## 2 Radar Techniques for Space Observation and Products
### Radar Imaging of Space Objects
#### 2.3.1 Imaging with the Ku-Band Wideband Radar  
Inverse synthetic aperture radar (ISAR) is a fully coherent processing method, which is the most commonly used technique to produce high-resolution images of rotating objects [12]. It is particularly adapted to intermediate tumblers. A fine resolution in range is achieved with a large signal bandwidth. In order to separate backscatterers in cross range, a spectral analysis is performed on the range profiles acquired over consecutive pulses. The cross-range scaling of the ISAR image is set by the effective angular velocity of the space object. The integration time is usually chosen to obtain similar resolutions in range and cross range. To illustrate the efficiency of the ISAR technique, Figure 7 shows the last ISAR image series of the European Space Agency (ESA)'s satellite AEOLUS before its re-entry. The time between two consecutive radar images is about 6 s. The effect of the rotational motion of the object is particularly visible in the image sequence. The different parts of the satellite (e.g., main body, solar panels) can be clearly identified. The reflections in the center part (see, e.g., the marked region with an ellipse in Figure 7f) are not caused by a system artifact but by the multiple reflections of the radar waves in the instrument payload Aladin (range extended returns). Due to the limited pulse repetition frequency (PRF), the raw data of fast rotating objects might be under-sampled. This violation of the Nyquist condition affects the signal phase over slow time (aliasing effect). As a result, the radar image processed with the ISAR principle is the superposition of the true image of the object (unambiguous signal part) with its ghost images (ambiguous signal parts). The distance between the unambiguous and ambiguous images depends on the rotational motion of the object. For high angular velocities, all the images are overlapping, and the object cannot be imaged properly. To illustrate this effect, Figure 8 shows an ISAR image of Jason-2. The apparent angular  
Figure 7: (**a**–**h**) Series of ISAR images of AEOLUS obtained during its last pass observed by TIRA on 28 July 2023 [13]. velocity was estimated to be about 9 deg/s. The additional solar panels at the edge of the image can be clearly identified as ghost images. The radar data of fast tumblers can be processed using the same tomographic approach that is used for medical imaging [14]. The tomography technique exploits the amplitude values of the range profiles over time. The achievable resolution depends on the transmitted signal bandwidth and on the covered aspect angle. The Russian satellite COSMOS-1408 is taken as example in the following. This satellite was hit by a Russian anti-satellite (ASAT) weapon in November 2021 [15]. The largest debris piece of the generated fragmentation cloud was observed with the TIRA system two weeks after the event. From the range profiles presented in Figure 9 [15], an apparent angular velocity of about 90 deg/s could be extracted. Because of the strong under-sampling, meaningful ISAR images could not be computed. Figure 9 shows a radar image generated with the tomographic approach. The figure reveals that the solar panels, the gravitational boom, and the signals intelligence antennas were destroyed by the ASAT weapon. Only a solar panel attachment is still visible in Figure 9 when comparing it with Figure 10. Radar images computed with tomography differ from the ones computed with ISAR. The longer integration time raises the requirement on the range profile alignment and on the stability of the rotational vector. Temporal variation in the angular velocity causes a smearing of the radar images and should be accounted for. This is also true for ISAR; however, it is less critical due to the shorter processing interval. Figure 8: Jason-2 (13 October 2022). Figure 9: Cosmos-1408 (1 December 2021) computed with an angular velocity of 92.3 deg/s. 2.3.2.