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Unexplained visual artifact(s)

A few weeks ago as a passenger in a car trip to Seattle I noticed that when I looked at power lines with my right eye (with my glasses off), I saw a double image.  If the scene was like this:



then what I saw with my right eye was something like this:




When we got to our first stop, I drew a small black dot on a piece of white paper:

and looked at it from a distance of about eight feet (with my right eye); what I saw was something like this:

Yesterday, I hooked up some LEDs to a battery and looked at them from a distance of about thirty feet.  With my glasses on, they appeared as well-defined dots.  With my glasses off, I saw something like this with my left eye:

The angles of the lines radiating from the center point remained constant (if I blinked or rubbed my eye).  There was a similar image on the other eye, but the angles and relative lengths of the lines were completely different.  I tried this with LEDs of various colors; the only difference I noticed was that the lengths of the lines were more similar with the blue LED than with the others (that is, the image was a bit closer to being symmetrical around the circle).

This morning, I did the black dot experiment again, and found that there were actually several dots, and that their orientation to the main dot was the same as the orientation of the strongest radiating lines in the LED experiment.

Then, I saw my optometrist, told him what I'd seen, and showed him the drawings.  He didn't have an explanation for what I was seeing.

I'm assuming that there's some kind of asymmetry in my lenses.  But I don't understand how it is that I can see these artifacts with my glasses off but not with my glasses on.

I just learned about wave-front glasses, and I think it's related ...