Originally posted by Professor Batty I don't have a clue as to how it works. Magic?
OK, here's my theory (no time to check it all out in practice right now).
On the "full frame" Q models, the camera does not
"switch to a mode where it utilizes a smaller part of the sensor corresponding to an 1/2.3 inch sensor"
as claimed on
SMC Pentax-Q 03 Fish-Eye 3.2mm F5.6 Reviews - Q-Mount Prime Lenses - Pentax Lens Reviews & Lens Database
Nor does it extrapolate to a 4000x3000 format,
in part because a routine for that is not included in the camera's limited processing.
But what the camera does have is a correction for barrel distortion, like you see with the 02 zoom.
So my guess is that the Q7 and Q-S1 just run a "barrel distortion correction"
to stretch out the corners of the image from the 03 so you don't see any vignetting in the JPGs.