What is the test for exhaustion in a motion for habeas corpus relief?

We are first confronted with a challenge to our jurisdiction. Prior to seeking federal habeas corpus relief, a detainee must exhaust his state remedies by fairly presenting his federal constitutional claim in the state courts. 28 U.S.C. 2254(b), (c). As we explained in Fielding v. LeFevre, 548 F.2d 1102, 1106 (2d Cir. 1977), the exhaustion requirement is not "a formal hurdle placed in the way of meritorious claims, but an essential element of federalism in the administration of criminal justice." The policy of affording the state courts an opportunity to address and rectify errors of constitutional dimension is especially compelling where the petitioner has sharply called into question the conduct of a state trial judge. Id.