AIR TAXI CARGO FLC DEPARTS USING ATIS STATED VISIBILITY BUT VISIBILITY HAS DROPPED TO FIVE EIGHTHS OF A MI. TKOF BELOW MINIMUMS.

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RECEIVED ATIS; VISIBILITY OK. RECEIVED CLRNC TO CPS. LOADED PLANE. STARTED ENGS. COPLT'S LEG TO FLY -- TAXIED OUT VIA TXWYS Y/K/F. BRIEFED COPLT ON TKOF PROCS. HIS DUTIES; MY DUTIES. DEPARTED #3 AFTER 2 COMPANY ACFT -- CLRED TO TKOF. ON TKOF ROLL; VISIBILITY RPTED AS 5/8 MI. VISIBILITY REQUIREMENT 3/4 MI; FAR PART 135. CONTRIBUTING FACTORS: ATTEMPTING TO AVOID MORNING RUSH HR DELAY. MEET ARR SCHEDULE. RAPIDLY FLUCTUATING VISIBILITY. BRIEFING COPLT. 2 COMPANY PLANES DEPARTED AHEAD -- ASSUMED THAT VISIBILITY WAS NOT A FACTOR. LOW CEILING. I FEEL THAT NO SAFETY WAS COMPROMISED; ONLY VISIBILITY REQUIREMENT MAY NOT HAVE BEEN MET. COMPANY POLICY IS VISIBILITY TO LOW '3/4 MI DOWN TO 0-0-' DEPART PART 91 AND PICK UP CARGO AT ARPT WITH VISIBILITY MINIMUMS. SEVERAL REPOSITION FLTS MADE IN LAST FEW WKS. ZONE MGR DEPARTED FIRST ASSUMED IT WAS 'OK.' SUPPLEMENTAL INFO FROM ACN 336608: FROM DEP END OF RWY 31C TO WHERE I BEGAN MY TKOF ROLL IS ABOUT 1 NM. I COULD SEE FROM ONE SIDE OF THE ARPT TO THE OTHER END. I DEPARTED RWY 31C WITH WHAT I COULD SEE AS AT LEAST 1 MI VISIBILITY. ON THE FOLLOWING DAY; AT MDW; I HEARD FROM COMPANY PLTS THAT WERE BEHIND ME; THAT TWR HAD RPTED VISIBILITY AS 5/8 MI. I HAD HEARD NO DISCUSSION OF VISIBILITY LESS THAN WHAT WAS RPTED BY ATIS (1 MI) ON GND CTL OR TWR FREQ BEFORE I DEPARTED. I DO NOT BELIEVE SAFETY WAS COMPROMISED IN ANY WAY. I WATCHED THE PRECEDING ACFT TKOF; CLB OUT AND TURN TO THE W UNTIL HE WAS APPROX AT 2000 FT MSL. CONTRIBUTING FACTORS: QUESTIONABLE ACCURACY IN WX RPTING AT THE MIDWAY ARPT. RECENTLY FOUND THE ARPT ON THE ILS TO RWY 4F AT 1200 FT MSL. WX RPTED AT THE TIME 5000 FT OVCST AND 7 MI VISIBILITY.