Check here: Bently Nevada

Then here: Search GlobalSpec

I had seen some in motion measurement software on a Quality Digest newsletter a few weeks ago but I couldn't find it.

Snoop around in here.

http://www.hexagonmetrology.com/automotive_266.htm

http://www.metris.com/motion_measurement/dmm_-_dynamic_motion_measurement/

You can use LVDT for it , Range is +/- 5 mm Least count 0.01 mm. I purchased from http://www.precision.net.in/products.html They also have Instruments 12 reading / s for it with data acquisition.

I believe laser measurement tools are available with programmable software. Here is a link example.

http://www.bksv.com/doc/bo0402.pdf

Trust this will help

Sounds like your precision requirements won't make this idea feasible, but just in case I mis-understand... here is a cheapish method... Take 2 'bars', can be any material so long as they are straight and won't bend/bow across the distance you are checking. mount these 'bars' on some sort of stand that is not in contact with the apparatus you are checking (in order to prevent vibration related issues) but places them as close as possible without contact. get a video camera and mount on a tripod so that the center of the lens is at the same height as the center of your shaft (be sure the camera is level). using the view-screen on the camera align the 'bars' so that they line up with the top and bottom of the shaft on the view-screen. roll tape, run the shaft up to speed and any variations/deflections should become apparent and will be documented on the video tape; this should give images at a rate of 30 per second (depending on the camera, in the US 30fps (frames/second) is pretty standard)...

A little time spent with a scale rule and still prints from the video and you should be able to get reasonably accurate measurements of any deflection, though I wouldn't think you'd get the .01 - 5mm precision range you are seeking (probably within 5mm, but that's pretty huge compared to .01mm). There are a lot of things to be aware of, any angle of the camera in relation to the shaft will affect accuracy, proximity of the 'bars' to the shaft or camera will affect the perceived distance of deflection so these things must be carefully placed and documented as well to prevent discrepancies between sessions.

'Bars' can be flat steel, wire rope, regular rope, twine, a piece of clear plastic with lines drawn on it... the thinner your 'bar' material is the better, just make sure there is no bow or vibration to it or all is for naught. Also try to use a strongly contrasting color on your 'bars' so they are highly visible against the shaft.

you could also use a still camera with a 'sport' or 'burst' setting, though there is more futzing involved so I would stick to video.

If you need certifiable measurements then you'll want to follow the links provided by previous posters.

Contact Keyance: They have a number of turn key solutions for this.