Facebook share image with target url

i am currently developing a "share on facebook" feature but i don't know if it is possible. The user should have a share button on a webpage, but with the button he doesn't share the page he shares an image.

When another user sees the image on facebook, and clicks on it, he should get redirected to a url i can choose.

i can't simply share the whole site and use open graph tags because the page where the share button is located is on a private area of the website and can only be accessed when you log in.

this whole thing must be done via javascript on client side. perfect solution for me would be if i can use sth. like

FB.ui(..., {image: 'path to image', url: 'url to call when image is clicked on fb'},... );

Any ideas?