Did any actual Puritan congregations impose scarlet letters on adulterers?

Nathaniel Hawthorne's (fictional) book, the Scarlet Letter, in my opinion, has seared a characterization in people's minds that Puritans were dour, hypocritical, legalistic, and shame-driven Christians. Having read many of the actual writings of the Puritans, this characterization seems completely foreign, almost to the point of thinking that Hawthorne was deliberately inventing a horrible community so he could drag the Puritans down. Are there any real historical examples of scarlet letters (figuratively or literally) on sinners for their sins? It is hard to imagine that the religious movement that produced Richard Baxter (himself a notorious drunk before conversion), Hugh Binning, John Owen, Jonathan Edwards, or Jeremiah Boroughs would be associated with something as antithetical to their doctrine as the public shaming of notorious sinners as a form of penance.