In the early 1950s, Golay studied binary sequence pairs whose autocorrelation properties allow the isolation of particular wavelengths in a multislit spectrometer design. Golay's initial results were disappointing, and he turned his attention to what are now called Golay complementary sequences. Jane Wodlinger and I revisited the original problem in 2012, showing that Golay had overlooked two examples and that all known examples can be constructed from perfect Golomb rulers.

In 2013, Mark Strange and I further developed the theory by showing that Golay's formulation of the problem in terms of binary sequences is unduly restrictive, and that infinitely many spectrometer designs satisfying all the original physical criteria can be found when the restrictions are relaxed. We gave constructions for such spectrometer designs, involving Golomb rulers and variants, that explain all nontrivial examples of length at most 26 found by exhaustive search.

Golay's multislit spectrometer design.