Here's something nice from those folks at THX. It's a free app (through February 4, then it's US$1.99) that allows you to assess the state of your home theater and make adjustments to improve audio and visual performance.
THX tune-up connects to your TV with the Apple Digital AV Adapter and an HDMI cable. You'll want the Lightning cable version if you have a newer device. It can also connect to your Apple TV with a wireless connection.
You can check your screen's aspect ratio, brightness, contrast color and tint. The app also