We learn the mitzvah of a married woman covering her hair from the verse in Bamidbar (5:18) וּפָרַע אֶת רֹאשׁ הָאִשָּׁה. The Talmud in various places expounds on the details.
While I am very aware that wearing a transparent hair covering is not in the "spirit" of the law, would it be technically considered permissible? The Torah says the hair of the Sotah was "uncovered", implying the mitzvah is to "cover".