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I am not sure of the peer reviewed science ! . . .
The focal length is really only half of the equation - on its own it doesnt give an answer, its the image scale that matters. So the size of the CCD pixels for Imaging and Guide cameras is equally as important as the focal lengths.
It is the image scale of the guide system compared to the image scale of the imaging system are what matters, considered against the guiding software's ability to resolve the centroid of the guide star.
What you are wanting to ensure is that the minimum resolution and correction by the guide system equates to 1 or less pixels on the image system (in a perfect world ! - but 2 or more is probably acceptable in the real world) - that way you dont get blurred stars (increased FWHM) of the image as a result of guiding errors - in this case we are concerned about an under correction.
Since most guiding software can resolve the centroid of a guide star to around 1/10 of a pixel, but certainly well under 1 pixel in good conditions.
It would seem logical to me that the image scale of the guide system could be significantly higher than that of the imaging system.
What amount I really dont know - but I would hazard a guess that it could be 5x bigger and still operate within the other errors of the average imaging system, maybe even as much as 10 times bigger.
Averaged out over time that error could conceivabley be even greater.
However if the guider image is highly undersampled (where a star is less than 1 pixel) this would impose an upper limit on the image scale - say maybe 3.0 to 6.0 arc secs/pixel
Depends a little bit on the star chosen - if its mag 3 you would be OK if its mag 8 you might struggle at the upper limits.
The fact that most guide cameras tend to have smaller pixels compared to the average imaging camera is in our favour in terms of the focal lengths of the guide scope being lower than the focal length of the imaging scope.
Not exactly a straight answer.
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