background texture for high resolution tablets.

I am currently developing a game on tablets for Android and IPad. My game requires a static background that fit the entire screen, I use orthographic camera for this. However, I found out that the resolution for IPad 3 is 2048x1536, some device are even higher. Does it mean in order not to loose any details of the background when running the game on these devices, I have to produce a 2048x1536 texture size and load it up in the game? I am hoping there is an alternative way so that I do not have to use a 1Mb size of picture for every level. Could someone please give me some tips please? Thanks alot!

If you want pixel-perfect images then, yes, you have to use as large an image as the resolution you are going to support is. But…you can scale that image down and use it on the lower resolution devices instead of importing multiple versions.