SLR camera gyroscopic stabilization - limited by rotation of the earth?

In this photography stackexchange answer it is stated that the limits of performance of gyroscopic stabilization of an Olympus handheld camera is related to the rotation of the earth. I'm further confused by the use of stops to rate the quality of gyroscopic stabilization - 6.5 stops seems to be considered the limit due to the Earth's rotation.

This can be read about further in photography trade sites here:

The in-body stabilization itself gives 5.5 stops, and the Sync IS gives 6.5 stops with OIS lenses. 6.5 stops is actually a theoretical limitation at the moment due to rotation of the earth interfering with gyro sensors.

There must be some physics at the bottom of this. How can a camera's rotational stabilization actually be limited by the rotation of the Earth, and how can that limit be expressed as 6.5 stops?

• Oct 27, 2016 at 7:48
• good question, the claim sounds fishy as the earth rotation appears to be insignificant in the time scale of a typical photo exposure May 27, 2017 at 23:00
• @szulat there used to be a pretty good answer here explaining the physics, but the owner deleted it though it was somewhat up voted. If you consider the angular width of a high-pixel modern camera with a medium FL lens, the length of time of a 6.5-stop overexposed photo would be with that lens, and the rotation of the earth all quantitatively it's not so fishy after all. The answer details involves the direction the camera is pointed wrt the Earth's axis and the local latitude. If nobody answers this one, I should probably do it myself eventually.
– uhoh
May 27, 2017 at 23:56
• @uhoh wow, that's unexpected! and what we learn unexpectedly is the best :-) May 28, 2017 at 0:53

Stops are a convenient way to measure the increase in exposure time you can tolerate for the same level of motion blur. If you can hand hold the picture at 1/250 s exposure but the stabilization will let you use 1/125s you gain 1 stop, if it let you use 1/60 you would gain 2 stops. So 6.5 stops is 2^6.5 = 90x as long (roughly)

The limit due to the earth's rotation is that your camera will become a Gyroscope and try and keep pointing in the same direction as the Earth rotates past you. If you could really have an exposure 90x as long then this could be several seconds which would be enough to blur the exposure for some reasonable focal length lens

(More details are in the deleted answer)

edit: Pentax's new K3 camera can use its stabilisation to cancel out the star trails caused by the Earth's rotation during long exposures

• Maybe I'm ignorant of an SE function, but what's the point of referring people to a deleted answer? May 28, 2017 at 0:46
• @AmagicalFishy, mostly to acknowlede and not steal credit from the original poster. Sufficiently high score users can see the deleted answer May 28, 2017 at 0:49
• Thank you! I can't see the deleted answer, if there are any other details you can retrieve that would be greatly appreciated. I think there was some discussion of the problem that any correction requires knowledge of the particular direction that the camera is pointed as well as the camera's orientation around that direction, and this would require some information not available from accelerometer and GPS alone. Simple example would be pointing north versus east versus down, upright versus on its side.
– uhoh
May 28, 2017 at 1:00
• I'm curious - how does the K3 handle this? If you think of setting up a portable telescope with a motorized drive and computer, you have to do at least two alignments on identified objects before the computer knows how to correctly track the motion of the Earth. Possibly one object if there is an independent, approximate measurement of the local vertical with an integrated accelerometer, not sure about that. Perhaps the K3 gyroscopically measures the motion of the Earth for a period of time (3-axis gyro plus 3-axis accelerometer), and then back-corrects buffered data? Then no need for GPS?
– uhoh
May 28, 2017 at 1:06
• @uhoh I doubt it uses the compass for anything more than "view facing north" label. But anti-shake algo can track a bright point in an image and shift the image to keep that staitonary. Detecting that a bunch of bright points on a dark background are moving in the same curved direction and canceling this separately from the movement of the rest of the image sounds easy. Especially if you have a dozen CPUs and 64Mb of program memory spare and are trying to think of features to add ! May 28, 2017 at 17:30