How to unlock iPad with broken display?

Today was my unlucky day - I just dropped my iPad and now it appears that my display is somehow broken - it is completely dark now.

No, the glass is still completely intact and the only physical damage is a small dent at one of the corners (at the corner where the volume rocker switch is). Also, it looks like the backlight is still working which I can see when pressing the sleep button in a dark room.

I immediately went to my computer and connected it to iTunes to see if there may be any other damage is and it seems that the iPad is functionaly ok - just the display does not show anything - because iTunes sees it and I can see the contents on the iPad.

So, just to be sure I wanted to immediately backup my iPad - unfortunately without luck. When clicking the "Back Up Now" button in iTunes, I am getting a message that iTunes is unable to backup my iPad because it is locked. This is absolutely correct because I enabled locking.

So, my question is, how can I possibly unlock my iPad to create a backup without a working display - since the display is not showing anything, I assume that also the touch-screen function is gone hence there is even no point in trying to enter my passcode blind.

I did not forget my passcode, so if there is a "backdoor" to unlock would help.

Regards,

-Uli