Using only part of a pot’s rotation with full resolution?

I have a device I'm designing with my Arduino that uses a rotary potentiometer. However, I only want to use part of the rotation (about 45 degrees) and I'm concerned I'll lose resolution by limiting to only that partial range.

Is there some kind of hack I can do with Arduino to get full resolution for a partial range of a pot? Or do I need a specialized pot with a smaller rotation?

Touch here for the full post on the Arduino Apprentices tumblr

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