Telescopes with adaptive optics (AO) have been in use for several decades. To my knowledge, the lowest wavelengths utilized are in the near-infrared. It's known that Fried parameters are smaller for visible versus infrared ranges.
Are there any earth-based observatories utlizing AO in the visible range? What are the technical issues to achieve acceptable AO Strehl ratios in the visible range?
They are rare because the size of the patch of atmosphere that can be corrected by a given guide star is so much smaller at shorter wavelengths and changes faster - so you are either limited to where you can observe (near a bright guide star), or you need complex and expensive laser guide star systems.
If you are purely imaging (rather than trying to use AO to feed a spectrograph) there is a common alternative. You image the object continually but only use those images where the atmosphere happened to be still enough to briefly give a good image. You can do this either by reading out the CCD in short exposures or using a separate shutter. You can combine this with a simpler AO system to make a "good" atmosphere into an "very good" one - eg the Magellan telescope has a visible AO system
The other big driver against a visible AO system purely for imaging is that you can always use the Space telescope instead.
As per my knowledge in visible range making workable AO compensation system is very difficult and no earth based observation telescope exits. If we assume that acceptable S=0.8, at the near-IR wavelength range (say, 1.5 um), then the strehl ratio at visible (say, 0.5 um) is 1/3*0.8. Because the S is proportional to (wavelength)^6/5.
