A B727 PIC PERFORMS AN UNAUTH TKOF WHEN THE RVR FOR THE TOUCHDOWN POINT IS CALLED BY TWR AS 500 FT DURING RWY ENTRY AT PDX; OR.

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TAXIED OUT FOR EARLY MORNING TKOF; ATIS RPTING 8 MI VISIBILITY WITH CLR SKIES. ENTERED DENSE FOG 1/2 WAY THROUGH TAXI TO RWY 10R. CREW BECAME DISTR WHEN WE STARTED DISCUSSING THE NEED FOR A TKOF ALTERNATE. THE TWR THEN CLRED US FOR TKOF WHILE WE WERE STILL TAXIING AND ABOUT 1000 FT FROM THE HOLD SHORT LINE. JUST AS WE WERE TAXIING PST THE HOLD SHORT LINE AND COMPLETING THE BEFORE TKOF CHKLIST THE TWR BROADCASTED A TOUCHDOWN ZONE RVR OF 500 FT; MID OF 6000 FT; AND ROLLOUT OF GREATER THAN 6000 FT. WE PROCEEDED WITH THE TKOF; REALIZING EARLY IN THE CLB THAT WE HAD TAKEN OFF BELOW MINIMA WHICH IS 600 FT RVR FOR OUR AIRPLANE. THE MAIN CAUSE OF THIS INCIDENT WAS THE UNEXPECTED FOG THAT BLANKETED THE ARPT VERY QUICKLY. WE PUSHED BACK FROM THE GATE IN CLR WX AND WERE SUDDENLY FACED WITH A DETERIORATING SIT. OUR FOCUS ON THE NEED FOR A TKOF ALTERNATE DISTR US FROM FOCUSING ON HOW BAD THE VISIBILITY WAS; AND WHETHER WE WERE EVEN LEGAL FOR THE TKOF. RWY 10L WAS CLR; AS THE FOG HAD NOT REACHED THAT SIDE OF THE ARPT; AND A TKOF ALTERNATE WAS NOT NEEDED. AT LEAST WE GOT THAT PART RIGHT.