Creating a feathered edge inside a circle

I am trying to create a feathered edge on the inside of a circular mask when processing an image to get a fisheye effect. 

Here is what I mean.

In the first picture I have applied the spherise filter to a square crop.


Then I can use the Elliptical Marquee tool with a feather to create a feathered circular mask. Then Control J to a new layer. Finally I added a black fill layer underneath.

Here is the layer stack:


Here is the result:


You can see the feather is applied inside and outside the circular mask.

The effect I want is to have a sharp outer edge to the circle and just feathering on the inside. Is there an easy way I can do this? Your advice would be appreciated. 


Kind regards
Chris