Peter Hyland, Brent Follin, and I just submitted a paper for publication in the journal Astronomy and Astrophysics. You can see it here.
Peter is a postdoc at McGill now, but he was a graduate student at the University of Wisconsin when we did the work. Brent is a rising senior here at U.R.
In this paper, we’ve solved a problem that’s an important part of the construction of a kind of telescope known as an adding interferometer. In an adding interferometer, a bunch of different signals from different antennas are mixed together, resulting in an output signal that is the sum of all of the inputs. We want to be able to extract information about the individual signals (specifically, pairwise correlations between the inputs, if you must know), not just the overall sum. To get this information out, we need to modulate all of the inputs in different ways. Finding the optimal way to do this — that is, the way that results in the smallest errors in the result — turns out to be a tricky problem. We’ve found a general method for finding the solution.
The reason we wanted to solve this problem is that we’re part of a group that’s trying to build an adding interferometer for observing the polarization of the cosmic microwave background radiation. We tested a prototype out at Wisconsin recently. Eventually, a much larger version could map the polarization in great detail, giving us new windows onto the very early Universe.