I don't have the means to 'show'. All I can do is draw inferences from the discussions I see on the net. With long telephoto lenses, lens shift appears to be more effective than sensor shift. Is this not the case?
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Ray, you have completely ducked the point. I was not discussing which works better, I am discussing you unjustified use of the wording "real optical stabilization" to apply only to lens wiggling and not sensor wiggling.
But as to those discussions about how well the different methods work with long lenses, I find them seriously lacking in quantitative basis. All they seem to show is that sensor wiggling might require grater sensor movements for longer focal lengths, but that gives no comparison to how well it compares to lens wiggling.
More important, it is the real focal length that matters, not the "35mm equivalent".
If you need enough sensor movement to keep up with camera movement before the exposure starts as well as during, the amount of movement needed (in mm) depends on the actual focal length, independent of the format. This is because a given angular twist of the cameras moves the image relative to the sensor by about (focal length)/(angle). In the Olympus digicam under discussion, the maximum true focal length is about 80mm, small relative to the focal lengths of interest in Sony and Pentax sensor stabilized cameras. (And I expect compact digicam lenses to stay under about 100mm.)
Sensor based stabilization might struggle with real 500mm lenses.
Life is even easier with "just in time" stabilization that is only active during exposure, not during composition. My estimate is that
1. Without stabilization, decent sharpness needs the image motion across the sensor during exposure to be 1/1000th or less of the sensor width, and a smaller fraction for higher resolution needs: maybe no more than about two pixel widths.
2 This presumably happens at traditional hand-holdable shutter speeds.
3. To get four stops of stabilization requires handling 16 times that traditional hand-holdable shutter speed, a situation where without stabilization the image might move as much as 16/1000's of the way across the sensor, but not more than about that.
4. So sensor moving stabilization only needs that much sensor movement during the exposure. For a compact digicam sensor, this means less than 0.2mm of movement. For a 35mm format sensor, it would mean less than 0.5mm.
And for any format, the amount of sensor movement needed during exposure does not depend on focal length or angular field of view! It depends only on how many stops you want to go beyond the hand-holdable limit.