I wrote code this weekend to look at the question of how we should visit
a star in the upcoming Terra Hunting Experiment. The current (straw-person) plan is that we will observe each visible star once per night for ten years, with one exposure of a sensibly-chosen exposure time at each visit. Is this a good idea? I was interested in this problem for two reasons. The first is that binning is sinning, with the corollary that bigger bins are worse than finer bins, and a single, long exposure is a very big bin. The second reason is that when there are non-trivial noise sources (like the quasi-periodic variations from p-mode oscillations of the surfaces of Sun-like stars), a few negatively- (or interestingly-) correlated noise draws can be combined in ways that are substantially more informative than by taking the average.
Of course, if you split an exposure (with a standard CCD, say) into sub-exposures, you take on real costs: There is a read time, which is time you aren't integrating, and there is a read noise, that affects each new exposure. So the best strategies are a complicated function of read time, read noise, and the signal-to-noise at which the stellar p-mode oscillations are visible in any realistic data. Related: There are amazingly different and interesting strategies with up-the-ramp detectors that are used in the infrared.
One final comment is that the objective, in my strongly held view, is to optimize the amount of information (about, say, the center-of-mass radial-velocity changes of the target star) per unit wall-clock time. We are paying for wall-clock time; let's get as much as we can out of it.
