Put the display to sleep without putting the whole computer to sleep?

Question

I like to use vnc on my ipad on my bed. I want the mac to go to a black screen so I can fall asleep while using the ipad, and not have to get up to shut down the mac afterwards. Is there anyway to turn off the imac screen without sleeping?

I'm open to anything that minimizes the light - so if the backlight is off, that would meet the needs even if the screen is still drawing content.

From a semantics standpoint, let's assume the following:

When the system sleeps, the display sleeps or a screensaver engages are all distinct states. The display is asleep when the backlight is off and the GPU doesn't bother drawing any signal to that display but continues to run. This is different than system sleep where everything except the RAM and network interfaces¹ are shut off.

^{1: Network interfaces that support wake on lan (WOL) only do so when power not from a battery is available.}