FLC OF ACR LTT ACFT TKOF BELOW TKOF MINIMUMS.

Narrative

UPON OUR CONTACTING GND CTL WE WERE TOLD THAT THERE WAS A 3 HR GND STOP FOR DTW; THE CONTINUATION OF OUR FLT. WE HAD 6 PAX ON BOARD BOUND FOR DTW AND WERE ENPLANING 4 MORE BOUND FOR DTW. JUST AFTER SHUTDOWN; GND CTL ASKED US HOW SOON WE COULD BE AIRBORNE AND IF IT WAS LESS THAN 15 MINS WE COULD BE RELEASED. MY FO AND I RUSHED THE PAPER WORK AND CHANGES TO OUR RELEASE; OBTAINED AND SUPERVISED DEICING; RAN CHKLISTS; STARTED ENGS AND CALLED FOR TAXI. MKG GND TOLD US TO TAXI TO RWY 6. JUST PRIOR TO DEP I WAS DISCUSSING DEICING INFO VIA RADIO WITH OUR COMPANY PERSONNEL UPON RETURNING TO THE ATC FREQ. MY FO ADVISED ME THAT THE TWR HAD CLRED US FOR DEP. DURING FLT; MY FO AND I WERE DISCUSSING THE EVENTS AND HE STATED THAT HE COULD NOT RECALL IF THE TWR HAD ADVISED HIM THAT THE VISIBILITY WAS 1 MI WHILE I WAS OFF FREQ. 1 MI IS REQUIRED FOR DEP OFF OF RWY 6. I STATED THAT WE NEEDED 1 MI AND THAT ATIS WAS BROADCASTING ONLY 3/4 OF A MI. I THOUGHT I CONVEYED TO GND THAT WE NEEDED TO WAIT FOR VISIBILITY OF 1 MI BEFORE DEP. SO I ASSUMED THAT WHEN WE HAD BEEN CLRED FOR TKOF (WHILE I WAS OFF FREQ) THAT THE VISIBILITY WAS RPTED AS 1 MI.