We’ve covered how physical maneuvers with attitude control system and beam steering allows one satellite to capture hundreds of images in the time it goes around the Earth. You can find out more about this in our Beyond the Echo: Rapid-fire imaging on repeat blog post .
We’ve covered how the phased array antenna can be pointed to a center location within the larger region and pulse-by-pulse phase corrections applied to multiplex individual locations into one coherent data collection.
And just when you thought we’ve said everything that needs to be said about beam steering and phased array antennas, we’re now digging into what can be done with these capabilities, the satellite imaging geometry that gets us there, and the flexibility of tasking you get as a result.
Sure, there’s a lot of math under the hood — but the big idea is actually pretty cool and easy to picture. Let’s unpack it with the help of Figures 1a - c (below).
Picture a satellite zipping around Earth. At every instant, we know “where it is” (a position vector) and “how fast it is going” (a velocity vector).
Now, the satellite isn’t just coasting — it’s also “oriented” in space. Engineers like to describe its posture using three familiar terms: roll, pitch, and yaw (just like pilots do for their aircraft).
This trio forms the satellite’s local body coordinate system — the reference frame that helps us aim its radar antenna.
Figure 1a. Multi-Spot imaging geometry with hybrid (mechanical/electronic) steering showing five imaging locations along the satellite track. Mechanical steering keeps the antenna locked on the subsurface target, causing the radar beam to sweep across the imaging locations. Overlaid electronic steering ensures that the radar dwells on each imaging point for the requisite time.
Figure 1c. Resulting SAR images.
The radar antenna sits fixed on the satellite body, pointing down toward Earth. But here’s the trick: the Earth isn’t flat, and what we want to see isn’t at the exact point directly beneath the spacecraft. In general, we want the radar beam to ‘look’ at a collection of different surface locations, having the antenna ‘stare’ at each one of them for a fixed amount of time.
Usually, when the satellite is in a Spotlight imaging configuration, ‘locking’ the beam on the imaging target is achieved by mechanically rotating the satellite around the pitch axis. So that the beam footprint, a projection of the radar antenna beam on the ground, stays fixed in place.
The mechanical rotation is quite a powerful and straightforward tool. We can give it any point in space, choose which side of the satellite should follow that point and the on-board attitude determination and control subsystem will do the rest.
An interesting phenomenon happens if we choose a mechanical rotation target that is below the Earth surface. The result is that the beam footprint doesn’t stay fixed in place on Earth, but rather ‘slides’ on it throughout the SAR image collection.
So now, let’s present ourselves with a challenge. Let’s see if we can electronically steer the beam, to keep it fixed on a surface location of interest, while the mechanical rotation sweeps the beam closer and away from it.
To achieve this, direction vectors and time dependent steering angles (Figure 1b above) in roll and pitch planes are calculated. Both are found by projecting surface and sub-surface direction vectors onto the right planes and measuring the angle between them (that’s where all those cross products and dot products in the equations come in). You can check out the equations in the Electro-mechanical multi spotlight: monitoring of high risk areas by small-satellite SAR research paper.
So here we are with this cool concept. The satellite’s antenna physically rotating at a steady rate, the mechanical part. At the same time, the radar beam is being nudged electronically to stay locked on the imaging locations, the electronic part.
The result?
The radar can start imaging a location even before the antenna physically points at it. Once done, it can smoothly switch to the next location with barely a pause, around 50ish microseconds in fact. The combination of mechanical sweep and electronic steering creates a Multi-Spot mode, which gives so much flexibility in acquiring images. Figure 1a (above) shows the concept from the satellite orbit geometry point of view, and Figures 1b and 1c (above) show how it looks from the ground perspective.
To actually plan an electro-mechanical Multi-Spot acquisition, you need two essentials: the surface imaging locations and the time window when the radar will be imaging them.
Everything else — steering angles, beam direction, and geometry — can be derived from these and the satellite’s orbit data. The challenge is that the solution has to obey strict rules:
Because the relationships between all these variables are non-linear, we rely on a numerical optimizer —an algorithm that searches for the best plan. It sets boundaries to stay within squint angle limits, enforces constraints to ensure no simultaneous tasks, and minimizes a cost function keeping pitch and roll steering as small as possible to improve image quality.
We end up with a feasible schedule where the satellite can efficiently swing its spotlight across multiple imaging locations without breaking the rules.
This kind of geometry isn’t just mathematical gymnastics. It lets satellites track locations and objects on the move and image multiple areas in one pass over the region.
Here is an example of how the technique allows us to capture images along curved lines, in this case following the Danube river in Austria (Figure 2.). The theoretical maximum is approximately 28 images (~139 km, 87 seconds of active imaging) in a ‘straight line’ pattern. Presumably, we do not need that ‘straight line’ pattern - as shown in Figure 2 - we could follow roads, rail lines, rivers, and military lines of control.
Yet another example of the flexibility in image capture is the so-called ‘Brickwall pattern’ — a 5 km × 5 km grid of imaging locations, each with a 5 km square footprint and spaced 4.5 km apart (Figure 3).
In this case, 22 out of 25 targets were successfully scheduled at 0.5 m resolution (1-look). To put that in perspective, this corresponds to an acquisition swath of 25 km at 0.5 m resolution — an incredible 50,000-to-1 ratio.
Conventional wisdom in single-aperture SAR design says this shouldn’t be possible under standard PRF constraints or normal imaging modes. And yet, here we are!
Building up on the capacity and flexibility provided by Multi-Spot, multiple satellites can do wonders for monitoring applications.
The animation below in Figure 4a, shows fantastic teamwork by four satellites monitoring a region in Bolivia - 43 images within a span of 10 minutes. Two of these satellites are flying in mid-inclination ascending orbit; Satellite 1 took a Stripmap image, closely followed by 24 images with Satellite 2 in Brickwall pattern around the first image. The other two satellites are in sun-synchronous descending orbit; Satellite 3 took 10 sparse images, followed by eight images in a Brickwall pattern by Satellite 4.
To reiterate the swath versus resolution advantage, consider a representative location (Figure 4b): Multi-Spot capability achieves the spatial resolution of a Spotlight imaging geometry (0.5 m) while maintaining the swath coverage of a Stripmap mode (25-30 km)—the best of both worlds. In addition, it offers flexibility in selecting the number of looks or radiometric resolution to tailor the acquisition for specific Earth observation applications.
Figure 4b. The best of both worlds - Multi-Spot capability achieves the spatial resolution of a Spotlight imaging geometry (0.5 m) while maintaining the swath coverage of a Stripmap mode (25-30 km).
As you can see, Multi-Spot and hybrid electronic and mechanical steering opens up a whole world of possibilities in acquiring SAR images, allowing satellites to track on the move and image multiple areas in a single pass.
We’re not just talking about a nice-to-have though. This is a capability that improves service delivery for sovereign missions, and for data customers.
For example, the flexibility of Multi-Spot increases the capacity of the fleet, allowing for multiple images in a single pass. We can guarantee capacity for time-sensitive acquisitions considering the flexibility in tasking and image collection with time-sharing the radar.
And capabilities like this scale with the fleet. As the number of satellites in the fleet grows, so does the ability to capture more ground targets in the same pass, reducing the need for multiple revisits.
The result? SAR imagery on-demand. That is incredibly valuable in situations where every minute counts.