Make texture wrap around half sphere?

I have a half sphere that I am trying to apply a texture to.

Im making the original file as a circle in photoshop with the edges as alpha. But when I apply it to the half sphere its distorted.

How should I be creating the texture so that it applies correctly?

Don't start with a circle. Start with a rectangle. SL wraps textures around spheres in a similar fashion to the way maps wrap around globes. The texture shouldn't be circular for the same reason that maps are not circular.

The way it works is the poles (top and bottom of the texture) get squeezed to a single point while the equator (middle of the texture) remains full size. Everything in between gets squeezed to a varying degree in accordance with proximity to the poles.

If you examine really closely, you'll notice that the texture actually gets cut into a sawtooth pattern as it gets very close to the poles, but since the texture you seem to be going for is pretty uniform, you don't really need to worry about that. Make your texture rectangular, and you should be okay.