Install an Electric Security Door to a Belt Mechanism

Any normal limit or proximity switch on the door, with contact in the control circuit.

You want a proximity sensor switch from a machine safety supplier, for example

Sick

Agree with Tornado.

Unless I misunderstand you question,

something like this should do nicely as a door position switch.

Google search Limit Switch will yield many different types. Plunger, lever arm, roller arm... many actuators to select from.

Before specifying you need to carry out a risk assessment in order to categorise what level of safety you require.

Without more detail on the type of equipment it's difficult to advise - for example is it heavy industrial equipment or a lightweight desktop printer?

An alternative method would be - the door can't be opened until the system is turned off (i.e. an electrical latch).

We use these type of electronic interlock switches on most of our access guards. Many brands and types available. Won't allow the guard to open unless an E-stop is activated.

Usually seen in elevator brake mechanism, use this type.

If you are in a part of the world where machinery safety directives are enforced, or if you are building a machine going to one of those areas, then you must use a qualified machine safety interlocking system after preforming a risk assessment as mentioned above.

If you are in North America where those safety directives are not yet enforced, simpler limit switches or proxy switches may suffice. But some companies are requiring that the IEC based machinery safety directives are used anyway, even though not technically required here yet, but knowing that it is coming they are beginning to demand it now in order to avoid having to retrofit a lot of equipment when it happens.

The normal and proper term is "interlock".

We use light curtains.