Lunar reflections during SLIM landing

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2024-02-10 18:00:02

In my previous post, I looked at the Doppler of the SLIM S-band telemetry signal during its landing on the Moon. I showed some waterfall plots of the signal around the residual carrier. In these, a reflection on the lunar surface was visible. The following figure shows a waterfall of the signal around the residual carrier, after performing Doppler correction and using a PLL to lock to the residual carrier. I was intrigued by the patterns made by these reflections, specially by some bands that look like a ‘1’ shape (the most prominent happens at 14:58).

The variable that we have to separate reflections from different points of the Moon’s surface is Doppler. This is only one variable. Since the lunar surface is two-dimensional, the problem of determining where the reflection comes from is undetermined. At any given instant there is a whole curve of points on the lunar surface that all have the same reflection Doppler. However, not all is lost, even if at some instant all the points in these curve have the same reflection Doppler, as time passes the points will have different Doppler versus time curves. So by assuming that there is a certain correlation in reflection strength over time for each point, we might be able to identify individual points on the lunar surface from their Doppler trajectories. Looking back at the figure above, the question becomes: “do the higher intensity patterns in the reflection match the Doppler trajectories of points on the lunar surface?”.

Here we are only interested in the frequency difference between a reflected signal and the direct line-of-sight signal. This is what is plotted in the vertical axis of the figure above. We can make some approximations when computing the Doppler of the reflected signal.

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