# Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers
## 3 Results  
### Satellite Optical Scattering Profile  
The profile of the optical power scattered from the wrinkled gold foil was highly variable due to the launched beam finding more or less favourable facets on the target. Repeated tests with different scales of wrinkles and translating the target found the profile to average to an approximately \(\sqrt{\cos\theta_{a}}\) relation, where \(\theta_{a}\) is the angle of incidence of the laser relative to the line between the target and receiving optic. This indicates broader scattering than predicted by assuming a Lambertian reflectance and suggests that the effectiveness of this method of disruption will be more effective at high angles of attack (larger distances between the laser terminal and the ground station) than first expected. However, this also means that less light than expected will reflect towards the ground station at low angles of incidence.  
With this experimentally determined scattering profile, and the size (4 m\({}^{2}\)) and albedo (0.3) of _Micius_ given in Table 1, we are able to estimate the optical scattering cross section of a _Micius_-type satellite as  
\[\sigma_{sat}=4\times 0.3\times\sqrt{\cos\theta_{a}}. \tag{11}\]  
For the scenario where excess photons scatter inside a satellite-borne QKD receiving optic and couple into the QKD detector, the scattering profile was found to be highly variable and dependent on the structure of the telescope. For example, the rim of the telescope optic was responsible for a significant fraction of detected photons. Scatter from objects placed near the receiving aperture greatly increased the excess photon rate. This means the effectiveness of this method of disruption is going to be highly dependent on the exact design of the telescope, and the design of the satellite. (For example, scatter of light off an antenna or other appendage on the satellite near the aperture will significantly increase number of photons coupled into the optical path of the receiver). This makes it difficult to make a good model for the internal scattering profile of the telescope.  
For the 50 mm Galilean-type telescope used in these laboratory tests, a scatter profile of \((\cos\theta_{a})^{2}\) gives a reasonable approximation for the scatter profile at angles of incidence greater than 5\({}^{\circ}\). However, it will underestimate the number of detected photons at low angles of incidence, leading to a very conservative estimate of the disruption potential at these low angles (short distances of less than 100 km between the mobile laser terminal and the QKD ground station). A scaling factor of \(10^{-7}\) is applied to the photon number, that is, the measurements show that only around one in \(10^{7}\) photons incident on the QKD receiver optic from high off-axis angles couples into the SPD.  
For a receiving optic of diameter \(D_{s}\) with similar scattering characteristics to the Galilean telescope used here, a scattering profile of  
\[\sigma_{rec}=10^{-7}\times\frac{\pi D_{s}^{2}}{4}\times\cos^{2}(\theta_{a}), \tag{12}\]  
gives a reasonable approximation for angles of incidence grater than \(5^{\circ}\).  
Because of the difficulty of developing a reliable scattering model that is applicable to a variety of different optics, detailed analysis of disruption of the satellite-side QKD receiver scenario will not be carried further in this paper. However, a general discussion will still be included because, since the laser terminal is directly targeting the receiving optic, rather than relying on scattered light returning to the ground, a significantly greater excess photon rate is likely to be achieved in this direct-targeting scenario.