Rayleigh limits are all about resolving two equally bright objects (such as stars), which is not what we are doing here. Our imaging and processing techniques allow us to do much better than Rayleigh to detect features..
Rayleigh limit is decided by the diameter of Airy disk, which is the smallest information unit you get on an image for a given aperture. In simple terms, if the Airy disk is 9um, covering 3 pixels, then adding a 2x Barlow lens would make it cover 6 pixels, but all those 6 pixels still represent only one valid data point, and is very blurred.
Take this Airy disk photo for example:
It took 20 pixels to reveal a star's Airy disk, but that give you a false feeling of an large object, in fact all these pixels represent only one valid data point
In Jupiter's case, you could use similar oversampling method, first using a 7x Barlow. Jupiter emit millions of data points, but all of them become an Airy disk after passing the telescope, they stack over each other, turns into a very blurred image, you have to resize the resulting image to regain sharpness. The overall result is no better than just sampling using 3 pixels per Airy disk
No amount of imaging and processing could change physical laws, unless that law itself is wrong. But I don't think that is the case, since all modern optical makers build their lens based on these calculations. If a 127mm telescope is really capable of resolving 0.25" details, why don't the telescope maker mark it proudly on their product page?
Edited by johnyj, 20 September 2023 - 12:22 AM.