What is the independent source exception in cases where police stumble upon evidence while engaging in an unlawful search or entry?

Courts have applied the independent source exception in cases where the police stumble upon evidence while engaging in an unlawful search or entry, but where there was an independent basis apart from the illegal entry to allow a warrant to issue. See, e.g., United States v. Herrold, 962 F.2d 1131, 1139-40 (3d Cir.) (holding that independent source exception allowed admission of cocaine and drug paraphernalia where agents had entered defendant's trailer unlawfully, seen the inculpatory evidence in plain view, and immediately applied for a search warrant without seizing the evidence), cert. denied, --- U.S. ----, 113 S.Ct. 421, 121 L.Ed.2d 344 (1992); United States v. Mulder, 889 F.2d 239, 241-42 (9th Cir.1989) (holding that independent source exception allowed admission of chemical tests conducted pursuant to a warrant after defendant's first conviction had been reversed because those same tests had been conducted without a warrant).