This is a really boring test, yielding interesting results :).
Anamorphic lenses usually don't focus very close, and most aren't really sharp, or even get fuzzy at apertures wider than f=5.6 or with longer focal length lenses.
Diopters not only help focusing closer, but they also improve the overall image sharpness making it possible to use the anamorphic at wider apertures for a narrow dof and with longer focal lengths.
This is a sharpness test using a focus through Soligor anamorphot (similar to the Century optics and the Panasonic LA7200). This type of lenses are great for shooting stopped down and with a wide angle lens to get cinemascope deep focus wide shots. But image can get blurry when you want to focus closer, shoot with an 85mm lens or open up the aperture to get shallow dof.
By using alternatively, or combining a +0.4 Tokina achromatic doublet and a set of low price diopters +1 and +2 I have been able to get quite sharp focus even wide open. I think this is impressive considering this is not Isco glass!
What seems to work best is to use a +1 diopter on top of the +0.4 (the achromat is always desirable to reduce chromatic aberrations), although I find that, on a budget, the +1 alone is not bad on a 50mm lens.
I don't have a test chart, so this is only a book shelf and the Sound After by Mind Things.
Let me know what you think.