Coherent integration: to real time or not to real time? That is the question.

Performing long coherent integrations is now widely accepted as one of the best methods for improving the signal-to-noise ratio of fringe measurements. There are two basic ways of carrying out coherent integration. One method, real-time coherent integration, stabilizes the fringes on a detector in real time using a separate detector and feedback loop. In order for this to work, the fringes must be stabilized (nominally to less than one radian) and the response-time of the fringe-tracking loop must be less than a coherence time. The other method, post-processing coherent integration, records the fringe and instrument data with minimum integration and assembles the coherently integrated visibilities after the fact. While recording fringe data for post-processing coherent integration it is only necessary to stabilize to less than the coherence length of the individual channels. In terms of fringe stabilization, in the absence of read-noise, post-processing performs significantly better than real-time coherent integration, one the order of a factor two smaller fringe tracking error. This results in improved SNR, reduced integration time, and the ability to coherently integrate on fainter targets. In cases of sufficiently large detector read noise the situation can change to the point where real-time coherent integration produces better SNR. Real-time coherent integration is thus the less efficient of the two, and should only be employed when detector read noise prevents post-processing coherent integration.