4.2. ISAR Imaging Simulations
In this section, ISAR imaging results of representative aircraft target are presented and discussed. The matrix of the backscattered field of representative aircraft targets is calculated by our GPU-accelerated SBR method, and then the echoes are focused to obtain ISAR images by utilizing the GPU-accelerated BP algorithm developed in this paper. For comparison, our GPU-accelerated BP algorithm was also applied to focus the backscattered field by employing the RL-GO method in the FEKO v2020 software to obtain focused ISAR.
Figure 14 shows the CAD model of a scaled A380 aircraft model with dimensions. This model has 3770 triangles.
Figure 15a–c illustrate three typical observation configurations with different azimuthal scanning ranges. The incidence angle is fixed at
. The ISAR imaging parameters for Figures 16 and 18 are set as in
Table 2.
Figure 16 presents ISAR imaging results for three typical observation configurations with different azimuthal scanning ranges. The incidence angle is fixed at
. Our GPU-accelerated BP imaging algorithm is applied to focus the backscattering fields to obtain focused ISAR images. In
Figure 16,
Figure 16d–f are RL-GO at a ray density of
without diffraction and
Figure 16g–i are RL-GO at a ray density of
with diffraction. Comparing
Figure 16a–c and
Figure 16d–f, it can be found that the results of this paper’s method and the RL-GO method are in better agreement with those obtained by FEKO’s RL-GO method under the condition of the same ray density, and it even outperforms the RL-GO at specific angles. For example, in
Figure 16a,d, the difference in the scattering in the engine part of the airplane can be seen to be more obvious, and the differences in the scattering in the engine area of the airplane can be seen to be more obvious in
Figure 16c,f;
Figure 16f has strong clutter that overwhelms the information such as the structural features of the airplane, and the results of
Figure 16f are not as good as the results of
Figure 16c. When the ray density is
, the echoes are able to record the geometrical structural features of the airplane in detail, so
Figure 16g–i have very good imaging results compared to
Figure 16a–c and
Figure 16d–f, which confirms the effectiveness of the GPU-accelerated BP imaging algorithms in this paper from the side.
Table 3 shows the computation time and peak memory comparisons for
Figure 16.
It can be concluded that when the ray density is the same, the results of the method in this paper are in good agreement with those of RL-GO. Next, we analyze the difference between the results of the two methods when the ray densities are not the same. In
Figure 16a, there are strong echoes from both the engine and the wing portion attached to the engine. The area indicated by the red arrow ① in (a) represents the wing position. At the observation angles
, the ray will be reflected once after striking the wing portion at position ①. Due to the flatness of this portion of the structure, the ray will subsequently leave the target after being reflected. In our GPU-accelerated SBR method, multiple scattering is taken into account by ray tracing, in which the maximum reflection number is 10, while the diffraction field due to target edges is not taken into account, which leads to a pronounced difference between position ① in (a) and position ② in (g). Scattering spots appear at the positions indicated by the green arrows ③, ④, ⑤, and ⑥ in
Figure 16a,b,g,h.
Figure 16a,b are the results calculated by the method in this paper, and
Figure 16g,h are the results calculated by the RL-GO with diffraction at a ray density of
in FEKO. Both our GPU-accelerated SBR and RL-GO in FEKO are ray-based methods. These scattering spots are related to the scattering mechanism of the electromagnetic waves and the ray tracing mechanism. Due to neglection of the diffraction field resulting from target edges, the target echo in
Figure 16c is weaker than that in
Figure 16i. A comparison of the ISAR imaging results of
Figure 16a–c with
Figure 16d–f and
Figure 16g–i demonstrates the feasibility and efficiency of our scheme by combining GPU-accelerated SBR with the BP algorithm for fast ISAR imaging simulation.
