## Wavelength Isolation Sequence Design

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.