The one-line estimate
The smear in an image is roughly the angle the camera turns during the exposure, divided by the angle one pixel sees. Smear in pixels ≈ angular rate × exposure time ÷ per-pixel field of view.
A narrow-field imaging telescope sees a tiny angle per pixel, so even slow rotation smears it across many pixels. That is why pointing stability matters more as resolution goes up.
Where the motion comes from
Slew. The satellite is deliberately turning, either between targets or to keep one target in view. Imaging during a fast slew smears everything.
Jitter. Small, fast vibrations from reaction wheels, solar-array drives and other moving parts. Jitter is too quick for the attitude controller to cancel, and it shows up as a blur or a wobble within one exposure.
Drift and knowledge error. Even when the platform is steady, errors in knowing where it points blur a stack of frames and throw off where the picture lands on the map.
The usual fixes, and what they cost
Wait to settle. Stop slewing, let the vibrations die down, then image. It works, and it costs collection time at every target.
Buy a quieter, stiffer bus. Better reaction wheels, vibration isolation and more precise attitude sensors. It works, and it moves cost, mass and lead time into the platform.
Shorten the exposure. Less time means less smear, and less light. Faint detail sinks into the noise.
Stacking short exposures
The other route is to take many short exposures, measure how the camera moved between them, shift each frame back into line and add them up. Each frame is too short to smear, and the stack recovers the light a single long exposure would have collected. Noise adds more slowly than signal, so the stacked image comes out sharp and clean.
The hard part is knowing the motion precisely enough. Our approach uses a star camera's attitude as the prior for that registration, and does the stacking on board.
Why it matters for geolocation
A sharp picture is only half the product. To be useful, every tile has to be placed on the ground accurately, and that depends on knowing where the camera pointed at the moment of exposure. The attitude that removes the blur is the same attitude that geolocates the tile.
On-board processing