number n represents the serial number of spectral channel and is a positive integer greater than or equal to 1; m the number of different BRDF in the overall scattering spectral speckle, $m \ge 0$, and $m\textrm{ = }0$ means that there is no information on the scattered characteristics of the target in the received signal; k the serial number of each component of the target, that is, it represents the different material types, and $m \ge k$. It is found impossible to obtain the absolute area directly due to the large variety of interference factors in distant target measurements. Equation (11) points out which the spectrum ratio of each component of the target to the overall spectra is regarded as the area ratio of such target material.Therefore, there is the mathematical model of remote target scattering spectrum imaging, it becomes possible to analyze the information of each component of the target on the premise that the BRDF of each different material is known.
2.2 Radial basis neural network model solution
At this point, assuming that the left side of Eq. (11) is a constant term of the linear equation system, the equation can be solved according to the system of chi-square linear equations. The system of equations is as follows:
By Cramer's law, if the determinant of equations is not equal to zero, then the equations have a set of solutions and are unique, which can be expressed as:
where ${Z_k}$ is the determinant of order m, which can be expressed as follows,In Eq. (14), if the reflectance function of each component is a known term, the ratio of such component of the target can be obtained directly. The main targets of this study are in-orbit artificial space satellites or artificially abandoned satellite debris, etc. Most of the surface materials used in their construction are publicly available and commonly used [25]. Therefore, in this study, six artificial satellite surface materials are firstly selected to establish a database of reflectance functions of the target materials. Then the data are fitted to find the material types and proportional relationships contained in the target. Although the established database of reflectance functions of the target materials is relatively comprehensive, the measured targets still contain parts of materials that may be unknown. Therefore, double fitting by least squares can provide support for determining the material information and unknown spectral information contained in the measured targets. The measured normalized spectral data are assumed to be a one-dimensional linear equation $D(x,y)$. The fitted sample data is the reflectance distribution functions of various materials, with k being the number of reflectance functions of various samples, $k \ge 1$,
Based on Eq. (17), a radial basis neural network algorithm is used for inversion fitting with the help of typical material BRDF database. Thus, the proportional relationship between the target material types contained in the measured target scattering spectral data and the corresponding materials in the inversion spectrum is obtained. The area ratio function of each material in the corresponding image is obtained at ${O_k}$.
3. Experimental measurements and analyses of results
3.1 Measurement experiments
The large-aperture telescope in the experiment provides the measurement infrastructure to provide higher spatial resolution. Meanwhile, a measurement environment with better visual nimbleness away from urban areas is chosen in order to minimize the interference of ambient light and aerosols, clouds, etc. The experiment was chosen to be carried out in Da Suihe town, Jilin Province and the measurement period was from October to November. The main indicators of the test system are listed in Table 1. In Fig. 3 the optical structure of the hyperspectral video measurement of space objects is shown.
Table 1. Ground-based hyperspectral video acquisition system
Fig. 3. Optical structure of hyperspectral video measurement. (a) The solar radiation curve and test system transfer function. (b) The telescope system schematic diagram. (c) The liquid crystal tunable high-speed spectral imaging system. (d) The geometric angle relationship between the scattered light, the projection surface of the target component and the detection equipment.
In the experiment, the target track information was queried by the orbit prediction platform HEAVENS ABOVE. The target was automatically tracked and locked by the telescope guide mirror system servo. The experiment measured the spectral video images of six space objects, including Nos. 33056, 32404, 32252, 32767, 44048, and 44034. The measurement results are shown in Fig. 4.
Fig. 4. Video images of space object spectra with spectral results.(a), (b), (c), (d), (e) and (f) are the spectral video images and the overall spectral intensity normalized curves of space objects Nos. 33056, 32404, 32252, 32767, 44048, and 44034 in the 400 nm - 720 nm wavelength band and with 5 nm resolution.
3.2 Inversion of results and analysis
In this experimental analysis, the spectral line pattern is the main factor to judge the experimental results, and the spectral intensity is the secondary factor to do so. Therefore, the maximum normalization method is used to perform the basic processing of the measured target spectral data, so as to ensure the uniform data standard and prevent data overflow [26]. The video images of the measured space object spectra and the spectral results are fitted and inverted according to the aforementioned model and algorithm, and the fitting results are evaluated by the goodness-of-fit ${R^2}$[27],that is, ${R^2} = {{\sum\limits_{i = 1}^n {{{({Y_i} - \overline Y )}^2}} } / {\sum\limits_{i = 1}^n {{{(\widehat Y - \overline Y )}^2}} }}$, where ${R^2}$ is the goodness of fit, ${Y_i}$ the intensity of the target spectrum to be fitted, $\overline Y$ the average intensity at the corresponding wavelength of the fitted spectral database, and $\widehat Y$ the intensity of the fitted spectrum.
The spectral information was measured for the overall beam channel of each space object, the results of the fitted inversion are shown in Table 2. The results show that the main material components of each target object are the gallium arsenide (GaAs) and carbon fiber (CF) materials that make up the solar panels and signal transceiver antennas attached to the body of the artificial satellite. Combined with the analysis of the actual object, some results are presented during the orbital operation of the space object. The ground-based detector mainly receives the scattered light signal from the object facing the earth due to the spatial geometric relationship between the sun, the target object, and the earth. While the antenna and the main body are the core components of the target object, most of them facing the earth.
