Airplay iPhone to vertically turned (portrait) HDTV

I have an iPhone and an LED HDTV turned vertically as a portrait-orientation display. I have a an AppleTV connected to the TV via HDMI. I would like to be able to airplay my iPhone to the TV and have it rendered vertically with the screen filling the screen rather that letterboxed on either side like it normally displays on a 16:9 landscape display.

Anyone know an easy way to do this? When I turn my phone in certain apps to render landscape, it fills the screen, but really what I'm looking for is to turn the image 90 degrees and fill the screen.

Alternatively, if anyone has built this into an app so that when it airplays it tricks the appleTV to think it is in landscape mode, that would also be helpful.

Thanks in advance!