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Application programming interface. In computing, this term generally refers to interfaces that bridge one computing domain to another. When used in relation to Finesse, this typically refers to the Python API, which is the mechanism by which users interact with Finesse via Python by creating classes, making calls to functions, and otherwise using the Finesse library.
The Python object that contains the elements that represent some optical setup: components and detectors, and the connections between them. Alternatively, the kat-script that defines the model may sometimes also be referred to as a model, but strictly this is just a set of instructions to define a model.