CS: Multiplexing in Interferometry - Diophantine Optics

I mentionned the work of Daniel Rouan before. His main problem is to acquire some signal in some analog fashion, multiplex it and then remove some pattern from it (within the analog process). He cannot digitized the signal because it would require him to deal with technology that still does not exist or is at a very low TRL.

As you might have guessed, Daniel Rouan does interferometry. He is interested in exoplanet detection through the removal of light coming from a star while observing/keeping the much lower (by 7 to 10 orders of magnitude) brightness of a nearby planet. He does this by devising nulling interferometers (nulling because it cancels out the main star) that implement a Prouhet-Tarry-Escott [2] (PTE) series in hardware so that the analog signal uses the cancellation property of that series as explained in Diophantine Optics explanation:

Each of the beams of light interact with a paved lattice. The two paved lattices implement each one side of the PTE series thereby producing beams that are then added together producing the nulling effect.

Different kinds of pavement can fulfill this condition, so additional constraints are added to avoid shadowing between tiles.... An example of a working tiling is shown below.

There are other examples of diophatine optics applied to inteferometry here. Back in 2004 when I first mentioned his work, he was mostly presenting the algebra of ultra-supressing inteferometers:

The last tiling cannot not remind some of you of similar tilings found in CS. The PTE series might well be very appropriate for star shining nulling, but one wonders if using other kinds of tilings and CS reconstruction techniques, one cannot get other type of results, i.e. not just nulling effects.

Sources:

[1] Diophatine Optics, Daniel Rouan
[2] Weisstein, Eric W. "Prouhet-Tarry-Escott Problem." From MathWorld--A Wolfram Web Resource.http://mathworld.wolfram.com/Prouhet-Tarry-EscottProblem.html