After waiting hours for a flight departure delayed because of heavy fog, I wonder why planes can perform an instrument landing with no visibility, but cannot take off without a minimum visibility.
Using a HUD, an airliner can take off with visibility as low as 300’, and land with visibility as low as 600’. Without a HUD, you need 500’ (and appropriate runway lights/markings, plus regulatory approval) for takeoff, and whatever your autopilot Cat III autoland system (along with the landing runway) is approved to for landing. (Or 1800’ for cases of no Cat II / Cat III capability.)
As noted, a pure “zero visibility” landing (a Cat IIIc) doesn’t yet exist, because while the autopilot can bring the aircraft to a stop on the runway, some visibility (300’) is still required to taxi clear and get to the parking spot.
Thankfully, visibilities below 500-600’ are pretty rare in most places. Not all airports have the taxiway lighting required for low-visibility (typically, below 1200’ lateral visibility) taxi operations. That is an airport limitation, not an aircraft limit.
Talking about so many feet of lateral visibility, the actual nomenclature is Runway Visual Range, or RVR. That is reported in feet in the U.S., and often in meters elsewhere.
Though your question does not explicitly say so, it implies that you're talking about flights that are carrying passengers or cargo for hire, and other answers address that. However, taking your question as explicitly stated, in other words not just air carrier operations, and applying it to U.S. operations, the phrase:
cannot take off without a minimum visibility
is not always correct. There is no takeoff minimum required for Part 91 operations (private aircraft if you will). In the 2017 edition of https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/instrument_procedures_handbook/media/FAA-H-8083-16B.pdf, you will find on page 1-8 the following:
Aircraft operating under 14 CFR Part 91 are not required to comply with established takeoff minimums. Legally, a zero/ zero departure may be made, but it is never advisable.
Takeoffs by corporate and personal aircraft without established takeoff minimums were common, though not frequent, in the rainy and foggy U.S. Pacific Northwest weather prior to my retirement, and I have no doubt Part 91 operators still take advantage of that regulatory flexibility. I made many such takeoffs without incident as did fellow corporate and personal pilots at my home field.
By the way, while everyone I think understands what they're saying when they say zero visibility, you can always see something, especially if you're sitting down low in a small aircraft.
They can take off at very limited visibility, and they do. Key is then of course to make sure that no other aircraft are on the runway, and this is in fact how the deadliest crash in aviation history happened: the collision between two B747s at Tenerife Airport in 1977.
The accident was not caused by the reduced visibility alone, but as usual by a long chain of individual factors. If all proper infrastructure and procedures are in place, take-off can take place in very low visibility.
When an aircraft lands in near zero visibility, it is a fully automated process that is actually done without input from the pilot. The pilots are only needed to taxi off the runway and park the aircraft. It is called "Autoland" and many of today's aircraft have it.
As of today no manufacturer has designed an aircraft with "Auto Takeoff" but I suppose it is not impossible.
I have departed in zero-zero conditions (twice.) In both cases, there was another airport very nearby without this problem and I was operating under Part 91.
The biggest danger in a zero-zero takeoff, after unseen planes/objects on the runway, is what are you going to do if the aircraft decides to malfunction on liftoff? Lose and engine (or the only engine.)
Commercial operations have limits for this, and other, reasons.
Under Part 91 operations an aircraft can takeoff with zero visibility (however dangerous that might be).
It all depends upon the equipment the aircraft has board, the infrastructure at the airport that is landing on, and the regulations under which the flight is being conducted under. Aircraft can, under certain circumstances, land in zero visibility conditions. But this requires both the aircraft be equipped to fly a Cat IIIc ILS, approach. The aircrew must have undergone specific training and certification to fly Cat IIIc instrument approaches, and the airport must be equipped with the infrastructure on the ground to support a Cat IIIc ILS approach. As for conducting a zero zero take off, for revenue carrying commercial and charter flights conducted under parts 121 and 135, this is not allowed; minimum visibilities are 1 sm with 2 or less engines and 1/2 sm with more than 2 engines. You may, however, conduct zero zero departures while operating under Part 91 regulations.
Zero zero instrument landings are flown by specifically designed auto pilot for this purpose.