Table 2. Results of fitting inversion of the spectral data of the overall beam channel of the space objects
Further analyses of the fitting results show that the area ratio of GaAs material is relatively high, which is a validation of the high reflectivity of this material and the relatively large adherence area on the surface of the target object. The evaluation of the fitting results is not very good, which is mainly due to the fact that only six types of material data were used for the fitting provided by the inversion, and that the space objects have been in space for a long time and some small changes in their spectral line pattern might have been caused by the cosmic ray and UV radiation [28].
For this reason, a spectral data of X populated material library belonging to the target object itself but with unknown components was added to the model and re-fitted for the calculation. The fitting results show a significant improvement at ${R^2}$, as shown in Table 3.
Table 3. Fitted inversion results of the spectral data of the whole beam channel of the space objects after modifying the model
From the results in Table 3, it can be found that the measured target spectral data mainly reflect the gallium arsenide (GaAs) material and occupy a relatively large area ratio, which is consistent with the previously described relationship with the optical reflectivity properties of the material and the spatial angle of the object.
According to the area ratio of the inversion, it can be found that there are obvious differences among the targets, which provides an effective support to realize the marker identification among the target objects. However, it is regrettable that the material types presented in the inversion results are slightly homogeneous. The other material information is overwhelmed by the main material information, which hampers the accurate identification of target structures.
The above basic model is further modified thanks to that the measurement system has the capability of hyperspectral video imaging. The acquired information has the complete scattered spot spectral image of the target object. It is known from the principle of optical imaging that all structural light field information of the same target in the field of view range propagates in a straight line and is constrained by the optical memory effect in the scattering medium, the same medium, phase angle, and the image structure position [29]. Therefore, it is known that the spot information received by the detector is correlated with the scattered light field structure of the target object. Then the spot image should be the result of the scattering projection of the target object under the effect of strong atmospheric scattering. Its imaging structure is severely blended at the edges and the overall signal is severely attenuated, but its texture structure is not missing. Therefore, according to the texture structure of the spectral image plane projection, the inversion model of multi-beam channel is established. The texture structure of each space object is divided as follows as in Fig. 5.
Fig. 5. Measured space object spectral image texture area with corresponding spectral data. (a), (b), (c), (d), (e) and (f) are spectral video images based on targets of Nos. 33056, 32404, 32252, 32767, 44048, and 44034. The texture regions are marked according to the image texture structure of each target, and the spectral intensity normalized curves of each texture region are extracted.
Based on Fig. 5, it is obvious that the spectral curve of different texture regions of each space object has a large difference with the spectral curve line shape of the overall beam channel. There is also a large difference between different texture regions of the same target object, whereas there is a large similarity in the spectral line shape of individual texture regions between different targets. For example, there are similarities between the spectral line pattern imaged in Area 5 of No. 33056 and Area 2 of No. 32404, in Area 3 of No. 32252 and Area 4 of No. 32767, and in Area 5 of No. 44048 and Area 3 of No. 44034. This is precisely because some of the materials are common among different target bodies although their structures and compositions are very different. This result provides favorable data support for the establishment of a common database for material identification of space objects. Also, the above finding coincides with the idea that the previously analyzed light spot images have different material structures.
Here the extracted beam channel information of each space object texture region in Fig. 5 is fitted and inverted according to the aforementioned model and algorithm, and the results are shown in Fig. 6. It can be found that the material types reflected in different texture regions of the spectral image of each space object are much richer than those in the overall beam channel, the area ratio of multiple materials in each texture region is also more refined. The inversion results of No. 33056 show that although GaAs is in five texture areas, Area 4 and Area 3 have the high area ratio, whereas the area of Areas 1, 5, and 2 is larger than that of gold insulation film and carbon fiber, which indicates that the main body of No. 33051 has GaAs panels attached on both sides and gold insulation film wrapped in the front and back. The carbon fiber is mainly the support arm or signal antenna. Based on the texture areas of each material, the instantaneous projection structure of No. 33051 can be preliminarily determined to be the right-rotating upward attitude of the main body. The texture areas of other space objects also reflect the strong representative material information, which is important for guiding the recovery of the instantaneous projection structure of the target.
Fig. 6. Results of inversion recognition of the texture region of each space object spectral image, the inversion results show the material types including: silicon based material (Si), golden insulation film material (GIF), carbon fiber material (CF), gallium arsenide material (GaAs), white paint material (WP), silver insulation film (SIF), and material data (X) that belong to the spectral information of the corresponding target object but are unknown in the material library, where R2 is the goodness of fitting.
4. Conclusion
In this paper, hyperspectral scattering imaging of space objects is performed using a ground telescope platform.The spectral video imaging experiments of the six space targets are carried out in the wavelength range from 400 nm to 720 nm. Based on the scattering spectral theory and optical memory effect, the scattering of the light reflected by the distant space objects under solar irradiation and the transmission process of the detection channel in the atmospheric medium are analyzed. In addition, a combined model of Rayleigh scattering and memory effect was established. The inversion results are analyzed by dividing the whole information beam into integrated spectral channel based on a point source and multiple spectral channels based on the spot texture distinguishing areas. On the one hand, in the integrated channel, the material types are separately compared with materials included or not included in the library. To be clearer, materials that are not included in the library may be modified by known materials or remain unidentified. This treatment improves the goodness of fit of the inversion analysis. On the other, the information of various materials on different substructures with good fit is obtained in the block inversion of the texture region. These two aspects have certain effects on the type of material identification, especially the latter can be further distinguished from the structure. The results in this paper lay on a foundation for the remote identification and image structure recovery of faint and distant targets.
Funding
Natural Science Foundation of Jilin Province (YDZJ202201ZYTS510, 20200201257JC).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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