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On Magnitude Limits for Point Source Detections

The notion of magnitude limits is formalized as a compromise between incompleteness and spurious detections. The best possible detection performance for given signal-to-noise is then computed for diierent point spread functions and pixel sizes. The resulting theoretical magnitude limits are much shallower than simple 3 arguments would predict (and the reason for this is explained), but are (as expected) somewhat deeper than magnitude limits achieved in practice.