Originally posted by mikesbike well, this is very interesting- what actually is "focus breathing"? Does it actually change the focal length of a lens? Or does the lens "act like" a different focal length? In the case of APS-C vs. FF a lens gives a cropped image, making it "act like" a lens of a different focal length. In any case, if we are using modern AF lenses, the lens info is fed to the camera system. We don't have to feed in the FL manually. Would it not be possible for the SR system to be set up within the camera system to detect which lens is being used, its FL, whether APS-C or FF is being used, and what the properties of the lens may be, including the distance to subject and the "focus breathing" characteristics of the lens?
The "focus breathing" phenomenon has been known for a long time, even before SR came along.
The answer depends on:
1) the definition of focal length (refraction versus angle-of-view definitions); and
2) the type of lens (simple primes versus everything else).
A physicist's optical definition of focal length measures how the lens refracts light and defines it in terms of a mathematical relationship between the distance to the in-focus object out in the world and the distance to the in-focus image inside the camera. A physicist or optical engineer would say that the focal length of a simple prime lens DOES NOT change when you focus from far to near, even in the case of a macro lens.
However a photographer's angle-of-view definition of effective focal length (how wide is the view) and the definition of focal length for SR purposes does imply that "effective focal length" does change with the focusing distance and any focus breathing does involve a change in "effective focal length". The SR system needs to know the angle-of-view of a pixel so that it can convert a measured angle of shake motion into some number of pixels of corrective shift movement. (Note:; the SR system does not care whether the sensor is full frame or APS-C -- the amount of required sensor shift to correct pitch and yaw shake doesn't depend on the format size)
For zoom lenses and complex internal-focus primes, both the physical and the angular measures of focal length can change as the zoom and focus mechanisms shift the internal elements. Note that whereas the effective focal length of a prime tends to increase with decreasing distance, the effective focal length of many zooms at the long end tends to decrease with decreasing distance.
As for your final question about automating this, the answer is yes. For newer Pentax lenses, the data pin tells the camera about the model number, focal length, and approximate focus distance of the lens. One can presume (or hope) that Pentax engineers created lens-specific tables for what SR focal length to use for a given lens, zoom focal length, and focus distance setting.