Photoshop :: Fish-eye Effect

I am trying to recreate a fish eye effect in photoshop that will look like the attached image.

Just wondering if there are any tips to keep it as precise and as accurate as possible.

I want to get the bend on the edges of the image to be exactly parallel to the edge of the semi-circle in which it is bordered.

I was thinking of using edit > transform > warp > fisheye;

Followed by... edit > transform > warp > custom

Obviously, I would overlay a similar black border to use as a guide first.