# Can image-stacking allow this 0.25 m satellite telescope achieve 0.65m resolution?

The BBC News item UK satellite to make movies from space describes this newly deployed satellite:

caption: Artwork: Manufacturer SSTL calls it Carbonite-2, but Earth-i refers to the satellite as VividX2

According to Gunter's Space Page it has a 25 centimeter aperture and at about 500 km altitude should have a ground resolution of about 1.5 meters. However, according to the BBC article:

"We can collect up to 50 frames per second which is a lot of information," explained Earth-i CEO Richard Blain.

"That allows us to stack the individual images and increase our effective resolution, achieving somewhere around 65cm to 75cm," he told BBC News.

How would a high video frame rate improve ground resolution to 65 centimeters for a ten-inch telescope at 500 km?

I have heard of techniques such as "lucky imaging" (it's a real thing) but this is usually to combat atmospheric seeing effects, not the diffraction limit. Also, this excellent answer points out that atmospheric effects are much less important looking down at the surface than looking up from the surface for apertures well below 2 meters, confirmed by this answer as well.

So here, I don't understand how the high frame rate can have such a profound effect so as to push well beyond the Airy Disk diffraction limit of say $$1.22 \lambda / D$$ which would be about 2.7E-06 radians, or 1.36 meters at a 505 km closest approach (assuming a 550nm central wavelength).

There are other techniques to push beyond this limit, such as Aperture Mask Interferometry as described in this answer, but that wouldn't be related to high frame rate.

The technique is known as "Super Resolution". Basically this involves a few steps, which the general outline is as follows:

1. Knowing the point source performance to a sub-pixel level of your system. You have to move the test target a fraction of a pixel at a time, and calculate the Point Source Function (PSF) for each point. The smaller you can do, the better.
2. Convert this PSF into a smooth function.
3. Take your source image, and deconvolve it, removing the diffraction errors.
4. Combine these with other photos slightly offset.
5. Solve for a solution such that the root image gives the desired value.

This is somewhat similar to images from the deblurred Hubble Space Telescope. The best image I can find of a deblurred Hubble image is this one:

To give a bit better example of how super resolution is used, take a look at this site. Image not included because I'm not sure of the copyright, but it shows that you can add multiple images together to get a reasonable image out. You need to have at least the same number of pixels of data to get a reasonable output, so to double the resolution, you would need at least 4-5 images. With 50 images per second, it seems reasonable that they could achieve the indicated resolution, albeit not as good as a single image would be with a larger telescope.

• Excellent! I had a hunch you'd nail the imaging question ;-)
– uhoh
Jan 12 '18 at 14:55