My first thought would be a homemade "camera bubble," so the pilot could take photos from the cockpit. The fuselage code is from the 387th Fighter Squadron, 365th Fighter Group, 9th AF. The 365th only flew a few fighter missions before they were trained and utilized as a ground attack unit on 8 March 1944. After that, they flew mostly ground attack missions. Perhaps this is one of the A/C they sent over either before or after their bombing missions, to get photos of the targets.
-Irish