NMAC OR AN UNAUTH FORMATION FLT.

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MY COMPANY WAS UNDER CONTRACT TO DO MAPPING ON A SITE NEAR HIGHWAY 295 ON THE W SIDE OF JACKSONVILLE; FL. THIS REQUIRED THAT WE USE OUR AERIAL MAPPING AIRPLANE/CAMERA AND FLY ALONG 3 SHORT FLT LINES AT AN ALT OF 1680 FT ABOVE THE GND. WE DSNDED INTO THE AREA FROM THE W WHILE WORKING WITH JACKSONVILLE APCH. JACKSONVILLE APCH GAVE US TFC INFO ON AN ACFT CIRCLING IN AN AREA NEAR OUR PROJECT SITE. I MADE VISUAL CONTACT WITH THIS TFC. IT WAS SOON OBVIOUS THAT THE TFC WAS A FLORIDA HIGHWAY PATROL ACFT LOOKING FOR SPDING CARS ON HIGHWAY 295. I MAINTAINED VISUAL SEPARATION WITH THIS ACFT; TIMING THE RUNS ON OUR FLT LINES SO AS TO AVOID GETTING TOO CLOSE TO THE OTHER ACFT. I ASKED JACKSONVILLE APCH IF HE HAD ANY WAY TO CONTACT THE HIGHWAY PATROL. HE SAID HE DID NOT HAVE TIME. SOON THE OTHER ACFT STARTED CHASING AFTER US AND SEEMED TO ATTEMPT FORMATION FLT WITH OUR ACFT. I KEPT TURNING AWAY AND THEN APPLIED FULL PWR AND CLBED AWAY. I ASKED JACKSONVILLE APCH IF HE WOULD HAVE THE WATCH SUPVR CALL FLORIDA HIGHWAY PATROL. HE SAID HE WOULD 'MAKE A NOTE OF IT.' WE THEN RESUMED OUR OP; STILL MAINTAINING VISUAL SEPARATION AND COMPLETED OUR WORK. WE CONTINUED FLT FOLLOWING TO OUR HOME ARPT AND LANDED. ONCE ON THE GND I TELEPHONED THE HIGHWAY PATROL OFFICE IN JACKSONVILLE. I GAVE THEM MY NAME AND PHONE # AND THE NATURE OF THE PROB. THEY THEN CONNECTED ME (VIA TELEPHONE) WITH THE PLT. IT WAS AN EXTREMELY BAD TELEPHONE CONNECTION AND I COULD NOT HEAR WHAT HE WAS SAYING VERY WELL. I EXPLAINED OUR OP TO HIM. HE SAID HE WAS TRYING TO SEE OUR 'N' #. HE SAID HE DID NOT WANT THERE TO BE ANY HARD FEELINGS AND APOLOGIZED. THE PROB COULD HAVE BEEN ELIMINATED IF FLORIDA HIGH PATROL WOULD WORK WITH THE APPROPRIATE ATC FACILITY WHEN THEY ARE WORKING IN OR NEAR CONGESTED AIRSPACE.