Figure 17a–c illustrate three typical observation configurations with different azimuthal scanning ranges. ISAR imaging results for three typical observation configurations with different azimuthal scanning ranges are shown in
Figure 18a, b, and c, respectively. In
Figure 18, the incidence angle is set as
, and the other parameters are the same as those in
Figure 16. In
Figure 18a–c, the backscattering fields are calculated by our GPU-accelerated SBR method. In
Figure 18d–i, the backscattering fields are obtained by the RL-GO method in FEKO v2020 software, where (d–f) are RL-GO at a ray density of
and (g–i) are RL-GO at a ray density of
. Since the ray densities are the same and none of them include the wrap-around field, the results for the corresponding angle ranges in (a–c) and (d–f) are in good agreement. A comparison of the results of (c) and (f) shows that the echo strength of the airplane body is very weak in (f). There is also noise. Only the engine area exhibits strong echoes, which makes this paper’s method work better under the same ray densities and it can better record the target’s geometric structure information. In general, the focused ISAR images of backscattered fields calculated by our GPU-accelerated SBR method are in good agreement with those obtained by FEKO’s RL-GO method. Some scattering spots can be observed as indicated by the red arrows in
Figure 18a,b,g,h, as in
Figure 16. This is due to multiple scattering of electromagnetic waves from the target surface. For rays reflected multiple times, the phase history of the electromagnetic wave is distorted. Therefore, the scattering spots indicated by the red arrows in
Figure 18a,b,g,h can be eliminated by reducing the reflection numbers in the ray tracing algorithm.
Table 4 shows the computation time and peak memory comparisons for
Figure 18.
Figure 19 shows a CAD model of an electrically large-sized aircraft target, which is in the electrically large-sized category with an electrical size of 171 × 104 wavelengths. This CAD model has 712 face elements. ISAR images for this model were computed using the method in this paper and the RL-GO method in FEKO. The ray densities for both the method in this paper and the RL-GO method are set to be
. The azimuth centers of
Figure 20a–c are
,
,
.
Figure 20 demonstrates three different azimuth ranges. In the following simulations of
Figure 21, the ISAR imaging parameters are set as in
Table 5.
Figure 21 shows the ISAR imaging results of both methods for electrically large-sized aircraft targets, with ray densities of
for this paper method and RL-GO in FEKO. Comparing
Figure 21b and
Figure 21e, ① and ② in
Figure 21b are the structural information of the airplane, and ① is the wing and ② is the tail, while
Figure 21e cannot show this structural information, so this paper’s method is better than the RL-GO imaging result when
. Comparing
Figure 21a and
Figure 21d, the result of
Figure 21a is obviously better than that of
Figure 21d, where phase history distortion occurs at the place indicated by the white arrows in
Figure 21d. Detailed information on the wings, nose, and tail of the aircraft can be clearly displayed in
Figure 21a. This also occurs in
Figure 21c,f, where the white arrows in
Figure 21c,f point. It can be clearly seen that the scattered spots that appear in these places indicated by the arrows are not aircraft structural information. It is a well-established fact that electromagnetic waves exhibit a multipath effect during propagation. This phenomenon entails that an incident wave traverses a multitude of paths to reach a designated receiving point. Changes in phase history data caused by these different paths can be superimposed, resulting in phase history distortion.
Table 6 shows the computation time and peak memory comparisons for
Figure 21.
From numerical simulations of ISAR imaging, it is clearly indicated that strong scattering centers as well as target profiles can be observed under large observation azimuth angles and wide bandwidth. It is also indicated that the ISAR images are heavily sensitive to observation angles. Due to multiple scattering, several triangular patches will be hit by identical rays, resulting in the phase history distortion of electromagnetic waves. Phase history distortion is a common problem with ray methods. Thus, obvious sidelobes can be observed in focused ISAR images. In comparison with RL-GO in FEKO v2020 software, the feasibility and efficiency of our scheme are demonstrated by combining GPU-accelerated SBR with BP algorithm for fast ISAR imaging simulations under wide-angle and wide-bandwidth conditions.