Not technically "independence" but at the dawn of the Meiji Restoration in 1868 it became evident that Japan had to modernize her monetary system, and opted for a Yen/Sen/Rin system pegged to the Spanish Dollar standard at 1 Yen = 1 Dollar. It would take 2 years to get the equipment ordered and employees trained, so a special issue of the traditional coinage was issued, with reduced fineness (Silver .968 -> .880; Gold .229 -> .223). The custom was to introduce changes to the calligraphy without changing the design itself, so on the 1 shu and 1 bu coins, "Jo" 常 was modified so that the top right stroke was straight and vertical. The gold 2 shu and 2 bu had the signature on the back very slightly modified. They were exchangeable for new coins until the 1890s.
4,000 mon = 16 shu = 4 bu = 1 yen
1 shu = 6.25 sen
2 bu = 50 sen
No bronze or iron coinage is definitively attributed to this time period. 1 shu silver are common, 1 bu silver are rare, 2 bu gold are common. I don't believe any Ryo are attributed to this time period, either.