It is a US Army Infantry Officer button. The basic design of the emblem on it was in service from the 1820s through 1902. The very-specific version you found, which has curved "serifs" on the letter I, dates from the latter part of the civil war to 1875. If you can tell us what the backmark says, I might be able to narrow down the date range a bit closer.
Edit: You added the backmark while I was typing my reply. That particular Extra Quality backmark dates "mostly" from the 1860s and 70s.