Date: 201810
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Light: Night
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Takeoff / Launch
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Confusion; Situational Awareness
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
Contributing factors: Procedure; Human Factors; Weather
Primary problem: Weather

Narrative: Preparing for takeoff from ZZZ Rwy XXR with everything going just fine. It was a nice morning with great visibility and I had no reason to believe anything different. I watched other takeoffs as I taxied to the runway and saw no problems. As we finished the checklist and neared the hold short line we were cleared for takeoff with the following call; 'Aircraft X; cleared for takeoff; midpoint RVR [Runway Visual Range] 400.' As we rolled onto the runway I was saying; wait; what did he say? I looked down the full length of the runway seeing everything clearly all the way to the far end. There was no restriction to visibility at all. With that I assumed I either heard something wrong or it was a bogus call. The First Officer and I both thought we were good for takeoff and continued. That was a mistake. The runway was perfectly clear; however; when we got to midfield our lights illuminated the fairly thick fog bank just beside the runway; obviously where the RVR equipment is placed. The call was midfield RVR 400 and I should have stopped; regardless of how unbelievable the call was; or how surprised I was by it. I was surprised enough by any RVR call at all that I didn't even think of it being below minimums. There had been absolutely zero visibility restrictions on the drive from the hotel or taxi out. I let the very last second nature of the information and the surprise of it distract me enough that we were airborne before I realized my error.


Second narrative: It was the first leg of day taking off on Runway XXR at ZZZ. I was PM [Pilot Monitoring]. All checklists were run and ready for takeoff. Tower cleared us for takeoff and included midpoint RVR [Runway Visual Range] reading of 400 feet at last second. ATIS [Automatic Terminal Information Service] and all weather information prior to this were indicating visibility of ten miles. This caught both the PF [Pilot Flying] and I by surprise and were already rolling onto runway. We elected to takeoff instead of confirming RVR reading and seeing if this was a limiting RVR reading. We rushed through the process instead of discussing it at the time and then reviewed the limitations once airborne. We then realized our mistake. PM was lulled into a false sense of security as looking down the runway the small patch of obscuring fog was on either side of runway; but not on runway; so PM felt safe continuing to takeoff. Even after going through with the takeoff it still felt very safe as we didn't actually encounter any visibility reduction on the runway. However; the numbers and regulations are black and white and we would do it differently if put in same situation.


Synopsis: B737 flight crew reported taking off with a mid-field RVR of 400 feet.